Lesson video

Hi, welcome to today's lesson on adding fractions with different denominators.

All you'll need today is a pencil and a piece of paper.

In today's lesson.

Then we'll add fractions, look at fraction sequences, move onto an independent task to practise what you've learnt, and then a quiz to test what you have learnt.

Now let's have a look at our first question.

We're going to represent addition of fractions.

Zaara has a packet of sweets.

3/8 of the sweets are purple.

A quarter of the sweets are blue.

What fraction of the whole packet are purple or blue sweets? Now we have an issue here, and that are two fractions have different denominators.

So the units are different.

We need the denominators to be the same in order to use them together.

So first, let's represent this question pictorially.

So, as I said, the different fractions have different units, which means the number of parts are different, but let's look at 3/8.

So for 3/8, it's been divided into eight equal parts, and three of them have been shaded.

So this part here represents 3/8 of the whole.

It's trickier for 1/4, because that does not relate to eighths, but we can use our knowledge of equivalence, and we know that 1/4 is equivalent to 2/8.

So rather than writing 1/4 here, I could write 2/8.

Looking at them with the same units makes it easier to work with them.

So what I've done here is I've done exactly that.

I've changed 1/4 into an equivalent fraction, so that both of the fractions have the common denominator eight.

Now I'm being asked to find what fraction of the whole packet are blue or purple sweets.

Let's think about what equation would we use to represent finding the total fraction of purple and blue sweets.

We're looking at 3/8 of the pack are purple, and 2/8 are blue.

So our equation is 3/8 plus 2/8, which is equal to 5/8.

So 5/8 of the packet are either purple or blue sweets.

One, two, three, four, five.

We can also see that this fraction of the packet are not purple or blue, and that represents 3/8.

3/8 of the packet are neither purple or blue.

Let's have a look at another one together.

Simone has a packet of sweets.

Half of the sweets are pink.

2/5 of the sweets are green.

And we're being asked what fraction of the whole packet are pink or green.

Again, the whole has been divided into different number of parts.

Here it's two parts, and here it's five parts.

So the first thing we need to think about is finding a common multiple of the two denominators.

So I've got two and five, and I'm looking for a common multiple.

You can probably look at them and see a common multiple.

But if you're not sure, you write your times tables.

Two, four, six, eight, 10, and then the five time table, five, 10.

So, 10 is my lowest common multiple.

So I know that I can convert them both to fractions with the denominator of 10, and that's step two.

To convert them both to fractions with the denominator of 10.

So 1/2 is equivalent to how many 10ths? I know that I multiply two by five to get to 10, and one by five gives me five.

So 1/2 is equivalent to 5/10.

2/5, I'll do here, is equivalent to how many 10ths? Five multiplied by two is 10, and two multiplied by two is four.

So I'm now dealing with 5/10 and 4/10.

The third step will be to represent this pictorially, which I'll do on the next slide.

So as we figured out from the last slide, a half is equivalent to 5/10, 2/5 is equivalent to 4/10.

Deal with these fractions together because they have the same units, because the denominators are the same.

So, using these equivalent fractions, pictorially, we can split our packet of sweets into 10 equal parts.

So now I have a pictorial representation of my packet, splitting to 10 equal parts.

Each part represents 1/10.

Now we know that half of the pack is pink, and that's equivalent to 5/10.

So we shade five out of the 10 parts pink.

We know that 2/5 of the pack is green, and that's equivalent to 4/10, so we shade four out of the 10 parts green.

So now we can see that 5/10 are pink, 9/10 are green.

We know that we're doing 5/10 plus 4/10, and that is equivalent to 9/10.

9/10 of the pack are either pink or green, and this bit left over here, 1/10, is neither pink nor green.

So it's your turn.

Pause the video while you work through the stages to add the fractions.

Liman has a packet of sweets, 3/5 of the sweets are orange, a quarter of the sweets are purple.

