Lesson video

Hi and welcome to our penultimate lesson on fractions.

Today, we'll be learning how to subtract fractions with different denominators.

As always, all you'll need is a pencil and a piece of paper.

Today's lesson agenda, we'll be learning to subtract fractions with different denominators.

Then we'll look at subtracting fractions, fraction sequences, before moving on to an independent task to practise what you've learned and then a quiz to test everything you've learned.

Now, let's start with a Do Now.

Have look at these two fractions, thinking back to the previous lesson, what was the first thing that we needed? So you'll remember that these fractions are hard to work with because their denominators are different, they're out of the different number of units.

So we needed to make the units the same in order to work with them.

We needed to change the denominators to a common denominator so that we could easily add them.

We're applying exactly the same principle to today's lesson, where we are subtracting fractions.

So we have 3/4 - 1/3.

We need to find a common denominator for the denominate four and three.

Thinking about our knowledge of times tables, we know that the common denominator here is 12.

So we're going to convert 3/4 into an equivalent fraction over 12.

I know that four multiplied by three is equal to 12 and I knew that three multiply by three is equal to nine.

So 3/4 is equivalent to 9/12.

Let me do the same for 1/3.

I'm going to change the fraction with the denominator of 12, three multiplied by four is equal to 12 and one multiplied by four is equal to four.

So now I'm looking at 9/12 - 4/12.

Let me have a look at this pictorially.

So my top bar model shows the 3/4 which was 9/12.

I'll put my equivalent fraction on there.

And then my bottom bar model shows the 4/12 which is 1/3.

So we can see from this representation that the difference between 9/12 and 4/12 is this number of twelves, one, two, three, four, five.

So 9/12 - 4/12 is equal to 5/12.

9 - 4 is equal to 5 and our denominators stay the same because it's out of the same number of units.

Let's look at another one together.

This time 3/4 - 1/5.

So start with the common denominator.

I know that the common denominator between four and five is 20.

So I'll convert them into equivalent fractions with a denominator of 20.

Four is multiplied by five to make 20, so I do the same to my numerator, Which makes it 15/20.

3/4 is equivalent to 15/20.

Do the same to my fifths.

An equivalent fraction with 20 as the denominator.

Five multiplied by four is 20 and one multiplied by four is four.

So now I'm dealing with fractions that have the same denominator.

So pictorially, I've got 15/20 shown, which is 3/4 and 4/20 which is 1/5 and I'm looking at the difference between these two bars.

So 15/20 is equal to 15 - 4 is equal to 11/20 and I'll check here in my pictorial representation.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11.

So the difference between 15/20 and 4/20 is equal to 11/20.

Now it's your turn.

Pause the video while you work out how to subtract these fractions.

Give you an answer in its simplest form.

So you will have seen that the common denominator was six.

Only the first fraction needed to be changed.

Three multiplied by two is equal to six and four multiplied by two is equal to four.

So you are working on 4/6 - 1/6.

4 - 1 is 3, stays the same and you may have also simplified because you know that three is a factor of both three and six.

So you could divide both of those numerator and denominator by three to get 1/2.

Let's look at some fraction sequences now.

So I need to first of all work out what is the term to term rule? What is happening between the first term and second term? Well, firstly, I can see that 7/9 is less than 1 1/3.

So I know that these fractions are decreasing in size, so we are subtracting.

Now I need to convert these fractions so that they have the same denominator so that I can find out what the difference is.

First of all, I'm going to convert this into an improper fraction, which will be 4/3.

Then I need these two fractions to have the same denominator.

The common denominator is nine, multiply it by three.

So that will be 12/9.

So now I can see that I'm looking at 12/9 take away 7/9 to find the term to term rule, 12 - 7 is 5/9.

So I can see that each time I'm going to be subtracting 5/9.

So the term to term rule is subtract 5/9.

Now I need to work out what is the next fraction in the sequence.

I'm doing 7/9 - 5/9.

7 - 9 is 2/9.

Now it's you turn.

Pause the video and work out the term to term rule and then find the next term in the sequence.

So let's have a look at this together.

So I've got 2 3/8 and then 1 7/8 and we can work out the difference to find out that term to term rule.

Now to support me to do this, I'm going to put these into improper fractions.

So I know that 2 3/8 is the same as 19/8 and 1 7/8 is the same as 15/8.

Okay and then I can clearly see that the difference if I take 15 from 19 and we're both using eighths, I'd be left with 4/8, so the difference is 4/8.

So each time we are subtracting 4/8.

What we need to do now to find out our next term would be to subtract another 4/8.

Okay and then again, I'm going to use that improper fraction to support me to do this.

So I know that 15, if I was to take away another 4/8 that would leave me with 11/8.

