Lesson video

Today's lesson is how to multiply a mixed number fraction.

We're going to start off with revision.

We're then going to look at different methods to multiply.

We'll then look at multiplying in context, and finally, we'll take our quiz.

I've mentioned already you'll need a pencil and a piece of paper.

Our star words for today are fraction, denominator, numerator, and vinculum, We'll be looking at proper fractions, improper fractions, and mixed number fractions, and we'll be using the word multiply.

In order to access this lesson, you'll need to understand that a fraction is part of a whole.

A denominator is the number of parts the whole is split into.

And the numerator is the number of parts of the whole.

The vinculum is the line between the numerator and the denominator.

A proper faction is where the numerator is less than the denominator.

And an improper fraction is where the numerator is greater than the denominator.

A mixed number fraction is a combination of a whole and a fraction.

Equivalent fraction represent the same number, and to simplify a fraction, we need to reduce the numerator and denominator at the same time.

We should know that to multiply fraction, you multiply the numerator by the whole number.

So our new learning for today is multiplying fractions.

Place the fraction in the correct place to make the calculation correct.

Where does the extra fraction go? Pause the video, and when you're ready, press play to continue.

I can see that one fifth times two is two fifths.

A sixth times three is three sixths.

An eighth times six is six eighths.

And a seventh times seven is seven sevenths.

It's worth noting that six eights is equivalent to three quarters and also seven sevenths is the same as one, whole one.

A bottle of water holds one and a quarter litres of water.

How much water would three bottles hold? I can represent this in a variety of ways.

I can represent this with repeated addition, which is here.

I can represent the same question on a number line.

I can say I've got one and one quarter.

I'm going to add one and one quarter, and we'll just need to count this.

So I've got 10, add to that one and one quarter.

So I've done three lots of one and one quarter.

I can also write down the calculation, I can say, one whole one times three is three.

I can say one quarter times three is three quarters.

Three, add three quarters is three and three quarters.

I can go back to my number line and see if that matches.

I've got three here, and I've got one, two, three quarters.

Yes, it does.

I could take it one step further.

And I could say that one and one quarter is the same as one whole one and one quarter.

I could say it's equivalent to five quarters.

I could say five quarters times three is 15 quarters.

I'll then need to convert it back to a mixed number fraction.

15 quarters is the same as, well, four quarters is one whole one, eight quarters is two whole ones, 12 quarters is three whole ones, and I have 13, 14 and 15; three quarters remaining.

Now have a look at the question on the screen.

Homework takes one and three quarters of an hour each day.

Homework is given the three days per week.

How long does the homework take each week.

Try to represent this as repeated addition, as a multiplication calculation, and if you can, draw it on a number line.

Pause the video, and when you're ready, press play to continue.

You can see here I have represented it as repeated addition.

So I've got one and one and one is three.

Three quarters and three quarters is six quarters.

And three more quarters is nine quarters.

However, I know that I can't write a mixed number fraction and an improper fraction together.

So I need to convert this nine quarters.

Well, four quarters is one whole one, eight quarters is two whole ones, and there's one quarter leftover.

So I've got my three whole ones, my two whole ones, so I've got five whole ones, and one quarter leftover.

I could represent it as a multiplication and I can split my one whole one and my three quarters.

I can multiply them.

I'll just three whole ones and nine quarters.

And it's the same method that I've before.

I know that three and nine quarters is the same as five and one quarter.

I could convert these to mixed number fractions.

So I know that one and three quarters is the same as seven quarters.

Seven quarters times three is 21 quarters.

I need to convert that back to a mixed number fraction.

So four quarters is one, eight quarters is two, 12 quarters is three, 16 quarters is four, 20 quarters is five, and I've got my one quarter left.

So 21 quarters is the same as five and one quarter.

Now it's time to develop our learning.

Have a look at the questions on your screen, have a go at them.

You need to solve the problem in at least two different ways.

Pause the video, and when you're ready, press play to continue.

Your answers are on the screen.

I have that one and one fifth multiplied by four is four and four fifths.

Question two, I have that one and two fifths multiplied by four gives me, on the number line, it gives me five and three fifths.

If I do it as a multiplication, the first step gives me four and eight fifths.

Eight fifths is an improper fraction, so I'll convert it.

And that's one and three fifths.

Add my four, gives me five and three fifths.

And so we'll carry on developing this learning, and we're looking at how to find the area of a shape.

I know that if I multiply the length by the width, it gives me the total area.

So have a go at this one, can you multiply the five by one and a half centimetres? It might help a little bit if I break it down so you can understand the different steps.

So my width is five centimetres, and my length, I can break down into one centimetre and one half of a centimetre.

I can look at that, and I can see that one times five is five, and one half times five is five halves.

Now, five halves is the same as two and a half.

So two twos is one whole one, four twos is just two whole ones.

And that leaves me one half left.

So I've got five, add on my two and a half, gives me seven and a half centimetres.

And because we're measuring in units squared, we say centimetres squared.

Now it's time for your independent task.

Look at the question on the screen.

Pause the video, and when you're ready, press play to continue.

I know that four multiplied by two and one fifth is eight and four fifths.

And I know that six multiplied by two and a quarter, I can do my six multiplied by two to get 12, and then I do six multiply by a quarter to get six quarters.

Six quarters is the same as one and two quarters.

So add that on to 12, gives me 13 and two quarters.

I can simplify that, and say that's the same as 13 and one half.

Congratulations on completing your task.

If you'd like to, please ask your parent or carer to share you work on Twitter, tagging @OakNational, and also hashtag #LearnWithOak.

Now, before we go, please complete the quiz.

So that brings us to the end of today's lesson on multiplying mixed number fractions.

A really big well done for all the fantastic learning that you've achieved.

Now, before you finish, perhaps quickly review your notes and try to identify the most important part of your learning from today.

Well, all that's left for me to say is thank you, take care, and enjoy the rest of your day.