What fraction of the whole packet are orange or purple sweets? So the common multiple of 3/5 and 1/4 is 20.

So 3/5 is equal to how many 20ths? Five multiplied by four is 20.

Three multiplied by four is 12.

So 3/5 is equivalent to 12/20.

1/4 is equivalent to how many 20ths? Four multiplied by five, same to the numerator, 3/5.

Sorry, 1/4 is equivalent to 15/20.

So now we have a common multiple denominator of 20.

We can split our pack into 20 equal parts.

12 out of those 20 parts are orange sweets, and five out of those 20 parts are purple sweets.

So we're looking now at 12/20 plus 5/20 is equal to 7/20s.

Sorry, 17/20.

17/20 of the pack are purple or orange.

Now we're looking at fraction sequence.

So now I'm looking at fraction sequence.

I need to work out the two next fractions in the sequence.

First of all, I need to work out what is the term to term rule.

That means what happens between one term to the next.

What was added to 3/8 to get to 3/4? First, we need to have the same units for these fractions.

The denominators must be the same.

I can see that the common denominator is eight, so 3/4 can be converted into an equivalent fraction with the denominator of eight, and that will be 6/8.

So now I can see to get from 3/8 to 6/8, 3/8 have been added.

So 3/8 plus 3/8 is equal to 6/8.

That means that the term to term rule is plus 3/8.

Plus 3/8.

So now I'm going to work out my next fraction.

I'm adding 3/8 to 6/8.

6/8 plus 3/8 is equal to 9/8.

And we can just have a look at this pictorially.

So we could see from the first one 3/8 to the second one 6/8, we added another 3/8.

Now we've gone onto 9/8, and then we're going to do one more.

In our sequence, we're going to add another 3/8.

So this time we're doing 9/8 plus 3/8 is equal to 12/8.

Now we can convert these improper fractions into mixed numbers.

So 9/8 is equivalent to 1 1/8.

And 12/8 is equivalent to 1 4/8.

So now it's 1 1/2.

Now it's your turn.

Pause the videos and find out what is the term to term rule, and then find the next two fractions in the sequence.

So your first step was to make sure that these had the same denominator.

You can see that the common denominator is six.

We only needed to change the second fraction, and that becomes 4/6.

So 1/6 plus something six is equal to 4/6.

We can see that we were adding 3/6.

So the term to term rule is to add 3/6 each time.

4/6 plus 3/6 is equal to 7/6.

And you may have convert that into a mixed number of 1 1/6.

It's always good practise doing that.

And then the final term, we're adding another 3/6.

7/6 plus 3/6 is 10/6, and convert it into a mixed number was 1 4/6, which simplifies to 1 2/3.

Now it's time for your independent task.

Pause the video and complete the task.

One you're finished, click resume video in the top-right hand corner of your screen, so that we can go through the answers.

In your first question, you are asked to add the fractions.

Again, you needed to make sure that they have the same denominators.

So in A, the first one would have been converted to 6/8.

So you are adding 6/8 plus 5/8 is 11/8.

You make it like that or converted it to 1 3/8 as a mixed number.

For the second one, again, only the first fraction needed changing into ninths, multiplying by three.

So you had 6/9 plus 7/9.

Six plus seven is 13, so that's 13/9, and you may have converted it to 1 4/9.

Part C, both fraction needed changing.

The common denominator is 12.

So we multiply by two to get 10/12.

We multiply by three, oops, to get 9/12.

10 plus nine is 19/12, which is equivalent to one and 7/12.

The final one needed converting here, the common denominator being 45.

Multiply it by five, you get 20/45.

Multiply it by nine, you get 18/45.

20 plus 18 is 38/45.

Onto the next question.

You are adding the fraction in the circles, and finding the total and putting them in the grey boxes.

So let's start on this side.

So we have a half plus a quarter.

Common denominator is four.

That is 2/4 plus 1/4 is equal to 3/5, and that's in its simplest form.

So that goes into our grey box.

