Inverse Operations: Multiplication and Division Worksheet for 9-Year-Olds

Instructions

1. Use multiplication and division facts to solve each problem.
2. Remember: multiplication and division are inverse operations because they undo each other.
3. Check your work by using the opposite operation.
4. Show your thinking. Use the hint when you need help.

Example:

• 4 × 6 = 24
• 6 × 4 = 24
• 24 ÷ 4 = 6
• 24 ÷ 6 = 4

These four equations make a fact family.

1. Complete the Fact Families

Fill in the three missing equations for each fact family.

Hint: Each fact family has two multiplication facts and two division facts.

2. Find the Missing Number

Write the missing number in each box. Then check your answer with the inverse operation.

1. 6 × = 30 Check: 30 ÷ 6 =
2. × 4 = 28 Check: 28 ÷ 4 =
3. 45 ÷ 5 = Check: × 5 = 45
4. 36 ÷ = 6 Check: 6 × = 36
5. 7 × = 56 Check: 56 ÷ 7 =
6. ÷ 8 = 3 Check: 3 × 8 =
7. 9 × = 81 Check: 81 ÷ 9 =
8. 72 ÷ = 9 Check: 9 × = 72

3. Choose the Inverse Operation

Circle the operation that would best check each answer.

1. 8 × 7 = 56

   • Addition
   • Subtraction
   • Division

2. 63 ÷ 9 = 7

   • Multiplication
   • Addition
   • Subtraction

3. 6 × 5 = 30

   • Division
   • Addition
   • Subtraction

4. 48 ÷ 6 = 8

   • Multiplication
   • Addition
   • Subtraction

4. Match the Related Equations

Write the letter of the equation that is the inverse of each equation.

1. 7 × 6 = 42 _____
2. 32 ÷ 4 = 8 _____
3. 9 × 3 = 27 _____
4. 56 ÷ 7 = 8 _____
5. 5 × 8 = 40 _____

• A. 27 ÷ 3 = 9
• B. 8 × 7 = 56
• C. 40 ÷ 5 = 8
• D. 8 × 4 = 32
• E. 8 × 7 = 56

Note: Some equations may use the same fact family. Look carefully at the numbers.

5. The School Snack Station

Use multiplication or division to solve each real-world problem. Write an equation for each answer.

1. There are 6 bags with 4 apples in each bag. How many apples are there altogether?

   Equation: __ Answer: ____

2. A teacher has 35 pencils and puts 5 pencils in each cup. How many cups can she fill?

   Equation: __ Answer: ____

3. There are 8 tables with 6 students at each table. How many students are there?

   Equation: __ Answer: ____

4. The cafeteria has 48 oranges. They place 8 oranges in each basket. How many baskets do they need?

   Equation: __ Answer: ____

5. A class makes 7 rows of 9 paper stars. How many paper stars do they make?

   Equation: __ Answer: ____

6. Spot the Mistake

Read each student’s work. Decide whether it is correct. If it is incorrect, fix it and use an inverse operation to explain why.

1. Mia says: 42 ÷ 6 = 8 because 8 × 6 = 42.

   Correct or incorrect? ____ Fix: ____ Check: __

2. Leo says: 7 × 5 = 35 because 35 ÷ 7 = 5.

   Correct or incorrect? ____ Fix: ____ Check: __

3. Ava says: 54 ÷ 9 = 6 because 6 × 9 = 54.

   Correct or incorrect? ____ Fix: ____ Check: __

7. Build Your Own Fact Family

Choose three numbers that belong in a multiplication and division fact family. Do not use the example numbers.

Now write the other two equations for one of your fact families:

8. Challenge Quest

Solve each problem. Explain how inverse operations help you.

1. A mystery number multiplied by 8 equals 64. What is the mystery number?

   Equation: __ Answer: ____

2. A number divided by 6 equals 7. What is the number?

   Equation: __ Answer: ____

3. Sam knows that 9 × 4 = 36. Write two different division equations from this fact.

   1. ---

   2. ---

4. Write your own word problem that can be solved using division. Solve it, too.

   Word problem: __

   ---

   Equation: __ Answer: ____

Answer Key

1. Complete the Fact Families

• 2, 7, 14: 2 × 7 = 14; 7 × 2 = 14; 14 ÷ 2 = 7; 14 ÷ 7 = 2
• 4, 6, 24: 4 × 6 = 24; 6 × 4 = 24; 24 ÷ 4 = 6; 24 ÷ 6 = 4
• 5, 8, 40: 5 × 8 = 40; 8 × 5 = 40; 40 ÷ 5 = 8; 40 ÷ 8 = 5
• 3, 9, 27: 3 × 9 = 27; 9 × 3 = 27; 27 ÷ 3 = 9; 27 ÷ 9 = 3
• 6, 7, 42: 6 × 7 = 42; 7 × 6 = 42; 42 ÷ 6 = 7; 42 ÷ 7 = 6

2. Find the Missing Number

1. 5; check: 5
2. 7; check: 7
3. 9; check: 9
4. 6; check: 6
5. 8; check: 8
6. 24; check: 24
7. 9; check: 9
8. 8; check: 8

3. Choose the Inverse Operation

1. Division
2. Multiplication
3. Division
4. Multiplication

4. Match the Related Equations

1. B or E
2. D
3. A
4. B or E
5. C

Note: The choices B and E show the same equation, so either may be used for the fact family involving 7, 8, and 56. A clearer matching set would pair 1 with B and 4 with E.

5. The School Snack Station

1. 6 × 4 = 24; 24 apples
2. 35 ÷ 5 = 7; 7 cups
3. 8 × 6 = 48; 48 students
4. 48 ÷ 8 = 6; 6 baskets
5. 7 × 9 = 63; 63 paper stars

6. Spot the Mistake

1. Incorrect. 42 ÷ 6 = 7. Check: 7 × 6 = 42.
2. Correct. Check: 35 ÷ 7 = 5.
3. Correct. Check: 6 × 9 = 54.

7. Build Your Own Fact Family

Answers will vary. Example:

• 3, 8, and 24
• 3 × 8 = 24
• 8 × 3 = 24
• 24 ÷ 3 = 8
• 24 ÷ 8 = 3

8. Challenge Quest

1. 8 × 8 = 64, so the mystery number is 8.
2. 7 × 6 = 42, so the number is 42.
3. 36 ÷ 9 = 4 and 36 ÷ 4 = 9.
4. Answers will vary. The problem should use division and include a correct equation and answer.