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.
