🔢 MathGrade 4Lesson 14
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Check Answers with Inverse Operations

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Learning Objectives

  • 1Identify the inverse operation for addition, subtraction, multiplication, and division
  • 2Use the inverse operation to check whether a calculated answer is correct
  • 3Detect and correct calculation errors using inverse checking
  • 4Apply inverse operations as a self-checking strategy in multi-step problems
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Mini Lesson

Every operation has an opposite called its inverse. Addition and subtraction are inverses of each other. Multiplication and division are inverses of each other. You can use the inverse operation to check whether your answer is correct — this is one of the most powerful self-checking strategies in mathematics.

Inverse Operation Pairs

  • Addition and Subtraction are inverses: if 47 + 28 = 75, then 75 − 28 should equal 47.
  • Subtraction and Addition are inverses: if 83 − 36 = 47, then 47 + 36 should equal 83.
  • Multiplication and Division are inverses: if 6 × 8 = 48, then 48 ÷ 8 should equal 6.
  • Division and Multiplication are inverses: if 96 ÷ 4 = 24, then 24 × 4 should equal 96.

How to Check Using the Inverse

  1. Identify which operation you used to get your answer.
  2. Apply its inverse to your answer and one of the original numbers.
  3. If the result matches the other original number, your answer is correct.
  4. If the result does not match, there is an error — go back and recalculate.

Fact Families

A fact family is a group of related number sentences that use the same three numbers. For 6, 8, and 48: you can write 6 × 8 = 48, 8 × 6 = 48, 48 ÷ 8 = 6, and 48 ÷ 6 = 8. These four facts all belong to the same family and show inverse relationships.

Fact family diamond for 6, 8, and 48Fact Family: 6, 8, 48numbers6, 8, 486 x 8 = 4848 / 6 = 88 x 6 = 4848 / 8 = 6
Checking 96 divided by 4 equals 24 using inverse operationChecking with Inverse1Original calculation:96 / 4 = 24inverse: multiply2Check with inverse:24 x 4 = 96Result matches — answer is correct!
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Tip: if your check does not give back the original number, you made an error somewhere. Use the inverse as a built-in calculator check every time.

Vocabulary
Inverse operation
The operation that undoes another (subtraction undoes addition)e.g. Subtraction is the inverse of addition.
Check
A step where you verify your answer is correcte.g. I check 23 + 12 = 35 by computing 35 − 12 = 23.
Fact family
A group of four facts that link the same three numberse.g. 6, 8, 48 form one fact family.
Sum
The answer to an addition probleme.g. The sum of 12 and 23 is 35.
Difference
The answer to a subtraction probleme.g. The difference between 35 and 12 is 23.
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