🔢 MathGrade 2Lesson 13
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Check Answers Using Inverse Operations

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Learning Objectives

  • 1Explain that addition and subtraction undo each other
  • 2Write the inverse subtraction for any addition equation
  • 3Use the inverse operation to check an answer is correct
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Mini Lesson

An inverse operation is the opposite operation. Addition and subtraction are inverses of each other — one undoes the other. This lets you check your work without re-doing the same sum.

The key idea

  • If 24 + 13 = 37, then 37 − 13 = 24 must also be true.
  • The three numbers 24, 13, and 37 form a fact family.
  • You can write four related equations with the same three numbers: 24 + 13 = 37, 13 + 24 = 37, 37 − 13 = 24, 37 − 24 = 13.

How to use the inverse to check

  • Step 1: Solve the problem. Example: 45 + 30 = 75.
  • Step 2: Write the inverse — start with the answer (75), subtract one addend (30): 75 − 30 = ?
  • Step 3: If the result equals the other addend (45), your answer is correct. 75 − 30 = 45.
  • If the result does not match, you made a mistake — go back and re-calculate.

Checking subtraction with addition

  • If you calculated 80 − 30 = 50, check with 50 + 30 = 80.
  • The answer + the subtrahend must equal the minuend.
Fact family triangle for 24, 13, and 37A triangle with 37 at the top, 24 at bottom-left, and 13 at bottom-right. Four equations are written below: 24 + 13 = 37, 13 + 24 = 37, 37 − 13 = 24, 37 − 24 = 13.Fact Family Triangle37241324 + 13 = 3713 + 24 = 3737 − 13 = 2437 − 24 = 13
Fact family triangle: 37 at the top, 24 and 13 at the base, with all four related equations below.
Three steps to check an addition using subtractionStep 1: Solve 45 + 30 = 75. Step 2: Write the inverse, 75 − 30 = ?. Step 3: Check — result 45 matches, so the answer is correct.Check with the Inverse1. Solve45 + 30 = 75↓2. Write the inverse75 − 30 = ?↓3. Check75 − 30 = 45 (matches!)
Three steps to check 45 + 30 = 75 using the inverse: write 75 − 30 = ?, solve it, confirm the result matches the first addend.
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Ask yourself: "Can I use the opposite operation with these three numbers to prove my answer is right?"

Vocabulary
Inverse operation
An operation that undoes another operatione.g. Subtraction is the inverse operation of addition.
Fact family
Three numbers that make four related equationse.g. 24, 13, and 37 are a fact family.
Check
To make sure an answer is correcte.g. I checked my answer by using the inverse.
Equation
A number sentence with an equals signe.g. 45 + 30 = 75 is an equation.
Undo
To reverse an actione.g. Subtraction undoes addition.
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← Lesson 12: Add and Subtract Using Number LinesLesson 14: Add with Regrouping →