Fraction Multiplication
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.