addition problem solving

Problem Solving on Addition

Problem solving on addition will help us to get the idea on how to solve the basic addition statement problems.

1.  Three boys were playing cricket. Two more boys came along and played cricket with them. How many boys altogether were playing cricket?

Number of boys were playing cricket = 3

Number of boys came along and played cricket with them = 2

Therefore, total number of boys were playing cricket = 3 + 2 = 5

2.  Harry had 5 stamps. Mother gave him 4 more. How many stamps in all did Harry have?

Number of stamps Harry had = 5

Number of stamps his mother gave him = 4

Therefore, total number of stamps he have = 5 + 4 = 9

3. Rachael had 6 stamps. Father gave her 2 stamps. How many stamps does Rachael have now?

Number of stamps Rachael had = 6

Number of stamps her father gave her = 4

Therefore, total number of stamps she have now = 6 + 4 = 10

4. In a classroom, there were 2 brown tables, 1 red table and 3 green tables. How many tables were there altogether?

Number of brown tables = 2

Number of red table = 1

Number of green tables = 3

Therefore, total number of tables in a classroom = 2 + 1 + 3 = 6

5. Jack spent 5 dollars for a pen, 3 dollars for a color box, 2 dollars for a pencil box. How much did he spend altogether?

Amount of money Jack spent for a pen = $5

Amount of money he spent for a color box = $3

Amount of money he spent for a pencil box = $2

Therefore, total amount of money he spend altogether = $5 + $3 + $2 = 10

6. There were 6 yellow hats, 2 red hats and 6 blue hats. How many hats were there?

Number of yellow hats = 6

Number of red hats = 2

Number of blue hats = 6

Therefore, total number of hats were there = 6 + 2 + 6 = 14

7. Alex had 4 books on cars, 5 on airplanes and 7 on boats. How many books did he have in all?

Number of books on cars Alex had = 4

Number of books on airplanes = 5

Number of books on boats = 7

Therefore, total number of books he have in all = 4 + 5 + 7 = 16

More examples on statement problem solving on addition:

8. In a game Mary had the best score. She made 8 in her first turn, 6 in her second and 5 in her third. What was her total score?

Number of score Mary had in her first turn = 8

Number of score in her second turn = 5

Number of score in her third turn = 7

Therefore, total number of score Mary had in a game = 8 + 5 + 7 = 20

9. Sarah had 25 cards. She got 7 cards more. How many cards did she have then?

Number of cards Sarah had = 25

Number of cards she got more = 7

Therefore, total number of cards she have then = 25 + 7 = 32

10. A farmer had 45 sheep before he bought 25 more. How many sheep did he have then?

Number of sheep a farmer had = 45

Number of sheep he bought more = 25

Therefore, total number of sheep he have then = 45 + 25 = 70

Word Problems on Addition:

11. A basket had 28 mangoes in it. 14 more mangoes are kept in the basket. How many mangoes are there in the basket now?

The basket had                 2 8    mangoes

Mangoes kept in       (+)   1 4                      

Now, there are                 4 2 mangoes in all

Thus, there are 42 mangoes in the basket now.

12. Aaron scored 33 runs in the first cricket match and 29 runs in the second. How many runs did he score in all?

Aaron scored                  3 3  runs in the first match

He scored                (+)  2 9  runs in the second match

He scored                       6 2  runs in all                      

Thus, he scored 62 runs in all.

2nd Grade Math Practice

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Addition Worksheets

Welcome to the addition worksheets page at Math-Drills.com where we will add to your learning experience in many positive ways! On this page, you will find Addition worksheets from addition facts and two-digit addition to column addition and addition with games. In the first section, we've included a few addition printables that should help out the beginning student. Teaching addition facts is best done with some interesting teaching strategies.

Some teachers and parents use addition manipulatives to help students understand the basic addition facts. For example, adding groups of "Apple Jacks" (a breakfast cereal) by counting will quickly lead students to understand the concepts of addition. The sooner you can introduce base ten blocks to your students, the better. If you haven't already used them for counting, use them for basic addition and show students how regrouping works.

Most Popular Addition Worksheets this Week

Addition Facts Tables

Disputably not a great way to learn addition facts, but undeniably a great way to summarize, addition facts tables are an invaluable resource in any home or school classroom. Addition works very well as a table since the addends can be sequential. Encourage students to look for patterns and teach them a variety of strategies to learn the addition facts. For students who have not yet memorized their addition facts but need to know them for a more advanced math lesson such as adding two-digit numbers, provide an addition facts table to them, so they can quickly look up addition facts. After a while, they will most likely learn the facts through the use of the table and become less reliant on it. To make the tables more durable, print them on card stock and laminate them. They can be displayed on a screen or enlarged and printed on poster paper for whole class use.

• Addition Facts in One Square Table Addition Facts Table 1 to 10 (Filled In) Addition Facts Table 1 to 10 (Blank) Addition Facts Table 0 to 9 (Filled In) Addition Facts Table 0 to 9 (Blank) Left-Handed Addition Facts Table Left-Handed Blank Addition Facts Table All Addition Facts Tables Addition Facts Tables With One Fact at a time highlighted
• Addition Facts in Separate Tables Single Addition Facts Tables in Gray 1 to 12 Single Addition Facts Tables in Color 1 to 12 Single Addition Facts Tables in Montessori Colors 1 to 12

Five Minute Addition Frenzies

Five minute frenzy charts are 10 by 10 grids for addition fact practice. In each square, students write the sum of the column number and the row number.

Called mad minutes or timed drills by some, five minute frenzies are meant to be timed to add a little more excitement to practicing addition facts. They are ideally used to increase a student's ability to recall addition facts quickly which has all sorts of benefits later in their school life including preventing high school teachers from complaining about "how their students can't even add single-digit numbers without using a calculator."

A general goal to achieve would be to complete one chart in less than five minutes and score 98 percent or better, however, we recommend setting personal goals for students based on an initial test. If they are banging their head against the wall after a couple of minutes with only a few questions done, they really shouldn't be completing a timed addition facts drill at the moment. They still have some learning to do. We would recommend breaking out the manipulatives at this point. If they blast through the questions in 1.5 minutes and get almost all of them correct, they are probably ready for something a little more challenging.

One-per-page addition frenzies are not the most efficient use of paper resources, but they are a good starting point especially for younger students who have not quite mastered their penmanship enough to fit their numbers into a smaller chart. They are also great for displaying on screens or monitors for group activities. For example, you might use an interactive white board to fill out the chart.

• Five Minute Addition Frenzies Addition Frenzy ( 1 to 10 ) Addition Frenzy ( 11 to 20 ) Addition Frenzy ( 21 to 50 ) Addition Frenzy ( 51 to 100 )
• Left-handed Five Minute Addition Frenzies Left-handed Addition Frenzy ( 1 to 10 ) Left-handed Addition Frenzy ( 11 to 20 ) Left-handed Addition Frenzy ( 21 to 50 ) Left-handed Addition Frenzy ( 51 to 100 )

A wiser use of paper and photo-copy limits, having four charts on a page allows for multi-day practice, collaborative work or through the use of a paper-cutter, a quick stack of practice pages for students who finish early.

• Five Minute Addition Frenzies (Four Per Page) Four Addition Frenzies ( 1 to 10 ) Four Addition Frenzies ( 11 to 20 ) Four Addition Frenzies ( 21 to 50 ) Four Addition Frenzies ( 51 to 100 )
• Left-handed Five Minute Addition Frenzies (Four Per Page) Left-handed Four Addition Charts Per Page ( 1 to 10 ) Left-handed Four Addition Charts Per Page ( 11 to 20 ) Left-handed Four Addition Charts Per Page ( 21 to 50 ) Left-handed Four Addition Charts Per Page ( 51 to 100 )

Single-Digit Addition

Most people would agree that being able to add single-digit numbers quickly and in your head is an essential skill for success in math. The various addition worksheets in this section focus on skills that students will use their entire life. These worksheets will not magically make a student learn addition, but they are valuable for reinforcement and practice and can also be used as assessment tools.

