Fraction Multiplication

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Rules for fraction multiplication

To get the product of two fractions

• We multiply the numerators.
• We multiply the denominators.
• If required, we cross cancel or simplify before multiplying.
• In such a case, we get a fraction in lowest terms.

Example

Multiply $\frac{4}{5}$ $\frac{7}{9}$

Solution

Step 1:

Multiply the numerators and denominators of both fractions as follows.

$\frac{4}{5}$ $\frac{7}{9}$ = $\frac{(4 7)}{(5 9)}$ = $\frac{28}{45}$

Step 2:

So, $\frac{4}{5}$ $\frac{7}{9}$ = $\frac{28}{45}$

Problem 1

Multiply $\frac{4}{5}$ $\frac{10}{16}$ and write the answer as a fraction in simplest form

Solution

Step 1:

We multiply the numerators and denominators of both fractions as follows.

$\frac{4}{5}$ $\frac{10}{16}$ = $\frac{(4 10)}{(5 16)}$ = $\frac{40}{80}$

Step 2:

Dividing numerator and denominator with the gcf of 40 and 80 which is 40.

So, $\frac{40÷40}{80÷40}$ = $\frac{1}{2}$

Step 3:

$\frac{4}{5}$ $\frac{10}{16}$ = $\frac{1}{2}$

This is the answer as a fraction in simplest form.

Problem 2

Multiply $\frac{3}{4}$ $\frac{12}{15}$ and write the answer as a fraction in simplest form

Solution

Step 1:

We cross cancel 3 and 15 diagonally; we also cross cancel 4 and 12 diagonally.

$\frac{3}{4}$ $\frac{12}{15}$ = $\frac{1}{1}$ $\frac{3}{5}$

Step 2:

We multiply the numerators. Then we multiply the denominators.

$\frac{1}{1}$ $\frac{3}{5}$ = $\frac{(1 3)}{(1 5)}$ = $\frac{3}{5}$

Step 3:

So $\frac{3}{4}$ $\frac{12}{15}$= $\frac{3}{5}$

This is already in simplest form.