The inverse relationship between multiplication and division means that a division equation can be verified by multiplying the divisor by the quotient; for exact division, this product equals the dividend. When a remainder occurs, the complete relationship is dividend = divisor × quotient + remainder, with the remainder nonnegative and less than the divisor. The focus is whole-number division; decimal, negative-number, and symbolic generalizations are outside this scope.
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- Learn “Check division using multiplication” with a detailed explanation of the concept
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- Download (or modify) a free worksheet on Check division using multiplication you can use at home or in class with practice problems that scaffold and explore “Check division using multiplication” from different perspectives.
- Start working on adaptive units like “Division 2 by 1 Digit” or “Division 3 by 1 Digit” that introduce, teach, or practice “Check division using multiplication” to maximize your learning.
Detailed Explanation: Check division using multiplication
To check a division problem, use multiplication:
- Multiply the divisor by the quotient.
- If there is a remainder, add it to the product.
- The answer should equal the dividend.
Example:
Here:
- Dividend:
- Divisor:
- Quotient:
- Remainder:
Check the answer:
The result is , which matches the dividend, so the division is correct.
Also, the remainder must be less than the divisor. Since , the remainder is valid.
Learn by doing: Check division using multiplication
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Practice:
Digit Solving - Long Division - Two Steps, With Remainder - Identify Dividend
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Download/Modify Free Grade 5 'Check division using multiplication' Worksheet
Print this free 'Check division using multiplication' worksheet to practice this skill away from the computer. Click 'Modify' to easily customize this worksheet to your exact needs.
This Worksheet Includes:
- Digit Solving - Long Division - Two Steps, With Remainder - Identify Dividend
- Division as Fraction - With Remainder 3 x 2
- Division as Fraction - With Remainder 3 x 1
- Division - Missing Value, Division 3 x 2 Digit
- Division - Missing Value, Multiplication 3 x 1 Digit
- Division - Missing Value, Multiplication 2 x 1 Digit
- Division - Missing Value, Division 3 x 1 Digit
- Division - Missing Value, Multiplication 2 x 2 Digit
Units Teaching This Skill
These adaptive units introduce, teach, or reinforce this skill (Check division using multiplication) through scaffolded problems that grow in difficulty as concepts are understood.