Lesson video

Hello, my name's Miss Parnham.

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

Here we have repeated edition of the same unit fraction.

One seventh add one seventh, add one seventh, add one seventh.

And we can rewrite this as one seventh multiplied by four, or because multiplication is commutative, four multiplied by one seventh which equals four sevenths.

Let's look at a non-unit fraction.

We have three eighths, add three eighths, add three eights.

And this can be rewritten as three eights multiplied by three or three multiplied by three eighths.

And we can see from the diagram, this is nine eighths.

Notice that the numerator is multiplied by the integer to give the numerator in the answer and the denominator remains constant.

We can rewrite nine eighths as a mixed number which is one and one eighths.

Let's look at an example without a diagram.

So negative two fifths multiplied by four.

Using what we've learnt already, we could rewrite it as negative two multiplied by four over five, or using commutativity write it as four multiplied by negative two over five, and then rewrite that as four multiplied by negative two over five.

Whichever way we write it we will still get negative eight over five, which as a mixed number is negative one and three fifths.

Now we have six multiplied by two thirds.

We can rewrite this as six multiplied by two over three which is 12 thirds.

But this will simplify to an integer of four.

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.

Most of these questions needed you to not only multiply the fraction by an integer but then also simplify the answer, including writing that in a mixed number form.

The last two parts on this question needed you to not only convert improper fractions to mixed numbers, but then the fraction part of those mixed numbers could be simplified.

So instead of five and five fifteenths you should have got five and one third for part g, and then part h, if you got four and 12 eighteenths that simplifies to four and two thirds.

Here are some more questions for you to try.

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

Here are the answers.

Question two needed some skills from the unit on adding fractions.

So when you add 10 and a half and four and two thirds together, you are adding 10 and three sixths to four and four sixths.

This would give you 15 and one sixth.

So that's why you need to buy 16 tins because you can't buy part of a tin.

Here we have repeated edition of a mixed number.

We can think of this as two multiplied by three, add a quarter multiplied by three.

Alternatively, we can think of two and a quarter as an improper fraction of nine quarters, so three lots of nine quarters.

And that would give us three multiplied by nine over four which is 27 quarters, which simplifies to a mixed number of six and three quarters.

And going back to that original way that we rewrote it, you can see that two multiplied by three would give us six, and a quarter multiplied by three would give us three quarters.

Now let's look at a further example.

We can rewrite this as three multiplied by four and five eighths multiplied by four, or think of three and five eighths as 29 eighths and four lots of 29 eighths would be four multiplied by 29 over eight which is 116 over eight.

This simplifies to a mixed number of 14 and four eighths.

We can go simpler because that is 14 and a half.

Going back to the original way that we wrote it, you would end up with 12 and 20 eighths.

So you would still have to simplify the 20 eighths down to two and half, and then put that with the 12 to make 14 and a half.

So often using the method of making the mixed number into an improper fraction before multiplying by the integer can be the most efficient.

Here we have seven multiplied by negative one and four ninths.

Let's rewrite that as seven multiplied by negative 13 ninths.

This is seven multiplied by negative 13 over nine, given as negative 91 over nine.

We can see that that's negative 10 and one ninth.

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.

Where we have a negative mixed number, that means converting to an improper fraction.

It's probably easiest to think about converting a positive value first.

So in part g for example, we have five multiplied by negative three and three tenths.

Now three and three tenths is equivalent to 33 tenths.

So negative three and three tenths is equivalent to negative 33 tenths.

So when we multiply that by five, we get negative 165 tenths or negative 16 and five tenths, and that of course simplifies to negative 16 and a half.

Here are 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.

In question six, the differences between these three numbers and 10 are two fifths, one seventh and five sixths respectively.

So we need to find out which one of those is the smallest because then that's the closest number to 10.

Now we know that five sixths is greater than a half so we can discount that because the other two are less than a half.

Now one fifth is greater than one seventh, so two fifths is definitely greater than one seventh.

So that is how we know that the one that is nearest 10 is nine and six sevenths.

That's all for this lesson, thank you for watching.