• Single-Digit Addition with Some Regrouping 100 Single-Digit Addition Questions with Some Regrouping ✎ 81 Single-Digit Addition Questions with Some Regrouping ✎ 64 Single-Digit Addition Questions with Some Regrouping ✎ 50 Single-Digit Addition Questions with Some Regrouping ✎ 25 Single-Digit Addition Questions with Some Regrouping ✎ 12 Single-Digit Addition Questions with Some Regrouping ✎
• Single-Digit Addition with No Regrouping 100 Single-Digit Addition Questions with No Regrouping 64 Single-Digit Addition Questions with No Regrouping 25 Single-Digit Addition Questions with No Regrouping 12 Single-Digit Addition Questions with No Regrouping
• Single-Digit Addition with All Regrouping 100 Single-Digit Addition Questions with All Regrouping 64 Single-Digit Addition Questions with All Regrouping 25 Single-Digit Addition Questions with All Regrouping 12 Single-Digit Addition Questions with All Regrouping
• Horizontally Arranged Single-Digit Addition Horizontally Arranged Single-Digit Addition Facts (100 Questions) ✎ Horizontally Arranged Single-Digit Addition Facts (50 Questions) ✎ Horizontal Numbers that Add to 10 Horizontally Arranged Single-Digit Addition Facts up to 5 + 5 (100 Questions) ✎ Horizontally Arranged Single-Digit Addition Facts up to 6 + 6 (100 Questions) ✎ Horizontally Arranged Single-Digit Addition Facts up to 7 + 7 (100 Questions) ✎ Horizontally Arranged Single-Digit Addition Facts up to 8 + 8 (100 Questions) ✎
• Horizontally Arranged Single-Digit Addition of More than Two Addends Adding 3 Single-Digit Numbers Horizontally Adding 4 Single-Digit Numbers Horizontally Adding 5 Single-Digit Numbers Horizontally Adding 10 Single-Digit Numbers Horizontally
• Horizontally Arranged Single-Digit Addition with No Regrouping Horizontal Addition Facts with No Regrouping 100 per page Horizontal Addition Facts with No Regrouping and No Zeros 100 per page Horizontal Addition Facts with No Regrouping 50 per page
• Horizontally Arranged Single-Digit Addition with All Regrouping Horizontal Addition Facts with All Regrouping 100 per page Horizontal Addition Facts with All Regrouping 50 per page

The make ten addition strategy involves "spliting" the second addend into two parts. The first part combines with the first addend to make ten and the second part is the leftover amount. The strategy helps students quickly add amounts over ten in their head. For example, adding 8 + 7, students first recognize that they need to add 2 to 8 to get 10, so they split the 7 into 2 + 5. The 8 + 2 makes 10 and 5 more makes 15. The skill can be extended to many situations, for example adding 24 + 9, students recognize that they need 6 more to get to 30 and 9 can be split into 6 + 3, so 24 + 6 = 30 and 3 more makes 33. Continuing on, students can work on recognizing "complements" of other important numbers (see section further down) to develop this strategy further.

• Make 10 Addition Strategy Make 10 Addition Strategy Make 10 Addition Strategy Blanks Make 20 Addition Strategy Make 30 Addition Strategy Make 40 Addition Strategy Make 50 Addition Strategy Make 60 Addition Strategy Make 70 Addition Strategy Make 80 Addition Strategy Make 90 Addition Strategy Make Multiples of 10 Addition Strategy

Focusing on one number at a time is necessary for some students. Maybe they get overwhelmed with too much information and need to experience success in small steps.

• Adding Focus or Target Facts (50 Questions) Adding 0 to Single-Digit Numbers (50 Questions) ✎ Adding 1 to Single-Digit Numbers (50 Questions) ✎ Adding 2 to Single-Digit Numbers (50 Questions) ✎ Adding 1 or 2 to Single-Digit Numbers (50 Questions) ✎ Adding 3 to Single-Digit Numbers (50 Questions) ✎ Adding 4 to Single-Digit Numbers (50 Questions) ✎ Adding 5 to Single-Digit Numbers (50 Questions) ✎ Adding 6 to Single-Digit Numbers (50 Questions) ✎ Adding 7 to Single-Digit Numbers (50 Questions) ✎ Adding 8 to Single-Digit Numbers (50 Questions) ✎ Adding 9 to Single-Digit Numbers (50 Questions) ✎
• Adding Focus or Target Facts (25 Large Print Questions) Adding 0 to Single-Digit Numbers (25 Large Print Questions) ✎ Adding 1 to Single-Digit Numbers (25 Large Print Questions) ✎ Adding 2 to Single-Digit Numbers (25 Large Print Questions) ✎ Adding 3 to Single-Digit Numbers (25 Large Print Questions) ✎ Adding 4 to Single-Digit Numbers (25 Large Print Questions) ✎ Adding 5 to Single-Digit Numbers (25 Large Print Questions) ✎ Adding 6 to Single-Digit Numbers (25 Large Print Questions) ✎ Adding 7 to Single-Digit Numbers (25 Large Print Questions) ✎ Adding 8 to Single-Digit Numbers (25 Large Print Questions) ✎ Adding 9 to Single-Digit Numbers (25 Large Print Questions) ✎
• Adding Focus or Target Facts (25 Questions) with Sums Limited to 12 Adding 1 to Single-Digit Numbers With Sums Limited to 12 (25 Large Print Questions) ✎ Adding 2 to Single-Digit Numbers With Sums Limited to 12 (25 Large Print Questions) ✎ Adding 3 to Single-Digit Numbers With Sums Limited to 12 (25 Large Print Questions) ✎ Adding 4 to Single-Digit Numbers With Sums Limited to 12 (25 Large Print Questions) ✎ Adding 5 to Single-Digit Numbers With Sums Limited to 12 (25 Large Print Questions) ✎ Adding 6 to Single-Digit Numbers With Sums Limited to 12 (25 Large Print Questions) ✎ Adding 7 to Single-Digit Numbers With Sums Limited to 12 (25 Large Print Questions) ✎ Adding 8 to Single-Digit Numbers With Sums Limited to 12 (25 Large Print Questions) ✎ Adding 9 to Single-Digit Numbers With Sums Limited to 12 (25 Large Print Questions) ✎
• Horizontally-Arranged Adding Focus or Target Facts 100 Horizontal Adding 1s to Single-Digit Numbers Questions 100 Horizontal Adding 2s to Single-Digit Numbers Questions 50 Adding 1s and 2s to Single-Digit Numbers Questions 100 Horizontal Adding 3s to Single-Digit Numbers Questions 100 Horizontal Adding 4s to Single-Digit Numbers Questions 100 Horizontal Adding 5s to Single-Digit Numbers Questions 100 Horizontal Adding 6s to Single-Digit Numbers Questions 100 Horizontal Adding 7s to Single-Digit Numbers Questions 100 Horizontal Adding 8s to Single-Digit Numbers Questions 100 Horizontal Adding 9s to Single-Digit Numbers Questions

Multi-Digit Addition

A variety of strategies can be used to learn multi-digit addition; it isn't necessary to rely only on paper and pencil methods. Base ten blocks can help students conceptualize addition. Teaching students a mental left-to-right addition skill will help them in future math studies and life in general. E.g. 34 + 78 would be 30 + 70 = 100, 100 + 4 = 104, 104 + 8 = 112. Don't forget about using estimation with these worksheets.

• Multi-Digit Addition with Some Regrouping 2-Digit plus 1-Digit Addition (25 Questions) ✎ 2-Digit Plus 1-Digit Addition (36 Questions) ✎ 2-Digit plus 1-Digit Addition (64 Questions) ✎ 2-Digit plus 1-Digit Addition (100 Questions) ✎ 2-Digit plus 1-Digit Addition ( Sums Less Than 100 ) (25 Questions) 2-Digit Addition (25 Questions) ✎ 2-Digit Addition (36 Questions) ✎ 2-Digit Addition (64 Questions) ✎ 2-Digit Addition (100 Questions) ✎ 3-Digit Plus 1-Digit Addition (25 Questions) ✎ 3-Digit Plus 1-Digit Addition (36 Questions) ✎ 3-Digit Plus 2-Digit Addition (25 Questions) ✎ 3-Digit Plus 2-Digit Addition (36 Questions) ✎ 3-Digit Plus 2-Digit Addition (49 Questions) ✎ 3-Digit Plus 2-Digit Addition (100 Questions) ✎ 3-Digit Addition (25 Questions) ✎ 3-Digit Addition (36 Questions) ✎ 3-Digit Addition (49 Questions) ✎ 3-Digit Addition (100 Questions) ✎ 4-Digit Plus 1-Digit Addition (25 Questions) ✎ 4-Digit Plus 1-Digit Addition (36 Questions) ✎ 4-Digit Plus 2-Digit Addition (25 Questions) ✎ 4-Digit Plus 2-Digit Addition (36 Questions) ✎ 4-Digit Plus 3-Digit Addition (25 Questions) ✎ 4-Digit Plus 3-Digit Addition (36 Questions) ✎ 4-Digit Plus 3-Digit Addition (49 Questions) ✎ 4-Digit Plus 3-Digit Addition (100 Questions) ✎ 4-Digit Addition (25 Questions) ✎ 4-Digit Addition (36 Questions) ✎ 4-Digit Addition (49 Questions) ✎ 4-Digit Addition (100 Questions) ✎ 5-Digit Addition (25 Questions) ✎ Various 2-digit to 4-digit Addition (25 Questions) ✎ Various 2-Digit to 4-Digit Addition (36 Questions) ✎ Various 2-digit to 5-digit Addition (20 Questions) ✎ Various 2-Digit to 5-Digit Addition (36 Questions) ✎ Various 3-digit to 5-digit Addition (20 Questions) ✎ Various 3-Digit to 5-Digit Addition (36 Questions) ✎ 6-Digit Addition (20 Questions) ✎ 7-Digit Addition (15 Questions) ✎ 8-Digit Addition (15 Questions) ✎ 9-Digit Addition (15 Questions) ✎ 3-Digit Expanded Form Addition

Regrouping is what long addition is all about; these worksheets give students a lot of practice since every step requires regrouping.