Down to the bottom, a quarter plus a fifth both needed converting to 20th, multiplying by five, multiplying by four.

So you should've got five plus four is 9/20.

Again, that cannot be simplified further.

Last one.

A half plus a fifth.

Both need converting into 10ths.

Multiplying it by five gives us 5/10.

Multiplying by two gives us 2/10.

And 5/10 plus 2/10 is equal to 7/10.

For question three, you are asked to complete the sequence, but the term to term rule being to add 3/4.

So the easiest way to do this one I think was to convert it to an improper fraction.

So 3/4.

Sorry, 1 3/4 is equivalent to 7/4.

So we're adding 3/4 each time, but we're asked to give our answers as mixed numbers in their simplest form.

So I'm going to do it as improper fractions, and then I'll go back to what have been asked in the question.

So I'm adding 3/4.

So that's 10/4, 13/4, and 16/4.

Now I need to make sure because I wouldn't get a mark for this.

I need to make sure they're mixed numbers in their simplest form.

So 10/4 is equivalent to 2 and 2/4, which is 2 1/2.

13/4 is equivalent to 3 1/4, and that's in its simplest form.

And 16/4 is equivalent to four.

On to question four.

The first question, it's best to convert them both into improper fraction so they're easier to work with.

So 1 4/5 becomes 9/5.

2 and 7/10 becomes 27/10.

Now I need them to have fractions with the same denominators.

So 9/5 becomes 18/10, and I add those two together, 18/10 and 27/10 is equal to 45/10.

If I convert that back to a mixed number, I get 4 5/10 which I can simplify to 4 1/2.

For B, common denominator is 22.

I'll multiply this fraction by two to get 24/22, this one by 11 to get 11/22.

I add them together to get 35/22, and that converts to 1 13/22.

For part C, again, I convert these to improper fractions.

27/8 plus 17/4.

Then I need them to both have the same denominators.

So, 17/4 multiplied by two to give me 34/8.

And then when I add these two together, 27/8 and 34/8, that is equal to 61/8, which converts to 7 5/8.

For part D, I'm converting them to improper fractions.

So this is 39/4 plus 22/9.

Both of these fractions is going to be changing.

Common denominator is 36.

These numbers are going to be big, I can tell already.

So I multiply the first fraction by nine, and we need to do a separate multiplication.

39 times nine.

Nine times nine is 81.

Three times nine is 27.

And I add on the eight to get 35.

So this is 351/36, and then I'm multiplying this side by four, 88/36.

I add them together, and we need to do a calculation on the side here of the two numerators.

351 plus 88.

One plus eight is nine.

eight plus five is 13, and three plus one is four.

So I get 439/36, which is massive, and I believe it is that.

We'll convert to 12 7/36.

That was a lot of working out.

I'm sorry that slide is quite messy.

Hopefully you followed along with that.

For question five, Fran, Hassan, and Novie ordered some pizzas.

Fran eats 6/8 of the pizza, Hassan eats 5/6, and Novie eats 1/4.

We're being asked how many pizzas did they order, and what fraction is left.

First of all, we need to make these fractions over the same denominator.

The common denominator is 24.

So I multiply Fran's fraction by three, which gives me 18/24.

Then I multiply Hassan's by four, which gives me 20/24.

And multiply Novie's by six, which gives me 6/24.

So I'm doing 18/24 plus 20/24 plus 6/24 to find out how much they ate altogether, so I know that adding those together, that's 44/24.

If I convert that back to a mixed number, they ate 1 20/24.

And I know that this can be simplified by dividing by five.

So they ate one whole pizza and 5/6 of a pizza.

I want to draw what they ate.

So I have pizzas split into six equal parts.

So they ate one whole.

One, two, three, four, five, six out of six parts, and then another five out of six parts.

That means that they must have bought two pizzas, and the fraction left over is 1/6.

Now it's time for your knowledge quiz.

Pause the video and complete the quiz to see what you have remembered.