Method

Dividing Fractions

Dividing a fraction by another fraction is the same as multiplying the first fraction by the reciprocal of the second fraction.

$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \cdot \frac{d}{c}$

Here,

b,

c,

and

d

are not

0 .

The division of two fractions can then be considered as a multiplication of two fractions. Consider the following division of two fractions.

\frac{1 2}{2 5} \div \frac{3}{5}

The quotient can be found in three steps.

Multiply by the Reciprocal of the Divisor

The division of fractions begins by keeping the first fraction as is. Then change the division sign with the multiplication sign and write the reciprocal of the second fraction. Note that the reciprocal of a fraction is found by switching the numerator and denominator of the fraction.

Multiply the Fractions

The result is now a multiplication of two fractions. The product of the fractions is equal to the product of the numerators divided by the product of the denominators.

\frac{1 2}{2 5} \cdot \frac{5}{3}

MultFrac

Multiply fractions

\frac{1 2 \cdot 5}{2 5 \cdot 3}

Multiply

\frac{6 0}{7 5}

Simplfy if Possible

The resulting fraction can be simplified because

60

and

75

have a common factor.

6075 = 2^{2} \cdot 3 \cdot 5 = 3 \cdot 5^{2}

The greatest common factor of the numbers is

3 \cdot 5 = 15 .

Simplify the fraction by

15 .

\frac{6 0}{7 5}

ReduceFrac

$\frac{a}{b} = \frac{a / 1 5}{b / 1 5}$

\frac{6 0 / 1 5}{7 5 / 1 5}

SimpQuot

Simplify quotient

\frac{4}{5}

The divison expression is equal to

\frac{4}{5} .

The same steps above are also used when dividing a fraction by a whole number. This is because every whole number can be thought of as a fraction with a denominator of

1 .

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