• Multi-Digit Addition with All Regrouping 2-Digit Plus 1-Digit Addition with ALL Regrouping in the Ones Place (25 Questions) ✎ 2-Digit Addition with ALL Regrouping (25 Questions) ✎ 2-Digit Addition with ALL Regrouping (36 Questions) ✎ 3-Digit Addition with ALL Regrouping (25 Questions) ✎ 4-Digit Addition with ALL Regrouping (25 Questions) ✎ 5-Digit Addition with ALL Regrouping (20 Questions) ✎ 6-Digit Addition with ALL Regrouping (20 Questions) ✎ 7-Digit Addition with ALL Regrouping (15 Questions) ✎ 8-Digit Addition with ALL Regrouping (15 Questions) ✎ 9-Digit Addition with ALL Regrouping (15 Questions) ✎

If you haven't quite mastered all the addition facts or the long addition algorithm, these might be the worksheets for you. These worksheets don't require any regrouping, so they provide an extra in-between skill for students who require a little more guidance.

• Multi-Digit Addition with No Regrouping 2-Digit Plus 1-Digit Addition with NO Regrouping (25 Questions) ✎ 2-Digit Addition with NO Regrouping (25 Questions) ✎ 2-Digit Addition with NO Regrouping (36 Questions) ✎ 2-Digit Addition with NO Regrouping (64 Questions) ✎ 2-Digit Addition with NO Regrouping (100 Questions) ✎ 3-Digit Plus 1-Digit Addition with NO Regrouping (25 Questions) ✎ 3-Digit Plus 2-Digit Addition with NO Regrouping (25 Questions) ✎ 3-Digit Addition with NO Regrouping (25 Questions) ✎ 4-Digit Plus 1-Digit Addition with NO Regrouping (25 Questions) ✎ 4-Digit Plus 2-Digit Addition with NO Regrouping (25 Questions) ✎ 4-Digit Plus 3-Digit Addition with NO Regrouping (25 Questions) ✎ 4-Digit Addition with NO Regrouping (25 Questions) ✎ 5-Digit Addition with NO Regrouping (20 Questions) ✎ 6-Digit Addition with NO Regrouping (20 Questions) ✎ 7-Digit Addition with NO Regrouping (20 Questions) ✎ 8-Digit Addition with NO Regrouping (15 Questions) ✎ 9-Digit Addition with NO Regrouping (15 Questions) ✎

Horizontal addition can encourage students to use mental math or other strategies to add numbers. One of the most common mental math strategies for addition is a left-to-right (also called front end) addition strategy. This involves adding the greater place values first. Other strategies for adding multi-digit numbers include using base ten blocks or other manipulatives, number lines, decomposing numbers and adding the parts, and using a calculator.

• Horizontally Arranged Multi-Digit Addition Adding to 20 with the Second Addend Greater 2-Digit Plus 2-Digit Horizontal Addition with no Regrouping Horizontally Arranged 2-Digit Plus 2-Digit Addition ✎ Horizontally Arranged 3-Digit Plus 2-Digit Addition ✎ Horizontally Arranged 3-Digit Plus 3-Digit Addition ✎ Horizontally Arranged Various 2- and 3-Digit Addition ✎ Horizontally Arranged 4-Digit Plus 3-Digit Addition ✎ Horizontally Arranged 4-Digit Plus 4-Digit Addition ✎ Horizontally Arranged Various 2- to 4-Digit Addition ✎
• Horizontally Arranged Multi-Digit Addition of More Than Two Addends Adding 3 Two-Digit Numbers Horizontally Adding 4 Two-Digit Numbers Horizontally Adding 5 Two-Digit Numbers Horizontally Adding 10 Two-Digit Numbers Horizontally
• Adding Focus or Target Facts Greater Than 9 25 Adding 10s Questions ✎ 50 Adding 10s Questions ✎ 50 Adding 11s Questions ✎ 50 Adding 12s Questions ✎ 50 Adding 13s Questions ✎ 50 Adding 14s Questions ✎ 50 Adding 15s Questions ✎ 50 Adding 16s Questions ✎ 50 Adding 17s Questions ✎ 50 Adding 18s Questions ✎ 50 Adding 19s Questions ✎ 50 Adding 20s Questions ✎

Using a comma to separate thousands is the most common way to format large numbers in the English world.

• Multi-Digit Addition with Some Regrouping (Comma-Separated Thousands) Adding 4-Digit Numbers (Comma Separated) (25 Questions) ✎ Adding 5-Digit Numbers (Comma Separated) (20 Questions) ✎ Adding 6-Digit Numbers (Comma Separated) (20 Questions) ✎ Adding 7-Digit Numbers (Comma Separated) (15 Questions) ✎ Adding 8-Digit Numbers (Comma Separated) (15 Questions) ✎ Adding 9-Digit Numbers (Comma Separated) (15 Questions) ✎
• Multi-Digit Addition with All Regrouping (Comma-Separated Thousands) Adding 4-Digit Numbers with ALL Regrouping (Comma Separated) (25 Questions) ✎ Adding 5-Digit Numbers with ALL Regrouping (Comma Separated) (20 Questions) ✎ Adding 6-Digit Numbers with ALL Regrouping (Comma Separated) (20 Questions) ✎ Adding 7-Digit Numbers with ALL Regrouping (Comma Separated) (15 Questions) ✎ Adding 8-Digit Numbers with ALL Regrouping (Comma Separated) (15 Questions) ✎ Adding 9-Digit Numbers with ALL Regrouping (Comma Separated) (15 Questions) ✎
• Multi-Digit Addition with No Regrouping (Comma-Separated Thousands) Adding 4-Digit Numbers with NO Regrouping (Comma Separated) (25 Questions) ✎ Adding 5-Digit Numbers with NO Regrouping (Comma Separated) (20 Questions) ✎ Adding 6-Digit Numbers with NO Regrouping (Comma Separated) (20 Questions) ✎ Adding 7-Digit Numbers with NO Regrouping (Comma Separated) (15 Questions) ✎ Adding 8-Digit Numbers with NO Regrouping (Comma Separated) (15 Questions) ✎ Adding 9-Digit Numbers with NO Regrouping (Comma Separated) (15 Questions) ✎

Using a space to separate thousands in large numbers is common in some languages. In the English world, you will most likely find Canadians formatting their numbers in this way.

• Multi-Digit Addition with Some Regrouping (Space-Separated Thousands) Adding 4-Digit Numbers (Space Separated) (25 Questions) ✎ Adding 5-Digit Numbers (Space Separated) (20 Questions) ✎ Adding 6-Digit Numbers (Space Separated) (20 Questions) ✎ Adding 7-Digit Numbers (Space Separated) (15 Questions) ✎ Adding 8-Digit Numbers (Space Separated) (15 Questions) ✎ Adding 9-Digit Numbers (Space Separated) (15 Questions) ✎
• Multi-Digit Addition with All Regrouping (Space-Separated Thousands) Adding 4-Digit Numbers with ALL Regrouping (Space Separated) (25 Questions) ✎ Adding 5-Digit Numbers with ALL Regrouping (Space Separated) (20 Questions) ✎ Adding 6-Digit Numbers with ALL Regrouping (Space Separated) (20 Questions) ✎ Adding 7-Digit Numbers with ALL Regrouping (Space Separated) (15 Questions) ✎ Adding 8-Digit Numbers with ALL Regrouping (Space Separated) (15 Questions) ✎ Adding 9-Digit Numbers with ALL Regrouping (Space Separated) (15 Questions) ✎
• Multi-Digit Addition with No Regrouping (Space-Separated Thousands) Adding 4-Digit Numbers with NO Regrouping (Space Separated) (25 Questions) ✎ Adding 5-Digit Numbers with NO Regrouping (Space Separated) (20 Questions) ✎ Adding 6-Digit Numbers with NO Regrouping (Space Separated) (20 Questions) ✎ Adding 7-Digit Numbers with NO Regrouping (Space Separated) (15 Questions) ✎ Adding 8-Digit Numbers with NO Regrouping (Space Separated) (15 Questions) ✎ Adding 9-Digit Numbers with NO Regrouping (Space Separated) (15 Questions) ✎

Using a period as a thousands separator is not generally seen in English-speaking countries, but since there are people from around the world who use these addition worksheets, they are included.

• Multi-Digit Addition with Some Regrouping (Period-Separated Thousands) Adding 4-Digit Numbers (Period Separated) (25 Questions) ✎ Adding 5-Digit Numbers (Period Separated) (20 Questions) ✎ Adding 6-Digit Numbers (Period Separated) (20 Questions) ✎ Adding 7-Digit Numbers (Period Separated) (15 Questions) ✎ Adding 8-Digit Numbers (Period Separated) (15 Questions) ✎ Adding 9-Digit Numbers (Period Separated) (15 Questions) ✎
• Multi-Digit Addition with All Regrouping (Period-Separated Thousands) Adding 4-Digit Numbers with ALL Regrouping (Period Separated) (25 Questions) ✎ Adding 5-Digit Numbers with ALL Regrouping (Period Separated) (20 Questions) ✎ Adding 6-Digit Numbers with ALL Regrouping (Period Separated) (20 Questions) ✎ Adding 7-Digit Numbers with ALL Regrouping (Period Separated) (15 Questions) ✎ Adding 8-Digit Numbers with ALL Regrouping (Period Separated) (15 Questions) ✎ Adding 9-Digit Numbers with ALL Regrouping (Period Separated) (15 Questions) ✎
• Multi-Digit Addition with No Regrouping (Period-Separated Thousands) Adding 4-Digit Numbers with NO Regrouping (Period Separated) (25 Questions) ✎ Adding 5-Digit Numbers with NO Regrouping (Period Separated) (20 Questions) ✎ Adding 6-Digit Numbers with NO Regrouping (Period Separated) (20 Questions) ✎ Adding 7-Digit Numbers with NO Regrouping (Period Separated) (15 Questions) ✎ Adding 8-Digit Numbers with NO Regrouping (Period Separated) (15 Questions) ✎ Adding 9-Digit Numbers with NO Regrouping (Period Separated) (15 Questions) ✎

For various reasons, sometimes you need addition questions in a larger font. These should fit the bill.