Now we need to write our answer here as a mixed number in its simplest form.

So we've got 11/8 here.

That would be the same as 1 and 3/8.

Okay, can I simplify that any further? No, I can't, it's in its simplest form already.

So my final answer would be 1 3/8.

Now it's time for your independent task.

Pause the video and complete the task.

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

For question one, you were asked to subtract the fractions, so converting them to have the same denominator.

For A, the common denominator was 30 and you are multiplying by five 25/30 and multiplying by six.

Subtract 6/30 is equal to 19/30.

For B, your common denominator was 48 and you multiplied by six here, so that's 42/48.

And eight here, so that's 8/48.

42 subtract eight is equal to 34/48.

You could it as this, or you could have simplified to 17/24 by dividing by two.

For C, you only needed to change your second fraction into its equivalent, 6/9.

7/9 - 6/9 is equal to 1/9.

And for D, both fractions needed converting to equivalent fractions with the denominate of 14.

So this is 10/14 - 7/14 which is equal to 3/14.

In your next question, you were asked to subtract the smaller fraction from the larger fraction to find the difference.

So first of all, you would need to convert them to have the same denominators.

So these two, 3/5 and 1/4 could be converted into twentieths.

So 12/20 and 5/20.

So now we can see that this is the greater fraction.

12/20 - 5/20 is equal to 7/20.

So that goes in the grey box here.

Now we'll look at 3/5 and 7/8.

The common denominator is 40.

So this time we're converting it into fortieths.

So both into fortieths there.

We're multiplying by eight.

So we have 24/40 and we have 35/40.

We can see that this is the greater fraction.

35/40 - 24/40 is equal to 11/40 and that goes into our grey box here.

Our last few fractions, 7/8 and 1/4.

We can see that 1/4 is the only one that needs to change here into 2/8.

7/8 is the greater fraction, so here we're looking at 7/8 - 2/8 which is equal to 5/8 and that goes into our middle box.

In the next question, in the term to term rule of subtract 3/4, so you converted your initial mix number into an improper fraction, which is 21/8.

And now if we're working in eights, we also are going to want to change our term to term rule into an equivalent fraction with eight as the denominator, 3/4 is equal to 6/8.

So from here to here, we're subtracting 6/8.

21/8 - 6/8 is equal to 15/8.

I'm going to leave it up here for now because it says to ensure that my answers are mixed numbers in their simplest form.

And I can see that 15/8 converts to 1 7/8.

then I'm subtracting another 6/8 15/8 - 6/8 is equal to 9/8 which converts to 1 1/8.

And my final term, 9/8 - 6/8 is equal to 3/8 and that cannot be put as a mixed number, so that must be in its simplest form.

The next question, these are mixed numbers to be converted to fractions.

So the first one, I'm actually going to leave them as mixed numbers and just change the second fraction here.

So one quarter is equivalent to 2/8, so this becomes 1 2/8.

I subtract the whole numbers, 2 - 1 is 1.

And then 5/8 - 2/8 is 3/8, so that's 1 3/8.

Here, I'm going to convert them to improper fractions with the same denominator.

The denominator is going to be twelfths here.

So this one we'll convert to 44/12 and this one will convert to 33/12 which is equivalent, which is equal to, sorry, I should say, 11/12.

This one, you were to convert it to improper fractions with the common denominator 21.

I'm going do it in one step.

You will have probably done it in two steps here and these are big numbers, 150/21 - 98/21 is equal to 52/21 which you may then have converted into a mixed number, 2 10/21.

Our final one needed to be converted, I can keep them as mixed numbers but I'm going to convert my fractions here into forty eighths, so this would be 40/48 and don't forget my whole number 6 and 40/48 subtract 2 and 6/48.

6 -2 is 4.

40 - 6 is 34/48 which can be simplified to 4 17/24.

Onto our last question.

For the school's sports day, students prepared 12 1/2 litres of lemonade.

At the end of the day, they had 2 5/8 of litres leftover.

How many litres of lemonade were used altogether? So we are being asked to do 12 1/2 - 2 5/8.

So what we needed to do was to have these as fractions with the same denominators.

So this becomes 2 4/8 - 2 5/8.

because I can't do 4/8 - 5/8, I need to convert these to improper fractions.

So this one as an improper fraction, sorry, I'll do it over here, I'll just write this out again.

12 4/8 - 2 5/8.

So as an improper fraction, this is 100/8 and this one is 21/8 which is equal to 79/8 which converts to 9 7/8 of a litre.

So that's how many litres were used.

Time for your final knowledge quiz, pause the video and complete the quiz to see what you've remembered.

Well, then you've worked really hard today.

I'm looking forward to meeting you back here for our final lesson in the fractions unit.

We'll be learning to solve problems involving fractions.

See you then.