# Lesson video

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Hello, my name is Miss Parnham.

In this lesson, we're going to learn how to multiply a fraction by a fraction.

We're going to multiply 2/3 by 4/5.

Let's draw a diagram to help.

So one side of this grid is split into thirds.

and the other into fifths.

So we're going to draw a rectangle that has got dimensions of 2/3 and 4/5.

So the area of that rectangle is 8/15.

Notice that we have multiplied the numerators together to get the numerator in our answer.

And we have multiplied the denominators together to get the denominator in our answer.

So if we need to multiply 4/7 by 3/8, we will simply do four multiply by three over seven multiplied by eight, which gives us 1256.

Now this can be simplified to 3/14.

Let's look at a negative fraction multiplied by a positive fraction.

We can think of this as negative two multiplied by nine, over three multiplied by 10.

Which is negative 18/30 and this will simplify to negative 3/5.

Let's think about negative 6/11 squared.

In other words, negative 6/11 multiplied by negative 6/11.

This gives us negative six multiplied by negative six, over 11 multiplied by 11, which is 36 over 121.

Here's some questions for you to try.

Pause the video to complete the task and restart the video when you're finished.

Some people prefer to cancel common factors before they've multiplied the numerators together and the denominators together.

Take part d for example, we have five multiplied by three over 12 multiplied by eight.

Now, if we cancel a common factor of three from both the numerator and denominator, that gives us five over four multiplied by eight or five over 32.

And no more simplifying is needed.

Here's some further questions for you to try.

Pause the video to complete the task and restart the video when you're finished.

If you've got a good knowledge of the first few square numbers and cube numbers, then these questions will not have taken you along.

So in question three, part a, we have the square root of four which is either two or negative two and the square root of 81, which is either nine or negative nine.

That's actually gives us four possible combinations of fraction, but only two of them at different.

Either 2/9, or negative 2/9.

In part b, we need to do the cube root of 27, which is three.

There's just one sort of solution and the cube root of 64 is four.

Again, one solution.

So there's just one solution of 3/4.

Now we're going to multiply a mixed number by a fraction.

We're going to go to convert the mixed number into an improper fraction.

So 3 2/3 becomes 11/3.

And when we multiply by 4/5, 11 multiply by four, it gives us 44 for our numerator.

And three multiplied by five gives us 15 as our denominator.

This can be converted to a mixed number, which is 2 14/15.

Let's look at an example where one value is negative.

Again, the mixed number of 5 4/9 can be rewritten as an improper fraction.

So this is 49/9 multiplied by negative 3/8.

49 multiplied by negative three, over nine multiplied by eight.

This gives us negative 147 over 72.

Now we can cancel a common factor of three, which is negative 49 over 24.

This is improper, so we can rewrite it as a mixed number of negative 2 1/24.

Let's look at an example where both fractions are negative.

And here we have mixed numbers.

So let's rewrite them both as improper fractions.

So we have negative 32/5 multiplied by negative 23/6.

Negative 32 multiplied by negative 23, over five multiplied by six.

We can cancel a common factor of two just to make things a little bit simpler.

And then negative 16 multiplied by a negative 23 is 368 and five threes are 15.

This simplifies to 24 8/15.

Here's some questions for you to try.

Pause the video to complete the task and restart the video when you're finished.

In part b, we have negative 25 over nine, multiplied by negative 27 over five.

If we cancel common factors, then we're cancelling nine and five from both the numerators and denominators.

And this gives us negative five multiplied by negative three, all over one, so that we have 15.

Here's another question for you to try.

Pause the video to complete the task and restart the video when you're finished.