• Large Print Multi-Digit Addition with Some Regrouping 2-digit Plus 1-digit Addition with SOME Regrouping (Large Print) (16 Questions) ✎ 3-digit Plus 1-digit Addition with SOME Regrouping (Large Print) (16 Questions) ✎ 4-digit Plus 1-digit Addition with SOME Regrouping (Large Print) (16 Questions) ✎ Various Plus 1-digit Addition with SOME Regrouping (Large Print) (16 Questions) ✎ 2-digit Plus 2-digit Addition with SOME Regrouping (Large Print) (16 Questions) ✎ 3-digit Plus 2-digit Addition with SOME Regrouping (Large Print) (16 Questions) ✎ 4-digit Plus 2-digit Addition with SOME Regrouping (Large Print) (16 Questions) ✎ Various Plus 2-digit Addition with SOME Regrouping (Large Print) (16 Questions) ✎ 3-digit Plus 3-digit Addition with SOME Regrouping (Large Print) (16 Questions) ✎ 4-digit Plus 3-digit Addition with SOME Regrouping (Large Print) (16 Questions) ✎ 4-digit Plus 4-digit Addition with SOME Regrouping (Large Print) (16 Questions) ✎ 5-digit Plus 5-digit Addition with SOME Regrouping (Large Print) (12 Questions) ✎ 6-digit Plus 6-digit Addition with SOME Regrouping (Large Print) (12 Questions) ✎
• Very Large Print Multi-Digit Addition with Some Regrouping 2-Digit Plus 1-Digit Addition with SOME Regrouping (Very Large Print) (9 Questions) ✎ 2-Digit Addition with SOME Regrouping (Very Large Print) (9 Questions) ✎ 3-Digit Plus 1-Digit Addition with SOME Regrouping (Very Large Print) (9 Questions) ✎ 3-Digit Plus 2-Digit Addition with SOME Regrouping (Very Large Print) (9 Questions) ✎ 3-Digit Addition with SOME Regrouping (Very Large Print) (9 Questions) ✎ 4-Digit Plus 1-Digit Addition with SOME Regrouping (Very Large Print) (9 Questions) ✎ 4-Digit Plus 2-Digit Addition with SOME Regrouping (Very Large Print) (9 Questions) ✎ 4-Digit Plus 3-Digit Addition with SOME Regrouping (Very Large Print) (9 Questions) ✎ 4-Digit Addition with SOME Regrouping (Very Large Print) (9 Questions) ✎ Various 2- to 4-Digit Addition with SOME Regrouping (Very Large Print) (9 Questions) ✎
• Large Print Multi-Digit Addition with All Regrouping 2-Digit Addition with ALL Regrouping (Large Print) (16 Questions) ✎ 3-Digit Addition with ALL Regrouping (Large Print) (16 Questions) ✎ 4-Digit Addition with ALL Regrouping (Large Print) (16 Questions) ✎ 5-Digit Addition with ALL Regrouping (Large Print) (12 Questions) ✎ 6-Digit Addition with ALL Regrouping (Large Print) (12 Questions) ✎
• Large Print Multi-Digit Addition with No Regrouping 2-Digit Addition with NO Regrouping (Large Print) (16 Questions) ✎ 3-Digit Plus 2-Digit Addition with NO Regrouping (Large Print) (16 Questions) ✎ 3-Digit Addition with NO Regrouping (Large Print) (16 Questions) ✎ 4-Digit Plus 3-Digit Addition with NO Regrouping (Large Print) (16 Questions) ✎ 4-Digit Addition with NO Regrouping (Large Print) (16 Questions) ✎ 5-Digit Addition with NO Regrouping (Large Print) (12 Questions) ✎ 6-Digit Addition with NO Regrouping (Large Print) (12 Questions) ✎ LP 2-Digit Addition with Sums up to 99 ( 25 Questions ) LP 2-Digit Addition with Sums up to 99 ( 12 Questions )

Multi-Digit Addition with Grid Support

Adding with grid support helps students who have trouble lining up place values themselves. Perhaps with a little practice, they might get a better understanding of not only lining up the place values, but why this is done. Pointing out that the 5 in 659 means 50, for example, is useful in helping students understand place value as it relates to addition.

• Adding 2 Addends With Grid Support Adding 2-Digit + 2-Digit Numbers on a Grid (2 Addends) Adding 3-Digit + 3-Digit Numbers on a Grid (2 Addends) Adding 3-Digit + 2-Digit Numbers on a Grid (2 Addends) Adding 4-Digit + 4-Digit Numbers on a Grid (2 Addends) Adding 4-Digit + 3-Digit Numbers on a Grid (2 Addends) Adding 4-Digit + 2-Digit Numbers on a Grid (2 Addends) Adding 5-Digit + 5-Digit Numbers on a Grid (2 Addends) Adding 5-Digit + 4-Digit Numbers on a Grid (2 Addends) Adding 5-Digit + 3-Digit Numbers on a Grid (2 Addends) Adding 5-Digit + 2-Digit Numbers on a Grid (2 Addends) Adding Various Digit Numbers on a Grid (2 Addends)
• Adding 3 Addends With Grid Support Adding 2-Digit Numbers on a Grid (3 Addends) Adding 3-Digit Numbers on a Grid (3 Addends) Adding 4-Digit Numbers on a Grid (3 Addends) Adding 5-Digit Numbers on a Grid (3 Addends) Adding Various-Digit Numbers on a Grid (3 Addends)
• Adding 4 Addends With Grid Support Adding 2-Digit Numbers on a Grid (4 Addends) Adding 3-Digit Numbers on a Grid (4 Addends) Adding 4-Digit Numbers on a Grid (4 Addends) Adding 5-Digit Numbers on a Grid (4 Addends) Adding Various-Digit Numbers on a Grid (4 Addends)
• Adding 5 Addends With Grid Support Adding 2-Digit Numbers on a Grid (5 Addends) Adding 3-Digit Numbers on a Grid (5 Addends) Adding 4-Digit Numbers on a Grid (5 Addends) Adding 5-Digit Numbers on a Grid (5 Addends) Adding Various-Digit Numbers on a Grid (5 Addends)

Various Other Addition Worksheets

Column addition is not just an exercise in accounting, it also develops mental addition skills that are useful in everyday life. Various strategies are available for adding columns of numbers. The traditional method is to use a pencil and paper approach, also known as right-to-left addition, where students add and regroup starting with the smallest place (ones in this case) and proceed up to the greatest place. A mental approach might involve students going from left-to-right where the greater place is added first. This is easier to keep track of in your head, but does require the occasional adjustment in previous answers. An example is to add 345 + 678 + 901. First add the 300, 600 and 900 to get 1800, then add 40, 70 and 0 in turn to get 1910, then deal with the 5, 8 and 1 to get 1924. Along the way you had to adjust your total, but keeping a running total in your head is a lot easier than transfering a pencil and paper method into your head.

• Column Addition with Single-Digit Numbers Adding Three Single-Digit Numbers Adding Four Single-Digit Numbers Adding Five Single-Digit Numbers Adding Six Single-Digit Numbers
• Column Addition with Two-Digit Numbers Adding Three Two-Digit Numbers Adding Four Two-Digit Numbers Adding Five Two-Digit Numbers Adding Six Two-Digit Numbers
• Column Addition with Three-Digit Numbers Adding Three Three-Digit Numbers Adding Four Three-Digit Numbers Adding Five Three-Digit Numbers Adding Six Three-Digit Numbers
• Column Addition with Four-Digit Numbers Adding Three Four-Digit Numbers Adding Four Four-Digit Numbers Adding Five Four-Digit Numbers Adding Six Four-Digit Numbers
• Column Addition with Various-Digit Numbers Adding Three Various-Digit Numbers Adding Four Various-Digit Numbers Adding Five Various-Digit Numbers Adding Six Various-Digit Numbers

Games help students develop mental addition skills but in a fun context. For the adding with playing cards worksheets, a Jack is counted as 11, a Queen as 12, a King as 13 and an Ace as 1. Playing math games while enjoying some social time with their friends is a great way to develop strategic thinking and math fluency in children.

• Adding With Games Adding 2 Playing Cards Adding 3 Playing Cards Adding 4 Playing Cards Adding 5 Playing Cards Adding 6 Playing Cards Adding 7 Playing Cards Adding 8 Playing Cards Counting Cribbage Hands Identify and Count Yahtzee! Combinations

Finding complements of numbers can help students a great deal in developing mental arithmetic skills and to further their understanding of number.

