Lesson video

It's our fourth lesson in the fractions topic.

Today we'll be multiplying and dividing with proper fractions.

Just a pencil and piece of paper for today's lesson.

Pause the video and get your things if you haven't done so already.

So here's our agenda.

We're multiplying and dividing with improper fractions today, starting with a knowledge quiz to test your knowledge from our previous lesson, then we'll be looking at multiplying improper fractions, then dividing an improper fraction by an integer before you go onto some independent learning and then a final quiz.

So let's start with our initial knowledge quiz, pause the video and take the quiz and click restart once you've finished.

Great job.

Now we're looking straight at multiplying improper fractions.

So we can approach this in the simple way that we know how to multiply fractions.

We multiply numerator by numerator.

So 50, sorry, five times three is 15, and then we multiply denominator by denominator; three times two is equal to six.

So 5/3 times 3/2 is equal to 15/6.

Then you can convert your answer to a mixed number.

So we would have 2 3/6 because there's two sixes in 15 with three remaining.

And then you can see that this 3/6 can be simplified so it's 2 1/2.

So it's really straightforward, with improper fractions the procedure is exactly the same as with proper fractions.

So with that in mind, pause of the video and complete the calculations.

So we're multiplying numerator by numerator, four multiplied by five is 20 and three multiplied by two is six, which converts to 3 2/6 which simplifies to 3 1/3.

For your second one, six times three is equal to 18.

Three times two is equal to six, which converts to three wholes because there are three lots of six in 18.

The final one, six, seven times six is 42, five times four is 20, and I'll convert this below.

So 42/20 is equal to 2 2/20 because there are two lots of 20 in 40 with two remaining, which simplifies to 2 1/10.

So now we need to think, what do we do if we're given to mixed numbers to multiply? Well, I'll start off by using my improper fraction method first.

So I'll convert these both to improper fractions and multiply.

1 3/4 is equivalent to 7/4 and 2 1/2 is equivalent to 5/2 that is equal to 35/8, which converts to 4 3/8.

Now I wonder if I'll get the same answer if I multiply the integers and then I multiply the fractions, let's check.

So if I do one times two, I get two.

Three times one is three.

Four times two is eight.

So you can see that these two answers are not the same, but why? Now what has happened when I've multiplied is that I haven't actually multiplied all of the parts.

What I needed to do was to multiply one by two and one by 1/2.

And I also needed to multiply two by one and two by 3/4.

So I can use the grid method to ensure that I multiply all of the parts.

So I start with one times two is two.

One times 1/2 is 1/2.

Two times 3/4 I would do it up here, two times 3/4.

Remember that I can express my integer as a fraction over one.

So that is equal to 6/4, which I can convert to 1 2/4, which is equal to 1 1/2.

So I'll put this in here 1 1/2, and then I multiply 3/4 by 1/2.

So I'm multiplying every part by each other.

Three times one is three, four times two is eight.

Then I know that I have to add all of these products to find my answer.

So I do this over here.

I'm adding two plus 1/2 plus 1 1/2 plus 3/8.

Now, you know that when you're adding fractions, we need them to all have the same denominator.

So now I have to convert them to have the same denominator.

And I know that the common denominator here is eight.

So I'm going to add two convert this into eight will be 4/8 plus 1 4/8, plus 3/8.

So now I can do my adding.

So I'll add the integers two and one is three, and I'll add the fractions.

Remember that the denominator is going to be eighths, four plus four is eight plus three is 11.

11/8 is an improper fraction.

So this isn't a mixed number yet, 11/8 is the same as 1 3/8.

So now we can add the three and one is equal to 4 3/8.

Now we have the same answer as when we converted them to improper fractions.

Now, I want you to think about how long this took me compared to how long it took me to convert them to improper fractions and then multiply.

We always want to go with the most efficient strategy.

And the most efficient is definitely to convert to improper fractions and then multiply and then convert back to a mixed number.

Just so you're aware that you cannot just multiply integer by integer and fraction by fraction.

That's why I showed you this method, but my recommended method is to convert mixed numbers to an improper fraction and then multiply.

So using that efficient strategy, pause the video and complete the calculations.

So we're using the efficient converting to improper fractions.

1 2/3 is 5/3 multiplied by 2 1/2 which is 5/2, which equals 25/6 which is equal to 4 1/6.

Convert it to improper fraction we have 13/3 multiplied by 9/4.

And here you may have had to do a column multiplication.

So that's 117/12.

And then you'd have to think about your knowledge of the twelves times tables.

