Dividing rational numbers
Find the reciprocal of a rational number and turn divisions of signed numbers into multiplications. See why dividing by zero makes no sense.
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Guide
This studio follows the Iranian Grade 8 lesson on multiplying and dividing rational numbers. The reciprocal of a rational number is the number that makes 1 when you multiply by it. Swap the numerator and denominator and keep the sign: the reciprocal of −34 is −43.
To divide, multiply by the reciprocal instead: (−47) ÷ (−57) = (−47)×(−75) = 45.
The product and quotient of two numbers with the same sign is positive; with different signs it is negative.
Any number divided by 1 stays the same. Dividing by zero has no meaning.