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Check calculations with inverse operations

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 divisor×quotient+remainder\text{divisor} \times \text{quotient} + \text{remainder}; it excludes advanced symbolic algebra and generalized inverse functions.

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:

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

Example: Check the calculation

348÷7=49 remainder 5348 \div 7=49\text{ remainder }5

  1. Identify the parts:

    • Divisor: 77
    • Quotient: 4949
    • Remainder: 55

  2. Multiply the divisor by the quotient:

7×49=3437\times49=343
  1. Add the remainder:
343+5=348343+5=348
  1. Compare the result with the original dividend. Since the check gives 348348, the same number we started with, the division is correct.

So,

7×49+5=3487\times49+5=348

The division calculation checks out.

Learn by doing: Check calculations with inverse operations

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    Long Division - No Remainder 2 x 1

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