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 Dependent Variable

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# Multiply by the Reciprocal

Two numbers are reciprocals if their product is 1. Since , this means that 9 and are reciprocals.

• The numbers 4 and are reciprocals, since .

• The fractions and are reciprocals, since

Key Idea

The reciprocal of any fraction can be obtained by inverting the fraction. In other words, the denominator of the original fraction becomes the numerator and the numerator of the original fraction becomes the denominator. In symbols, the reciprocal of is .

is the reciprocal of .

is the reciprocal of .

is the reciprocal of .

Since 7 Ã· 9 and are both equal to , then . Also, we know that 9 and are reciprocals. So, dividing by a number and multiplying by the reciprocal of that number give the same result.

We can easily find that . Since 2 Ã— 4 is also 8, this means that . So, dividing by a fraction and multiplying by its reciprocal give the same result.

Key Idea

Dividing a number by a fraction is equivalent to multiplying the number by the reciprocal of the fraction.