Inverse Operations: Multiplication & Division Worksheet

Instructions

1. Use multiplication and division facts to solve each problem.
2. Remember: multiplication and division are inverse operations. They are opposite operations that can check each other.
3. For each fact family, use the same three numbers.
4. Show your thinking when you can. Use the hint if you get stuck.
5. Complete the challenge at the end if you are ready for an extra puzzle.

Example:

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

These four equations are a fact family.

1. Find the Inverse Operation

Write M for multiplication or D for division.

1. 7 × 5 = 35: __
2. 42 ÷ 6 = 7: __
3. 8 × 4 = 32: __
4. 27 ÷ 3 = 9: __
5. 9 × 6 = 54: __
6. 64 ÷ 8 = 8: __

2. Complete the Fact Family

Use the three numbers in the box to write two multiplication equations and two division equations.

Example: 3, 5, 15

• 3 × 5 = 15
• 5 × 3 = 15
• 15 ÷ 3 = 5
• 15 ÷ 5 = 3

3. Use the Inverse to Check

Solve the first equation. Then use the inverse operation to check your answer.

Example:

6 × 4 = 24

Check: 24 ÷ 6 = 4

1. 7 × 3 = __

   Check: __ ÷ 7 = __

2. 8 × 6 = __

   Check: __ ÷ 8 = __

3. 9 × 4 = __

   Check: __ ÷ 9 = __

4. 36 ÷ 6 = __

   Check: __ × 6 = __

5. 56 ÷ 7 = __

   Check: __ × 7 = __

6. 72 ÷ 8 = __

   Check: __ × 8 = __

4. Missing Number Mystery

Fill in the missing number. Think about which inverse operation will help.

1. 5 × __ = 40
2. __ × 7 = 63
3. 48 ÷ __ = 6
4. __ ÷ 8 = 7
5. 9 × __ = 81
6. 64 ÷ __ = 8
7. __ × 6 = 42
8. 54 ÷ 9 = __

Hint: If you see 7 × ? = 35, solve 35 ÷ 7 to find the missing number.

5. Real-Life Math: The School Garden

A class is planting flowers in equal rows. Use multiplication and division to solve each problem.

1. There are 6 rows with 4 flowers in each row. How many flowers are there altogether?

   Equation: ____

   Answer: _____

2. The class has 35 seeds and puts 5 seeds in each pot. How many pots can they fill?

   Equation: ____

   Answer: _____

3. There are 8 trays with 7 plants in each tray. How many plants are there?

   Equation: ____

   Answer: _____

4. The gardener has 54 flowers and places 6 flowers in each basket. How many baskets are needed?

   Equation: ____

   Answer: _____

5. Write a multiplication equation and a division equation that tell about the same garden situation.

   Multiplication: ___

   Division: ____

6. True or False? Explain Your Thinking

Circle True or False. If the statement is false, correct it.

1. 4 × 8 = 32, so 32 ÷ 4 = 8. True / False

   Correction or explanation: ____

2. 6 × 7 = 42, so 42 ÷ 6 = 6. True / False

   Correction or explanation: ____

3. 9 × 5 = 45, so 45 ÷ 9 = 5. True / False

   Correction or explanation: ____

4. Multiplication and division can be used to check each other. True / False

   Explanation: _____

7. Create Your Own Fact Family

Choose three numbers that make a multiplication and division fact family. Then write all four equations.

My three numbers: __, __, and __

Optional Challenge: The Number Code

Each letter has a number value. Use inverse operations to solve the clues and reveal the secret word.

• A = 4 × 3
• B = 36 ÷ 4
• C = 7 × 5
• D = 48 ÷ 6
• E = 9 × 6

Match each answer to its letter.

1. 12 = __
2. 54 = __
3. 35 = __
4. 9 = __
5. 8 = __

Secret code: __ __ __ __ __

Reflection

Complete the sentence.

I can use division to check multiplication because ____

Answer Key

1. Find the Inverse Operation

1. M
2. D
3. M
4. D
5. M
6. D

2. Complete the Fact Family

• 4 × 7 = 28

• 7 × 4 = 28

• 28 ÷ 4 = 7

• 28 ÷ 7 = 4

• 6 × 8 = 48

• 8 × 6 = 48

• 48 ÷ 6 = 8

• 48 ÷ 8 = 6

• 5 × 9 = 45

• 9 × 5 = 45

• 45 ÷ 5 = 9

• 45 ÷ 9 = 5

• 7 × 8 = 56

• 8 × 7 = 56

• 56 ÷ 7 = 8

• 56 ÷ 8 = 7

• 6 × 9 = 54

• 9 × 6 = 54

• 54 ÷ 6 = 9

• 54 ÷ 9 = 6

3. Use the Inverse to Check

1. 7 × 3 = 21; 21 ÷ 7 = 3
2. 8 × 6 = 48; 48 ÷ 8 = 6
3. 9 × 4 = 36; 36 ÷ 9 = 4
4. 36 ÷ 6 = 6; 6 × 6 = 36
5. 56 ÷ 7 = 8; 8 × 7 = 56
6. 72 ÷ 8 = 9; 9 × 8 = 72

4. Missing Number Mystery

1. 8
2. 9
3. 8
4. 56
5. 9
6. 8
7. 7
8. 6

5. Real-Life Math: The School Garden

1. 6 × 4 = 24; 24 flowers
2. 35 ÷ 5 = 7; 7 pots
3. 8 × 7 = 56; 56 plants
4. 54 ÷ 6 = 9; 9 baskets
5. Answers will vary. Example: 4 × 6 = 24 and 24 ÷ 4 = 6.

6. True or False?

1. True
2. False; 42 ÷ 6 = 7
3. True
4. True

7. Create Your Own Fact Family

Answers will vary. Example using 2, 8, and 16:

• 2 × 8 = 16
• 8 × 2 = 16
• 16 ÷ 2 = 8
• 16 ÷ 8 = 2

Optional Challenge: The Number Code

1. 12 = A
2. 54 = E
3. 35 = C
4. 9 = B
5. 8 = D

Secret code: A E C B D

Reflection

Answers will vary. A complete answer should explain that division reverses multiplication, such as 6 × 4 = 24 and 24 ÷ 6 = 4.