Lesson video

Hello, my name is Miss Parnham.

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

We'll start with some prior learning.

8/9 divided by four can be rewritten as 8/9 multiplied by 1/4, and eight multiplied by one over nine multiplied by four is 8/36.

And this simplifies to 2/9.

So now that we know 8/9 divided by four is 2/9, we can rearrange an 8/9 divided by 2/9 is four.

Notice that the denominator is the same in both fractions, and the answer is the result of the first numerator divided by the second numerator, 8/2.

So here we have a general rule; a over b divided by c over b is a over c.

And we're going to use this general rule for the rest of our examples.

We have 4/9 divided by 7/12.

In order to do this division, let's rewrite these fractions with the same denominator.

And the lowest common multiple of nine and 12 is 36.

So this is 16/36 divided by 21/36.

So the answer is 16/21 and that can't be simplified further.

Let's look at another example.

We have eighths and 12ths.

So these can be rewritten as 24ths.

So we have 21/24 divided by 10/24.

This gives us 21/10.

This is an improper fraction, and we can rewrite it as two and 1/10.

And finally, let's try an example where one is negative.

We have negative 4/9 divided by 2/5.

The lowest common multiple of nine and five is 45.

So let's rewrite these fractions as negative 20 over 45 divided by 18 over 45.

And negative 20/18 is negative one 2/18, which simplifies to negative one and 1/9.

Here are some questions for you to try.

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

Here are the answers.

You'll see from your solutions that dividing a fraction by a fraction can give us proper fractions, mixed numbers or even integer solutions.

So for example in part e, we have negative 2/3 divided by 1/12.

Well, that's negative 8/12 divided by 1/12, hence negative eight.

Here's another question for you to try.

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

Here are the answers.

You may prefer Tommy's method of multiplying by reciprocals or perhaps not.

As long as you understand the process, use the method of your choice.

Now we'll consider some examples involving mixed numbers.

Three and 5/9 divided by 7/12 can be rewritten by replacing the mixed number with an improper fraction, 32/9 divided by 7/12.

Now we need to make sure that the denominator is the same before we perform the division.

So the lowest common multiple of nine and 12 is 36.

This is 128/36 divided by 21/36.

And 128 over 21 is improper, but we'll simplify to six and 2/21.

The next example has two mixed numbers within the division.

Let's rewrite them both as improper fractions first.

23/8 divided by 23/6.

The lowest common multiple of eight and six is 24.

So equivalent fractions gives us 69/24 divided by 92/24, which will simplify to 69 over 92.

We know that these have a common factor of 23 because we multiply 23 by three and four in order to get them.

So this simplifies to 3/4.

In this last example, one of the numbers is negative.

It is still exactly the same process.

Let's convert five and 4/7 and negative three and 2/5 into improper fractions first.

So we have 39/7 divided by negative 17/5.

The lowest common multiple of seven and five is 35.

So we must rewrite this as 195/35 divided by negative 119/35.

This gives us 195 over negative 119.

This simplifies to negative one and 76/119.

Here are some questions for you to try.

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

Here are the answers.

If we can keep the value of the numerators and denominators as low as possible, it reduces chances of mistakes and this means less simplification is needed for the final step.

So in part f, 13/6 divided by negative 29/8, if we rewrite that using the lowest common denominator, that would be 52/24 divided by negative 87/24 and our answer is just 52 over negative 87, or it can be written as negative 52 over 87.

There is some further questions for you to try.

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

Here are the answers.

So in question five, 15 inches as a fraction of a yard because the yard is 36 inches is 15/36, or for simplicity, 5/12.

So that's why we've divided by 5/12.

So in effect, we've got 129/24 divided by 10/24 which is 12 and 9/10.

Now, don't be tempted to say that he can wrap ribbon in about 13 boxes because, yes, that does round to 13.

But you can only actually complete 12 of them.

That's all for this lesson.

Thank you for watching.