• Adding Complements of 9, 99 and 999 Adding Complements of 9 (Blanks in First or Second Position Mixed) Adding Complements of 9 (Blanks in First then Second Position) Adding Complements of 9 (Blanks in First Position Only) Adding Complements of 9 (Blanks in Second Position Only) Adding Complements of 9 (Blanks in Any Position, Including Sums) Adding Complements of 99 Adding Complements of 999
• Adding Complements of 10, 100 and 1000 Adding Complements of 10 Adding Complements of 100 Adding Complements of 1000
• Adding Complements of 11 Adding Complements of 11 (Blanks in First or Second Position Mixed) Adding Complements of 11 (Blanks in First then Second Position) Adding Complements of 11 (Blanks in First Position Only) Adding Complements of 11 (Blanks in Second Position Only) Adding Complements of 11 (Blanks in Any Position, Including Sums)

Using an adding doubles strategy can help students to process addition questions more quickly using mental math. To use this strategy, students must recognize that the two numbers are close to the same value (usually by one or two). They also must recognize by how much and whether it is greater or less than the first addend. A typical dialogue with the question, 15 + 16, might be, "I see that the second number is greater than the first number by 1. If I double the first number and add 1, I will get my answer. 15 doubled is 30 plus one is 31. 15 + 16, therefore, is 31."

• Adding Doubles Up to 9 Adding Doubles (Up to 9) Adding Doubles Plus One (Up to 9) Adding Doubles Plus Two (Up to 9) Adding Doubles Minus One (Up to 9) Adding Doubles Minus Two (Up to 9) Adding Doubles Mixed Variations (Up to 9)
• Adding Doubles Up to 15 Adding Doubles (Up to 15) Adding Doubles Plus One (Up to 15) Adding Doubles Plus Two (Up to 15) Adding Doubles Minus One (Up to 15) Adding Doubles Minus Two (Up to 15) Adding Doubles Mixed Variations (Up to 15)
• Adding Doubles Up to 30 Adding Doubles (Up to 30) Adding Doubles Plus One (Up to 30) Adding Doubles Plus Two (Up to 30) Adding Doubles Minus One (Up to 30) Adding Doubles Minus Two (Up to 30) Adding Doubles Mixed Variations (Up to 30)

Not commonly taught in modern schools, adding in other base number systems can stretch students' minds and have quite a few important applications, especially in technology. For example, you will find binary, octal and hexadecimal systems are quite often used in computer technology. Quaternary numbers can be used in genetics to store DNA sequences. The duodecimal system is sometimes suggested as a superior system to the decimal system

• Adding in Other Base Number Systems Adding Binary Numbers (Base 2) Adding Ternary Numbers (Base 3) Adding Quaternary Numbers (Base 4) Adding Quinary Numbers (Base 5) Adding Senary Numbers (Base 6) Adding Octal Numbers (Base 8) Adding Duodecimal Numbers (Base 12) Adding Hexadecimal Numbers (Base 16) Adding Vigesimal Numbers (Base 20) Adding Hexatrigesimal Numbers (Base 36) Adding Various Numbers (Various Bases)

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Addition Word Problem Worksheets

The addition word problem worksheets presented here involve performing addition operations with regrouping and without regrouping. Our extensive and well-researched word problem worksheets feature real-life scenarios that involve single-digit addition, two-digit addition, three-digit addition, and addition of large numbers. These pdf handouts are designed to provide ample practice for elementary school children. Free worksheets are included.

Single-digit Addition Word Problems

These printable practice worksheets involve simple addition of single-digit numbers. Read the word problems and perform addition operations to arrive at the answers.

• Download the set

Addition Word Problems: Sum up to 20

Featured in these worksheets are engaging word problems whose sums add up to 20. Addends may have a combination of single-digit and two-digit numbers.

Addition Problems: Two-digit and Single-digit

A number of real-life scenarios in the form of word problems featured in the addition worksheets here involve single digit and two-digit addends.

Two-digit Addition Problems - No Regrouping

The word problems in this section do not require regrouping or carrying. Find the answers to the word problems that feature two-digit addends.

Two-digit Addition Problems - With Regrouping

All two-digit addition word problems presented in this set of worksheets here require regrouping (carry over). Follow the place value columns to sum up the two-digit addends.

Theme based Word Problems

Presented here are worksheets with three colorful themes - Fall Season, Aquarium and Theme Park. Read the questions and solve the word problems. Answer keys are included.

Three-digit and Two-digit Addition

A total of 15 addition word problems spread over three PDF worksheets presented here require you to sum up three-digit addends with the two-digit addends.

Three-digit Addition Word Problems

Enhance your arithmetic skills. Read the word problems and sum up three-digit addends in these printable worksheets. Some problems may require regrouping. Answer key included in each worksheet.

Multi-digit Addition Word Problems: Adding Large Numbers

The word problems presented in the worksheets here feature large numbers with addends up to eight digits.

Related Worksheets

» Subtraction Word Problems

» Multiplication Word Problems

» Division Word Problems

» Math Word Problems

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Addition is ...

... bringing two or more numbers (or things) together to make a new total.

Example: When we add 2 and 3 we get 5 .

We can write it like this:

Write this down, with the answer, using numerals :

You should get:   4 + 3 = 7  

Have a Play

Drag the numerals to the two blue boxes see how addition works:

Swapping Places

Swapping the position of the numbers we are adding still gets the same result!

More Examples:

5 + 1 = 1 + 5 = 6

7 + 11 = 11 + 7 = 18

4 + 100 = 100 + 4 = 104

You get better at addition with practice, so we have:

Math Trainer - Addition (train your memory)

Kindergarten Worksheets (easy addition)

Addition Worksheets (normal and advanced)

Tips and Tricks

Learn more on our Addition Tips and Tricks page

Addition Table

We can also "look up" answers for simple addition using the Addition Table (but it is really best to learn to remember the answers).

Example: Find 3 + 5

• find the row starting with "3"

• move along to be under the column "5"

• and there is the number "8", so 3 + 5 = 8

Larger Numbers: Use Addition in Columns

Other names for Addition are Sum, Plus, Increase, Total

And the numbers to be added together are called the " Addends ":

Addition Word Problems (1-step word problems)

These lessons look at some examples and solutions of addition word problems that can be solved in one step. We will illustrate how block diagrams (used in Singapore Math) can be used to help you to visualize the addition word problems in terms of the information given and the data that needs to be found.

Related Pages Addition & Subtraction Word 2-Step Word Problems and Bar Models More Word Problems More Singapore Math Lessons

Example: There are 1030 books in the library. We bought 67 more books for the library. How many books are there in the library now?

1030 + 67 = 1097

There are 1097 books in the library now.

Example: 1085 girls and 531 boys took part in an art competition. How many students took part in the competition altogether?

1085 + 531 = 1616 1616 students took part in the competition altogether.

Example: After giving $1085 to his wife, Simon had $746 left. How money had he at first?

1085 + 746 = 1831

Simon had $1831 at first.

Example: Margret sold 1392 meatballs on Friday. She sold 1940 more meatballs on Saturday than on Friday. How many meatballs did she sell on Saturday?

Solution: 1392 + 1940 = 3332 She sold 3332 meatballs on Saturday.

A visual way to solve world problems using bar modeling This type of word problem uses the part-whole model. Because the whole is missing, this is an addition problem.

Example: Mr. Gray sold 64 drinks in the morning. Mr. Frank sold 25 drinks at night. How many drinks did they sell altogether?

How to solve addition problem using part-whole model?

Example: Maya had some stamps. She gave 7 stamps to her younger brothers. Maya then had 14 stamps. How many stamps did Maya have at first?

Examples of 4th Grade word problems and bar models

Example: Dad bought two hammers. One cost $18 and the other costs $28 more. What was his total bill?

Model Drawing - addition word problems

Example: A girl jumps 42cm for her first jump in a high jump competition. Her second jump is 46cm. How high did she jump in total?

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Addition word problems

 Addition word problems arise in any situations where there is a gain or an increase of something as a result of combining one or more numbers. Think of addition as combining parts to form a whole.

Consider the following situations. Problem #1: John has 800 dollars in his checking account. He received from his job a check for 1,200 dollars and deposit the amount in his checking account. How much money does he have in his checking after the deposit? Solution The fact of receiving money from his job is a gain. Therefore, we need to perform addition.

Total amount in checking account = 800 + 1200 = 2000 dollars Problem #2: Peter sells ice cream for a living. On Monday his revenue was 150 dollars. On Tuesday, his revenue was 100 dollars. Finally, on Wednesday, his revenue was 50 dollars. How much is Peter's revenue so far? Solution Peter is experiencing a gain in revenue. Therefore, we use addition.

Peter's revenue = 150 + 50 + 100 = 300 dollars Problem #3: Eiffel Tower is about 1063 feet high. The Statue of Liberty along with its foundation and pedestal is about 305 feet. If you could put the Statue of Liberty on top of the Eiffel Tower, how high up in heaven will the two monuments reach? Solution The situation above is a combination of parts to form a whole. Therefore, we use addition.

Problem #4:

Ana found a 15 dollar bill on the floor on Saturday.

Then on Sunday her parents gave her 155 dollars. How much does Ana have all together?

