Method

Multiplying Fractions

The product of two fractions is equal to the product of the numerators divided by the product of the denominators. The resulting fraction is then simplified to its lowest terms, if possible.

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

Here,

b

and

d

are not

0 .

When multiplying fractions, it makes no difference whether they are like or unlike fractions. Consider multiplying

\frac{5}{6}

\frac{3}{4} .

\frac{5}{6} \cdot \frac{3}{4}

The result of this multiplication can be found in three steps.

Multiply the Numerators

The numerator of the first fraction is

5

and the numerator of the second is

3 .

The product of the numerators is then

15 .

\frac{5}{6} \cdot \frac{3}{4}

MultFrac

Multiply fractions

\frac{5 \cdot 3}{6 \cdot 4}

Multiply

\frac{1 5}{6 \cdot 4}

Multiply the Denominators

The product of the denominators is

6 \cdot 4 = 24 .

\frac{1 5}{6 \cdot 4}

Multiply

\frac{1 5}{2 4}

Simplify if Possible

Note that

3

is the greatest common factor of

15

and

24 .

Divide both the numerator and the denominator by

3

to simplify the fraction.

\frac{1 5}{2 4}

ReduceFrac

$\frac{a}{b} = \frac{a / 3}{b / 3}$

\frac{1 5 / 3}{2 4 / 3}

SimpQuot

Simplify quotient

\frac{5}{8}

Therefore, the product of

\frac{5}{6}

and

\frac{3}{4}

simplified to its lowest terms is

\frac{5}{8} .

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