To think about how many twelves go into 117, and that's nine with nine remaining.

And that can simplify to 9 3/4.

And then your third one, convert it to 13/5 times 11/4 and that's 143/20 which converts to 7 3/20.

Now let's look at dividing an improper fraction by an integer.

So here we have our question, 4/3 divided by two.

Think back to our previous lesson where we linked division to multiplication.

So 4/3 divided into two groups is the same as finding 1/2 of 4/3, which is the same as doing 1/2 times 4/3.

And we know that 1/2 times 4/3 is 4/6, which can be simplified to 2/3.

Now you can use that knowledge from yesterday.

It's exactly the same when it's an improper fraction and apply it to these questions.

Pause the video now.

So you will have represented this as finding 1/3 of 5/3, which is 5/4 times 1/3, which is equal to 5/12.

Here divided by two is the same as finding 1/2 which is equal to 5/6.

And here it's finding 1/2 which is equal to 6/20, which can be divided by two to give us 3/10.

Now it's time for some independent learning.

So pause the video and complete your task.

Click restart once you're finished and we'll go through the answers together.

So your first question, you were asked to complete the calculation, giving your answers either as a proper fraction in its simplest form or as a mixed number.

So here we have 15/8, which converts to 1 7/8.

Then we have 28/18, which is equal to 1 10/18.

We wouldn't leave it as that though, because it's not in its simplest form, 1 5/9.

Then our third one, we have 72/35, which is equivalent to 2 2/35.

Then we move on to mix numbers, we know to be efficient, we convert them to improper fractions then multiply.

So we have 7/4 multiplied by 5/2, which equals 35/8, which converts to 4 3/8.

Then this one converts to 19/6 multiplied by 4/3, which is equal to 76/18, and some long division was required here.

4 4/18 which is equal to 4 2/9.

And our last one, numbers are getting very big here.

14/5 multiplied by 22/7 is equal to 308/35, which converts to 8 4/5.

Next one was some division calculations, you were asked to give you answer as proper fractions in their simplest form.

So we're thinking if we're dividing by two, we are finding 1/2.

1/2 of 5/4 is equal to 5/8.

Dividing by five we're finding 1/5.

1/5 of 7/6 is equal to 7/30.

Dividing by three we're finding 1/3.

1/3 of 8/5 is equal to 8/15.

Then we're converting to an improper fraction and then simply multiplying again.

So this is 7/4 and if we are dividing by two we're finding 1/2, which is equal to 7/8.

This one is 19/6 and we're finding 1/3.

So that's 19/18, which is 1 1/18.

And then our final one is 14/5, dividing by four we're finding 1/4, which equals 14/20, which simplifies to 7/10.

Okay, for the next one, you had to find the area of each shape.

So I know that to find area we need to multiply the length by the widths.

This first shape is a square.

So I know that this amount will also be 2 4/5 metres.

So I need to multiply that with itself.

I'm going to put them into improper fractions to begin with.

So that will give us 14/5 multiplied by 14/5.

A good opportunity for you to practise your multiplication here.

14 times 14 will get us 196 and we multiply the two denominators 25th, okay? Now I'm just going to put that back into a mixed number, which will leave me with 7 21/25.

Now, remember we are working out the area, we need to finish off by putting metres squared.

Okay, let's look at the second one.

We've got 1 3/4 and we're going to multiply that by the length here, which is 3 1/6 of a metre.

So again, I'm going to convert these into my improper fractions, which will give me 7/4 multiplied by 19/6 which will get me 133 over 24.

Let's put that back into a mixed number now, five and 13, over 24.

And what do we need to do to finish off our answer? Put our unit of measure, metres squared.

Finally, question four.

Aleeyah has a pet cat called Marmalade.

Each day Marmalade eats 1 1/4 cans of cat food.

How many cans of cat food should Aleeyah buy to last a week? So we need to think a week is seven days.

So we need to multiply.

We need seven lots of 1 1/4 convert it to an imperfection so it's 5/4 time seven, and we can convert seven to a fraction over one, five times seven is equal to 35, four times one is equal to four so it's 35/5.

So that means that she needs, if we convert it to a mixed number, 8 3/4 tins, but you can't buy 3/4 of a tin.

So she would have had to have bought nine tins.

You needed to round that up.

Amazing work today.

Let's move on to the final quiz, pause the video and complete the quiz and then click restart once you're finished.

Well done, you've worked really hard today.

In our next lesson, we will be solving fraction problems involving all four operations.

I'll see you then.