CLUE: Saturday~15 dollars Sunday~155 dollars

Solution: 15+155 = 170 dollars all together

Subtraction word problems

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Addition Word Problems 2nd Grade Addition Problems within 100

Welcome to our Addition Word Problems 2nd Grade Worksheets. Here you will find a wide range of free printable addition word problem worksheets, which will help your child practice solving a range of addition problems using numbers with a sum of up to 100.

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• Addition Word Problems within 100
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• More related resources
• Addition Word Problems up to 100 Online Quiz

Addition Word Problems 2nd Grade

Addition problems within 100.

Each sheet consists of adding two or three numbers with a total of up to 100.

There is a space on each sheet for working out, so that your child can write out the problem and solve it.

We have split the worksheets up into word problems with and without regrouping.

Using these sheets will help your child to:

• add up two or three numbers within 100;
• solve addition word problems with and without regrouping.

Addition Word Problems 2nd Grade within 100

There are two versions of each sheet.

The first version (version A) contains problems where no regrouping is needed.

The second version (version B) contains similar problems but regrouping is needed to solve them.

Sheets 1A, 1B, 2A, 2B, 3A and 3B have just two addends to add up.

Sheets 4A, 4B, 5A and 5B have three addends to add together.

Addition Word Problems within 100 with 2 Addends

• Addition Word Problems within 100 Sheet 1A (no regrouping)
• PDF version
• Addition Word Problems within 100 Sheet 1B
• Addition Word Problems within 100 Sheet 2A (no regrouping)
• Addition Word Problems within 100 Sheet 2B
• Addition Word Problems within 100 Sheet 3A (no regrouping)
• Addition Word Problems within 100 Sheet 3B

Addition Word Problems within 100 with 3 Addends

• Addition Word Problems within 100 Sheet 4A (no regrouping)
• Addition Word Problems within 100 Sheet 4B
• Addition Word Problems within 100 Sheet 5A (no regrouping)
• Addition Word Problems within 100 Sheet 5B

Looking for some easier worksheets?

Take a look at our Addition word problems for first graders.

On this page, your child will learn to work out basic addition word problems with sums up to 20.

• 1st grade Addition Word Problems

Looking for some harder worksheets?

We have a range of 3-digit addition worksheets set out in columns.

• Addition Word Problems 3rd Grade (3- and 4-digits)
• 3-Digit Column Addition Worksheets

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

Addition & Subtraction Worksheets 2nd Grade

• Add and Subtract Within 20 Worksheets
• 3 Digit Addition and Subtraction Worksheets

More 2nd Grade Addition Worksheets

Here you will find some more of our 2nd Grade Addition Worksheets.

The link below will open our 2nd-grade-math-salamanders website in a new browser window.

• Addition Word Problems 2nd grade at 2nd-grade-math-salamanders.com
• Number Bonds to 20
• Math Addition Facts to 20

More 2nd Grade Math Word Problems

Here are a range of problems solving sheets for 2nd graders. Most of the sheets contain 'real-life' problems related to animal facts.

Using the sheets will help your child to:

• apply their addition, subtraction, and multiplication skills;
• apply their knowledge of rounding and place value;
• solve a range of 'real life' problems.

These sheets involve solving one or two more challenging longer problems. This link opens in a new tab.

• Second Grade Math Problems

These sheets involve solving many 'real-life' problems involving data.

• 2nd Grade Math Word Problems

These sheets involve solving a range of addition and subtraction word problems up to 100.

• 2nd Grade Addition and Subtraction Word Problems

These sheets involve solving a range of subtraction word problems up to 100.

• Subtraction Word Problems 2nd grade

These sheets involve solving a range of multiplication problems.

• Multiplication Word Problems 2nd Grade

Addition Word Problems to 100 Online Quiz

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This quick quiz tests your knowledge and skill at solving addition word problems within 100.

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• David Arnold
• College of the Redwoods

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Let’s start with the definition of a variable.

A variable is a symbol (usually a letter) that stands for a value that may vary

Next we follow with the definition of an equation.

An equation is a mathematical statement that equates two mathematical expressions.

The key difference between a mathematical expression and an equation is the presence of an an equals sign. So, for example,

2 + 3[5 − 4 · 2], x2 + 2x − 3, and x + 2y + 3

are mathematical expressions (two of which contain variables), while

3 + 2(7 − 3) = 11, x +3=4, and 3x = 9

are equations. Note that each of the equations contain an equals sign, but the expressions do not.

Next we have the definition of a solution of an equation.

What it Means to be a Solution

A solution of an equation is a numerical value that satisfies the equation. That is, when the variable in the equation is replaced by the solution, a true statement results.

Show that 3 is a solution of the equation x + 8 = 11.

Substitute 3 for x in the given equation and simplify.

\[ \begin{array}{rlrl}{x+8} & {=11} & {} & { \textcolor{red}{ \text { The given equation. }}} \\ {3+8} & {=11} & {} & {\textcolor{red}{ \text { Substitute } 3 \text { for } x .}} \\ {11} & {=11} & {} & {\textcolor{red}{ \text { Simplify both sides. }}}\end{array}\nonumber \]

Since the left- and right-hand sides of the last line are equal, this shows that when 3 is substituted for x in the equation a true statement results. Therefore, 3 is a solution of the equation.

Show that 27 is a solution of the equation x − 12 = 15

Is 23 a solution of the equation 4 = y − 11?

Substitute 23 for y in the given equation and simplify.

\[ \begin{array}{ll}{4=y-11} & {\textcolor{red}{ \text { The given equation. }}} \\ {4=23-11} & {\textcolor{red}{ \text { Substitute } 23 \text { for } y}} \\ {4=12} & {\textcolor{red} {\text { Simplify both sides. }}}\end{array}\nonumber \]

Since the left- and right-hand sides of the last line are not equal, this shows that when 23 is substituted for y in the equation a false statement results. Therefore, 23 is not a solution of the equation.

Is 8 a solution of 5 = 12 − y ?

Equivalent Equations

We start with the definition of equivalent equations.

Two equations are equivalent if they have the same solution set.

Are the equations x + 2 = 9 and x = 7 equivalent?

The number 7 is the only solution of the equation x + 2 = 9. Similarly, 7 is the only solution of the equation x = 7. Therefore x + 2 = 9 and Answer: No. x = 7 have the same solution sets and are equivalent.

Are the equations x = 4 and x + 8 = 3 equivalent?

Are the equations x 2 = x and x = 1 equivalent?

By inspection, the equation x 2 = x has two solutions, 0 and 1. On the other hand, the equation x = 1 has a single solution, namely 1. Hence, the equations x 2 = x and x = 1 do not have the same solution sets and are not equivalent.

Are the equations x = 2 and x 2 = 2 x equivalent?

Operations that Produce Equivalent Equations

There are many operations that will produce equivalent operations. In this section we look at two: addition and subtraction.

Adding the Same Quantity to Both Sides of an Equation

Adding the same quantity to both sides of an equation does not change the solution set. That is, if

\[a = b,\nonumber \]

then adding c to both sides of the equation produces the equivalent equation

\[a + c = b + c.\nonumber \]

Let’s see if this works as advertised. Consider the equation x − 4=3. By inspection, 7 is the only solution of the equation. Now, let’s add 4 to both sides of the equation to see if the resulting equation is equivalent to x − 4 = 3.

\[ \begin{array}{rlrl}{x-4} & {=3} & {} & {\textcolor{red}{ \text{The given equation. }}} \\ {x-4+4} & {=3+4} & {} & {\textcolor{red}{ \text{Add 4 to both sides of the equation.} }} \\ {x} & {=7} & {} & {\textcolor{red}{ \text{Simplify both sides of the equation. }}}\end{array}\nonumber \]

The number 7 is the only solution of the equation x = 7. Thus, the equation x = 7 is equivalent to the original equation x − 4 = 3 (they have the same solutions).

Important Point

Adding the same amount to both sides of an equation does not change its solutions.

It is also a fact that subtracting the same quantity from both sides of an equation produces an equivalent equation.

Subtracting the Same Quantity from Both Sides of an Equation

Subtracting the same quantity from both sides of an equation does not change the solution set. That is, if

then subtracting c from both sides of the equation produces the equivalent equation

\[a − c = b − c.\nonumber \]

Let’s also see if this works as advertised. Consider the equation

\[ x + 4 = 9.\nonumber \]

By inspection, 5 is the only solution of the equation. Now, let’s subtract 4 from both sides of the equation to see if the resulting equation is equivalent to x + 4 = 9.

\[ \begin{array}{rlrl}{x+4} & {=9} & {} & {\textcolor{red}{ \text { The given equation. }}} \\ {x+4-4} & {=9-4} & {} & {\textcolor{red}{ \text { Subtract 4 from both sides of the equation. }}} \\ {x} & {=5} & {} & {\textcolor{red}{ \text { Simplify both sides of the equation. }}}\end{array}\nonumber \]

The number 5 is the only solution of the equation \(x = 5\). Thus, the equation \(x = 5\) is equivalent to the original equation \(x + 4 = 9\) (they have the same solutions).

Subtracting the same amount from both sides of an equation does not change its solutions.

