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Check division using multiplication

Division and multiplication are inverse operations: a division equation can be checked by multiplying the divisor by the quotient to recover the dividend when the division is exact. For division with a remainder, the check is divisor×quotient+remainder=dividend\text{divisor} \times \text{quotient} + \text{remainder} = \text{dividend}, with the remainder less than the divisor; this connects the parts of division and helps identify an incorrect quotient or remainder.

Detailed Explanation: Check division using multiplication

To check a division problem, use multiplication to see whether you can get back to the original dividend.

For division with a remainder, use:

divisor×quotient+remainder=dividend\text{divisor} \times \text{quotient}+\text{remainder}=\text{dividend}

Example:

47÷6=7 R 547 \div 6=7\text{ R }5

  1. Identify the parts:

    • Divisor: 66
    • Quotient: 77
    • Remainder: 55
    • Dividend: 4747

  2. Multiply the divisor by the quotient:

6×7=426 \times 7=42
  1. Add the remainder:
42+5=4742+5=47

The answer is correct because we got back to the dividend, 4747.

Also, check that the remainder is less than the divisor:

5<65<6

So, 47÷6=7 R 547 \div 6=7\text{ R }5 is correct.

Learn by doing: Check division using multiplication

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    Long Division - With Remainder 4 x 1

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