Skill: Check calculations with inverse operations

Explanation and Free Practice Resources

Inverse operations undo one another: addition and subtraction form an inverse pair, as do multiplication and division, allowing a numerical result to be checked by applying the corresponding operation in reverse. This reasoning applies to whole-number, decimal, and fraction calculations, including checking division with $\text{divisor} \times \text{quotient} + \text{remainder}$ ; it excludes advanced symbolic algebra and generalized inverse functions.

On this page:

Learn “Check calculations with inverse operations” with a detailed explanation of the concept
Master “Check calculations with inverse operations” with unlimited, free practice problems
Download (or modify) a free worksheet on Check calculations with inverse operations you can use at home or in class with practice problems that scaffold and explore “Check calculations with inverse operations” from different perspectives.
Start working on adaptive units like “Division - Long Division - Practice” or “Division 2 by 1 Digit” that introduce, teach, or practice “Check calculations with inverse operations” to maximize your learning.

Detailed Explanation: Check calculations with inverse operations

Inverse operations undo each other, so you can use them to check whether an answer is correct.

For division, check using:

\text{divisor} \times \text{quotient}+\text{remainder}

Example: Check the calculation

348 \div 7=49\text{ remainder }5

Identify the parts:
- Divisor: $7$
- Quotient: $49$
- Remainder: $5$
Multiply the divisor by the quotient:

7\times49=343

Add the remainder:

343+5=348

Compare the result with the original dividend. Since the check gives $348$ , the same number we started with, the division is correct.

So,

7\times49+5=348

The division calculation checks out.

Learn by doing: Check calculations with inverse operations

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

Your results

Practice with unlimited practice problems

Long Division - No Remainder 2 x 1

Earned ?

Download/Modify Free Grade 6 'Check calculations with inverse operations' Worksheet

Print this free 'Check calculations with inverse operations' worksheet to practice this skill away from the computer. Click 'Modify' to easily customize this worksheet to your exact needs.

Units Teaching This Skill

These adaptive units introduce, teach, or reinforce this skill (Check calculations with inverse operations) through scaffolded problems that grow in difficulty as concepts are understood.