Writing Mathematics

When solving equations, observe the following rules to neatly arrange your work:

1. One equation per line . This means that you should not arrange your work like this:

\[ x+3=7 \quad x+3-3=7-3 \quad x=4\nonumber \]

That’s three equations on a line. Rather, arrange your work one equation per line like this:

\[ \begin{aligned} x+3 &=7 \\ x+3-3 &=7-3 \\ x &=4 \end{aligned}\nonumber \]

2. Add and subtract inline. Don’t do this:

\[ \begin{array}{r} x -7 & = & 12 \\ +7 & & + 7 \\ \hline x & = & 19 \end{array}\nonumber \]

Instead, add 7 to both sides of the equation “inline.”

\[ \begin{aligned} x-7 &=12 \\ x-7+7 &=12+7 \\ x &=19 \end{aligned}\nonumber \]

Wrap and Unwrap

Suppose that you are wrapping a gift for your cousin. You perform the following steps in order.

• Put the gift paper on.
• Put the tape on.
• Put the decorative bow on.

When we give the wrapped gift to our cousin, he politely unwraps the present, “undoing” each of our three steps in inverse order.

• Take off the decorative bow.
• Take off the tape.
• Take off the gift paper.

This seemingly frivolous wrapping and unwrapping of a gift contains some deeply powerful mathematical ideas. Consider the mathematical expression \(x+ 4\). To evaluate this expression at a particular value of x , we would start with the given value of x , then

Suppose we started with the number 7. If we add 4, we arrive at the following result: 11.

Now, how would we “unwrap” this result to return to our original number? We would start with our result, then

• Subtract 4.

That is, we would take our result from above, 11, then subtract 4, which returns us to our original number, namely 7.

Addition and Subtraction as Inverse Operations

Two extremely important observations:

The inverse of addition is subtraction. If we start with a number x and add a number a , then subtracting a from the result will return us to the original number x . In symbols,

\[x + a − a = x.\nonumber \]

The inverse of subtraction is addition. If we start with a number x and subtract a number a , then adding a to the result will return us to the original number x . In symbols,

\[x − a + a = x.\nonumber \]

Solve \(x − 8 = 10\) for x .

To undo the effects of subtracting 8, we add 8 to both sides of the equation.

\[ \begin{aligned} x-8=10 & \textcolor{red}{\text { Original equation. }} \\ x-8+8=10+8 & \textcolor{red}{ \text { Add 8 to both sides of the equation. }} \\ x=18 & \textcolor{red}{ \text { On the left, adding "undoes" the effect }} \\ & \textcolor{red}{ \text { of subtracting 8 and returns } x . \text { On the right, }} \\ & \textcolor{red}{10+8=18.} \end{aligned}\nonumber \]

Therefore, the solution of the equation is 18.

To check, substitute the solution 18 into the original equation.

\[ \begin{aligned} x - 8 = 10 & \textcolor{red}{ \text{ Original equation. }} \\ 18 - 8 = 10 & \textcolor{red}{ \text{ Substitute 18 for} x. } \\ 10 = 10 & \textcolor{red}{ \text{ Simplify both sides. }} \end{aligned}\nonumber \]

The fact that the last line of our check is a true statement guarantees that 18 is a solution of x − 8 = 10.

Solve \(x + 5 = 12\) for x .

Solve \(11 = y + 5\) for y.

To undo the effects of adding 5, we subtract 5 from both sides of the equation.

\[ \begin{aligned} 11 = y + 5 & \textcolor{red}{ \text{ Original equation. }} \\ 1 - 5 = y + 5 - 5 & \textcolor{red}{ \text{ Subtract 5 from both sides of the equation. }} \\ 6 = y & \textcolor{red}{ \text{ On the right, subtracting "undoes" the effect }} \\ & \textcolor{red}{ \text{ of adding 5 and returns } y. \text{ On the left, }} \\ & \textcolor{red}{ 11 - 5 = 6. } \end{aligned}\nonumber \]

Therefore, the solution of the equation is 6.

\[ \begin{aligned} 11 = y + 5 & \textcolor{red}{ \text{ Original equation. }} \\ 11 = 6 + 5 & \textcolor{red}{ \text{ Substitute 6 for } y.} \\ 11 = 11 & \textcolor{red}{ \text{ Simplify both sides. }} \end{aligned}\nonumber \]

The fact that the last line of our check is a true statement guarantees that 6 is a solution of 11 = y + 5.

Solve \(y - 8 = 11\) for y .

\(y = 19.\)

Word Problems

The solution of a word problem must incorporate each of the following steps.

Requirements for Word Problem Solutions

• Statements such as “Let P represent the perimeter of the rectangle.”
• Labeling unknown values with variables in a table.
• Labeling unknown quantities in a sketch or diagram.
• Set up an Equation . Every solution to a word problem must include a carefully crafted equation that accurately describes the constraints in the problem statement.
• Solve the Equation . You must always solve the equation set up in the previous step.
• Answer the Question . This step is easily overlooked. For example, the problem might ask for Jane’s age, but your equation’s solution gives the age of Jane’s sister Liz. Make sure you answer the original question asked in the problem. Your solution should be written in a sentence with appropriate units.
• Look Back . It is important to note that this step does not imply that you should simply check your solution in your equation. After all, it’s possible that your equation incorrectly models the problem’s situation, so you could have a valid solution to an incorrect equation. The important question is: “Does your answer make sense based on the words in the original problem statement.”

Let's give these requirements a test drive.

Four more than a certain number is 12. Find the number.

In our solution, we will carefully address each step of the Requirements for Word Problem Solutions.

1. Set up a Variable Dictionary . We can satisfy this requirement by simply stating “Let x represent a certain number.”

2. Set up an Equation . “Four more than a certain number is 12” becomes

\[ \begin{aligned} \colorbox{cyan}{4} & \text{ more than } & \colorbox{cyan}{a certain number} & \text{ is } & \colorbox{cyan}{12} \\ 4 & + & x & = & 12 \end{aligned}\nonumber \]

3. Solve the Equation . To “undo” the addition, subtract 4 from both sides of the equation.

\[ \begin{aligned} 4 + x = 12 & \textcolor{red}{ \text{ Original equation.}} \\ 4 + x - 4 = 12 - 4 & \textcolor{red}{ \text{Subtract 4 from both sides of the equation. }} \\ x = 8 & \textcolor{red}{ \text{ On the left, subtracting 4 "undoes" the effect}} \\ & \textcolor{red}{ \text{ of adding 4 and returns } x. \text{ On the right, }} \\ & \textcolor{red}{12 - 4 = 8.} \end{aligned}\nonumber \]

4. Answer the Question . The number is 8.

5. Look Back . Does the solution 8 satisfy the words in the original problem? We were told that “four more than a certain number is 12.” Well, four more than 8 is 12, so our solution is correct.

12 more than a certain number is 19. Find the number.

Amelie withdraws $125 from her savings account. Because of the withdrawal, the current balance in her account is now $1,200. What was the original balance in the account before the withdrawal?

In our solution, we will carefully address each step of the Requirements for Word Problem Solutions .

1. Set up a Variable Dictionary. We can satisfy this requirement by simply stating “Let B represent the original balance in Amelie’s account.”

2. Set up an Equation . We can describe the situation in words and symbols.

\[ \begin{aligned} \colorbox{cyan}{Original Balance} & \text{ minus } & \colorbox{ Amelie's Withdrawal } & \text{ is } & \colorbox{cyan}{ Current Balance } \\ B & - & 125 & = & 1200 \end{aligned}\nonumber \]

3. Solve the Equation . To “undo” the subtraction, add 125 to both sides of the equation.

\[ \begin{aligned} B - 125 = 1200 & \textcolor{red}{ \text{ Original equation. }} \\ B - 125 + 125 = 1200 + 125 & \textcolor{red}{ \text{Add 125 to both sides of the equation. }} \\ B = 1325 & \textcolor{red}{ \text{ On the left, adding 125 "undoes" the effect}} \\ & \textcolor{red}{ \text{ of subtracting 125 and returns } B. \text{ On the right, }} \\ & \textcolor{red}{ 1200 + 125 = 1325.} \end{aligned}\nonumber \]

4. Answer the Question . The original balance was $1,325.

5. Look Back . Does the solution $1,325 satisfy the words in the original problem? Note that if Amelie withdraws $125 from this balance, the new balance will be $1,200. Hence, the solution is correct.

Fred withdraws $230 from his account, lowering his balance to $3,500. What was his original balance?

The perimeter of a triangle is 114 feet. Two sides of the triangle measure 30 feet and 40 feet, respectively. Find the measure of the third side of the triangle.

1. Set up a Variable Dictionary. When geometry is involved, we can create our variable dictionary by labeling a carefully constructed diagram. With this thought in mind, we draw a triangle, then label its known and unknown sides and its perimeter.

