Multiplying Fractions

Multiply the numerators: $3\times 2=6$. Multiply the denominators: $5\times 7=35$.

So $\frac{3}{5}\times \frac{2}{7}=\frac{6}{35}$. The numbers 6 and 35 share no common factor, so this is already in its simplest form.

Notice the answer is smaller than both fractions: multiplying by a fraction less than 1 always makes a value smaller.

"Of" means multiply, so work out $\frac{7}{5}\times 15$.

Find one fifth first: $15÷5=3$. Then multiply by the numerator: $3\times 7=21$.

Using fractions throughout: write 15 as $\frac{15}{1}$, cross-cancel the 5 with the 15 to leave 1 and 3, then $7\times 3=21$ over $1\times 1=1$, giving 21. Since $\frac{7}{5}$ is bigger than 1, the answer is larger than 15.

Simplify each fraction first: $\frac{15}{35}=\frac{3}{7}$ (divide top and bottom by 5) and $\frac{5}{10}=\frac{1}{2}$ (divide top and bottom by 5).

Multiply the numerators: $3\times 1=3$. Multiply the denominators: $7\times 2=14$. So the answer is $\frac{3}{14}$.

If you multiply without simplifying first you get $\frac{75}{350}$, which cancels down to the same answer, $\frac{3}{14}$.

Simplify each fraction first: 16 and 24 both divide by 8, giving $\frac{2}{3}$; 18 and 27 both divide by 9, giving $\frac{2}{3}$.

Now multiply: $2\times 2=4$ for the numerator and $3\times 3=9$ for the denominator, giving $\frac{4}{9}$.

Multiplying without simplifying first gives $\frac{288}{648}$, which cancels down to the same answer, $\frac{4}{9}$.

Cross-cancel diagonally. The 25 and the 50 both divide by 25, becoming 1 and 2. The 40 and the 32 both divide by 8, becoming 5 and 4.

The calculation is now $\frac{1}{5}\times \frac{4}{2}$. Multiply: $1\times 4=4$ and $5\times 2=10$, giving $\frac{4}{10}$, which simplifies to $\frac{2}{5}$.

Multiplying without cancelling gives $\frac{800}{2000}$, which cancels down to the same answer, $\frac{2}{5}$.

First change the mixed number into an improper fraction: $2\frac{1}{3}=\frac{2\times 3+1}{3}=\frac{7}{3}$.

Now cross-cancel: the 9 and the 3 both divide by 3, becoming 3 and 1. The calculation is $\frac{7}{1}\times \frac{3}{4}$.

Multiply: $7\times 3=21$ and $1\times 4=4$, giving $\frac{21}{4}$ (which is $5\frac{1}{4}$). Without cancelling you get $\frac{63}{12}$, the same value.