To multiply two fractions together, simply multiply the numerators together, and then multiply the denominators together.

Example: Evaluate \dfrac{3}{4}\times \dfrac{2}{11}. Write your answer in its simplest form.

The result of multiplying two fractions together will be a fraction. The numerator will be the product of the two numerators, and the denominators will be the product of the two denominators.

\dfrac{3}{4}\times \dfrac{2}{11}=\dfrac{3\times 2}{4\times 11}=\dfrac{6}{44}

Cancelling out a factor of two from top and bottom, we get the answer (in its simplest form) to be

\dfrac{6}{44}=\dfrac{3}{22}

Example: Evaluate 4\times \dfrac{3}{7}

To multiply a whole number by a fraction, remember that any number divided by 1 is just itself. So, we can write

4=\dfrac{4}{1}

Therefore, the multiplication becomes

\dfrac{4}{1}\times \dfrac{3}{7}=\dfrac{4\times 3}{1\times 7}=\dfrac{12}{7}

You may see that what happens when you multiply a whole number by a fraction, is that the number is multiplied only by the numerator. If you feel confident, you can just go right ahead and multiply the number by the numerator and avoid the intermediate steps.

Example: Evaluate 3\frac{1}{4}\times\dfrac{2}{5}.

To multiply a mixed number by a fraction, first convert the mixed number to an improper fraction.

3\frac{1}{4}=\dfrac{(3\times4)+1}{4}=\dfrac{13}{4}

Now we can do the multiplication as usual.

\begin{aligned}3\frac{1}{4}\times\dfrac{2}{5}&=\dfrac{13}{4}\times\dfrac{2}{5} \\ &=\dfrac{13 \times 2}{4\times 5}=\dfrac{26}{20}\end{aligned}

This fraction could be simplified, but as the question doesn’t ask us to, there’s no need.

Note: if negative numbers are involved, normal rules of multiplying apply:

1. If you multiply one positive fraction with one negative fraction, the answer should be negative.

2. If you multiply two negative fractions together, the answer should be positive.

### Example Questions

1) Evaluate \dfrac{3}{8}\times\dfrac{3}{10}

We have to multiply across the top and across the bottom of the fraction,

\dfrac{3}{8}\times\dfrac{3}{10}=\dfrac{3\times 3}{8\times 10}=\dfrac{9}{80}

2) Evaluate 9\times \dfrac{5}{12}

Give your answer in its simplest form.

Writing 9 as \dfrac{9}{1}, we get

\begin{aligned}9\times\dfrac{5}{12}&=\dfrac{9}{1}\times\dfrac{5}{12} \\ &=\dfrac{9 \times 5}{1\times 12}=\dfrac{45}{12}\end{aligned}

Now, simplifying by cancelling a factor of 3 from top and bottom, we find

\dfrac{45}{12}=\dfrac{15}{4}

3) Evaluate -\dfrac{8}{9}\times \dfrac{5}{4}

Give your answer in its simplest form.

Multiplying the numerators and denominators, as usual, we get,

-\dfrac{8}{9}\times \dfrac{5}{4}=-\dfrac{8\times 5}{9\times 4}=-\dfrac{40}{36}

Simplifying by canceling a factor of 4, we find,

-\dfrac{40}{36}=-\dfrac{10}{9}

4) Evaluate \dfrac{10}{7}\times \dfrac{4}{5}

Give your answer in its simplest form.

Multiplying the numerators and denominators, as usual, we get,

\dfrac{10}{7}\times \dfrac{4}{5}=\dfrac{10\times 4}{7\times 5}=\dfrac{40}{35}

Simplifying by canceling a factor of 5, we find,

\dfrac{40}{35}=\dfrac{8}{7}

5) Evaluate \dfrac{5}{2}\times \dfrac{5}{3}

Give your answer as a mixed fraction.

Multiplying the numerators and denominators, as usual, we get,

\dfrac{5}{2}\times \dfrac{5}{3}=\dfrac{5\times 5}{2\times 3}=\dfrac{25}{6}

Writing this a mixed number fraction,

\dfrac{25}{6}=4\dfrac{1}{6}

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