The figure makes it clear that x represents the length of the unknown side of the triangle. The figure also summarizes information needed for the solution. 2. Set up an equation. We know that the perimeter of a triangle is found by finding the sum of its three sides; in words and symbols,

\[ \begin{aligned} \colorbox{cyan}{ Perimeter } & \text{ is } & \colorbox{cyan}{ First Side } & \text{ plus } & \colorbox{cyan}{ Second Side } & \text{ plus } & \colorbox{cyan}{ Third Side } \\ 114 & = & x & + & 30 & + & 40 \end{aligned}\nonumber \]

Simplify the right-hand side by adding 30 and 40; i.e., \(30 + 40 = 70\).

\[ 114 = x + 70\nonumber \]

3. Solve the Equation. To “undo” adding 70, subtract 70 from both sides of the equation.

\[ \begin{aligned} 114 = x + 70 & \textcolor{red}{ \text{ Our equation. }} \\ 114 - 70 = x + 70 - 70 & \textcolor{red}{ \text{ Subtract 70 from both sides. }} \\ 44 = x & \textcolor{red}{ \text{ On the right, subtracting 70 "undoes" the effect}} \\ & \textcolor{red}{ \text{of adding 70 and returns to } x. \text{ On the left,}} \\ & \textcolor{red}{ 114 - 70 = 44.} \end{aligned}\nonumber \]

4. Answer the Question . The unknown side of the triangle is 44 feet.

5. Look Back . Does the solution 44 feet satisfy the words of the original problem? We were told that the perimeter is 114 feet and two of the sides have length 30 feet and 40 feet respectively. We found that the third side has length 44 feet. Now, adding the three sides, 30+ 40+ 44 = 114, which equals the given perimeter of 114 feet. The answer works!

The perimeter of a quadrilateral is 200 meters. If three of the sides measure 20, 40, and 60 meters, what is the length of the fourth side.

In Exercises 1-12, which of the numbers following the given equation are solutions of the given equation? Support your response with work similar to that shown in Examples 1 and 2.

1. x − 4 = 6; 10, 17, 13, 11

2. x − 9 = 7; 17, 23, 19, 16

3. x + 2 = 6; 5, 11, 7, 4

4. x + 3 = 9; 6, 9, 7, 13

5. x + 2 = 3; 8, 1, 4, 2

6. x + 2 = 5; 10, 3, 6, 4

7. x − 4 = 7; 12, 11, 18, 14

8. x − 6 = 7; 13, 16, 20, 14

9. x + 3 = 4; 8, 4, 2, 1

10. x + 5 = 9; 5, 11, 7, 4

11. x − 6 = 8; 17, 21, 14, 15

12. x − 2 = 9; 11, 14, 12, 18

In Exercises 13-52, solve the given equation for x .

14. x + 6 = 19

16. 10 = 8 + x

17. 13 + x = 17

18. 7+ x = 15

19. 9+ x = 10

20. 14 + x = 17

21. 19 = x − 3

22. 2= x − 11

23. x − 18 = 1

24. x − 20 = 8

25. x − 3 = 11

26. x − 17 = 18

27. 2+ x = 4

28. 1+ x = 16

29. x − 14 = 12

30. x − 1 = 17

32. x + 11 = 14

33. 11 + x = 17

34. 11 + x = 18

35. x + 13 = 17

36. x + 1 = 16

37. 20 = 3 + x

39. 20 = 8 + x

40. 10 = 3 + x

41. 3= x − 20

42. 13 = x − 15

43. x + 16 = 17

44. x + 6 = 12

45. 5= x − 6

46. 10 = x − 7

47. 18 = x − 6

48. 14 = x − 4

49. 18 = 13 + x

50. 17 = 5 + x

51. x − 9 = 15

52. x − 11 = 17

53. 12 less than a certain number is 19. Find the number.

54. 19 less than a certain number is 1. Find the number.

55. A triangle has a perimeter of 65 feet. It also has two sides measuring 19 feet and 17 feet, respectively. Find the length of the third side of the triangle.

56. A triangle has a perimeter of 55 feet. It also has two sides measuring 14 feet and 13 feet, respectively. Find the length of the third side of the triangle.

57. Burt makes a deposit to an account having a balance of $1900. After the deposit, the new balance in the account is $8050. Find the amount of the deposit.

58. Dave makes a deposit to an account having a balance of $3500. After the deposit, the new balance in the account is $4600. Find the amount of the deposit.

59. 8 more than a certain number is 18. Find the number.

60. 3 more than a certain number is 19. Find the number.

61. Michelle withdraws a $120 from her bank account. As a result, the new account balance is $1000. Find the account balance before the withdrawal.

62. Mercy withdraws a $430 from her bank account. As a result, the new account balance is $1200. Find the account balance before the withdrawal.

63. Foreclosures . Between January and March last year, 650,000 homes received a foreclosure notice. Between the first three months of this year, there were 804,000 foreclosure notices. What was the increase in home foreclosure notices? Associated Press Times-Standard 4/22/09

64. Home Price . According to the Humboldt State University Economics Department’s Humboldt Economic Index, the median home price in the US fell $1500 over the last month to $265,000. What was the median home price before the price drop?

65. Unmanned Areal Vehicle . Northrup Grumman’s Global Hawk unmanned drone can fly at 65,000 feet, 40,000 feet higher than NASA’s Ikhana unmanned aircraft. How high can the Ikhana fly?

66. Tribal Land . The Yurok Tribe has the option to purchase 47,000 acres in order to increase its ancestral territory. The first phase would include 22,500 acres in the Cappel and Pecman watersheds. The second phase plans for acreage in the Blue Creek area. How many acres could be purchased in the second phase? Times-Standard 4/15/09

63. 154,000

65. 25,000 feet

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Addition word problems (1-3 digits)

Addition word problems with numbers under 1,000.

These grade 2 word problem worksheets are solved by forming addition equations involving 1, 2 or 3 digit numbers.   Sums are under 1,000.  Most questions have only 2 addends though some have 3.  

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Addition and Subtraction KS1

This collection is one of our Primary Curriculum collections - tasks that are grouped by topic.

Number Balance

Can you hang weights in the right place to make the the number balance balanced?

What Was in the Box?

This big box adds something to any number that goes into it. If you know the numbers that come out, what addition might be going on in the box?

This project challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask?

Arranging Additions and Sorting Subtractions

Order these four calculations from easiest to hardest. How did you decide?

Domino Sorting

Try grouping the dominoes in the ways described. Are there any left over each time? Can you explain why?

One Big Triangle

Make one big triangle so the numbers that touch on the small triangles add to 10.

Subtraction Slip

Can you spot the mistake in this video? How would you work out the answer to this calculation?

Pairs of Numbers

If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?

Butterfly Flowers

Can you find two butterflies to go on each flower so that the numbers on each pair of butterflies adds to the number on their flower?

Equivalent Pairs

Can you match pairs of cards which show the same amount?

Number Lines

A resource to try once children are familiar with number lines, and they have begun to use them for addition. It could be a good way to talk about subtraction. Leah and Tom each have a number line. Can you work out where their counters will land?

Two Spinners

What two-digit numbers can you make with these two dice? What can't you make?

The Add and Take-away Path

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

What Could It Be?

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

Find all the numbers that can be made by adding the dots on two dice.

Unit Differences

This challenge is about finding the difference between numbers which have the same tens digit.

Cuisenaire Counting

Here are some rods that are different colours. How could I make a yellow rod using white and red rods?

What's in a Name?

What do you notice about these squares of numbers? What is the same? What is different?

Sort Them Out (1)

Can you each work out the number on your card? What do you notice? How could you sort the cards?

Ladybirds in the Garden

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

Secret Number

Annie and Ben are playing a game with a calculator. What was Annie's secret number?

Eggs in Baskets

There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. How many eggs are in each basket?

Birthday Cakes

Jack's mum bought some candles to use on his birthday cakes and when his sister was born, she used them on her cakes too. Can you use the information to find out when Kate was born?

Find the Difference

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

Noah saw 12 legs walk by into the Ark. How many creatures did he see?

Heads and Feet

On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?

Jumping Squares

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

Number Round Up

Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.

The Brown Family

Use the information about Sally and her brother to find out how many children there are in the Brown family.

The Tall Tower

As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

This is an adding game for two players. Can you be the first to reach the target?

Doing and Undoing

An investigation looking at doing and undoing mathematical operations focusing on doubling, halving, adding and subtracting.

Sitting Round the Party Tables

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

How Do You See It?

Here are some short problems for you to try. Talk to your friends about how you work them out.

What could the half time scores have been in these Olympic hockey matches?

Strike it Out

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

Dicey Addition

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Mathematics > Analysis of PDEs

Title: global existence for wave and beam equations with double damping and a new power nonlinearity.

Abstract: We consider the Cauchy problem in $\mathbb{R}^{n}$ for wave and beam equations with frictional, viscoelastic damping, and a new power nonlinearity. In addition to the solution and its total energy, we define the following quantity: $$Q[u](t):=\|u_{t}(t,\cdot)+(-\Delta)^{\sigma}u(t,\cdot)\|_{L^{2}(\mathbb{R}^{n})}.$$ Our aim is to show that the interaction between frictional and viscoelastic damping in a linear model leads to an exponential decay of $Q[u](t)$ as $t\to \infty$. This decay motivates us to define a new power nonlinearity of the form $N[u]:=|u_{t}+(-\Delta)^{\sigma}u|^{p}$. Surprisingly, $N[u]$ can be considered a small perturbation for any $p>1$, in the sense that, the decay estimates of the unique global solution, the total energy and $Q[u](t)$ coincide with those for solutions to the corresponding linear Cauchy problem with vanishing right-hand side.

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