The inverse relationship between multiplication and division provides a way to verify a quotient: multiplying the divisor by the quotient should reproduce the dividend in an exact division fact. For division with a remainder, the check is divisor × quotient + remainder = dividend, with the remainder less than the divisor; this applies to whole-number problems within 100 and does not extend to larger-number long-division procedures or algebraic generalizations.
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- Learn “Check division with multiplication” with a detailed explanation of the concept
- Master “Check division with multiplication” with unlimited, free practice problems
- Download (or modify) a free worksheet on Check division with multiplication you can use at home or in class with practice problems that scaffold and explore “Check division with multiplication” from different perspectives.
- Start working on adaptive units like “Division 2 by 1 Digit” or “Division 3 by 2 Digit” that introduce, teach, or practice “Check division with multiplication” to maximize your learning.
Detailed Explanation: Check division with multiplication
To check a division answer, use multiplication because multiplication and division are opposites.
Suppose you solve:
This means:
- is the divisor.
- is the quotient.
- is the remainder.
Check your answer in two steps:
- Multiply the divisor by the quotient:
- Add the remainder:
The answer matches the dividend, , so the division is correct.
Also check that the remainder is smaller than the divisor:
Therefore, is correct.
Learn by doing: Check division with multiplication
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Practice:
Division Equation - With Remainder 2 x 1
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Download/Modify Free Grade 3 'Check division with multiplication' Worksheet
Print this free 'Check division with multiplication' worksheet to practice this skill away from the computer. Click 'Modify' to easily customize this worksheet to your exact needs.
This Worksheet Includes:
- Division Equation - With Remainder 2 x 1
- Division as Fraction - With Remainder 2 x 1
- Long Division - No Remainder 2 x 1
- Division as Fraction - No Remainder 2 x 1
- Division - Missing Value, Multiplication 1 x 1 Digit
- Division - Missing Value, Division 2 x 1 Digit
- Multiplication - Missing Value, 2 x 1 Digit
- Division Cards Model - Deck and Player Count to Hand Size - With Remainder (1 Digit)
Units Teaching This Skill
These adaptive units introduce, teach, or reinforce this skill (Check division with multiplication) through scaffolded problems that grow in difficulty as concepts are understood.