Lesson video

Hi there.

My name is Mr. Tazzyman and I'm really looking forward to teaching you this lesson today from the unit, all about the composition of non unit fractions.

Some people can find fractions a bit tricky sometimes, but I hope with what I'm about to show you, I can make sure that you finish this lesson feeling really confident and ready to tackle any fractions that come your way.

Okay, we are gonna get started.

Here's the outcome then.

By the end of the lesson, we want you to be able to say, I can subtract fractions from a whole by converting the whole to a fraction.

These are the key words that you are going to hear.

I'm gonna say them and I want you to repeat them back to me.

I'll say my turn, say the word and then you can repeat it back.

Ready? Okay.

My turn, minuend, your turn.

My turn, subtrahend, your turn.

My turn, numerator, your turn.

My turn, denominator, your turn.

Okay, well done.

Now let's just make sure that we know what each of these keywords means.

The minuend is the number being subtracted from.

A subtrahend is a number subtracted from another.

There can be more than one.

You can see an equation there at the bottom.

Seven subtract three is equal to four.

In this example, seven is the minuend and three is the subtrahend.

A numerator is the top number in a fraction.

It shows how many parts we have.

A denominator is the bottom number in a fraction.

It shows how many parts a whole has been divided into.

This is the structure of today's lesson then.

Subtract fractions from a whole by converting the whole to a fraction.

There's gonna be two parts.

Firstly, we're gonna look at subtracting fractions from a whole, and secondly, we're gonna look at applying the concept to new contexts, which means some different situations.

Okay.

Let's meet a couple of people.

In this lesson you're gonna meet Izzy and Sam.

They're our maths friends today, and they're gonna help us by discussing what we see on screen, giving us some ideas, maybe some new thoughts, and maybe even giving us some hints and tips for any answers that you might need to find.

Alright, let's get started then.

Sam and Izzy have a slice of buttered toast each.

They both cut their whole slice into equal parts.

Then they each eat a fraction of their slice.

Have you got a favourite way to cut toast? I wonder if it's gonna be the same.

Let's see how they like to do it.

The number of parts of the toast is reducing, so this is subtraction.

I agree, we are subtracting fractions from the whole slice of toast.

Sam likes to have slices of one half.

Izzy likes to have slices of one quarter.

Sam eats one half of her slice of toast.

How much of the slice of toast is left? Sam started with a whole slice and ate one half.

There's one whole written as a bar.

Then we have two halves underneath.

They are two parts, two equal parts that make that whole.

One of them has been eaten, one of the equal parts, one of the halves.

There's one half left over.

Here it is as an equation.

One subtract one half is equal to one half.

Izzy eats one quarter of her slice of toast.

How much of the slice of toast is left? Izzy started with one whole slice and ate one quarter.

There's the one to represent the whole slice in a bar.

There are the quarters, the four quarters that make up one whole and there's one of them that's been eaten or subtracted.

Here it is as an equation.

One, subtract one quarter is equal to three quarters.

Okay, it's your turn to have a go at something similar just to check that you've understood what we've done so far.

A slice of toast is cut into three equal parts.

One third of the slice is eaten.

How much of the slice is left over? Pause the video here and have a go at that.

(no audio) Welcome back.

Let's see how you got on.

Here's a bar model representing this problem.

You can see that we've got one representing a whole slice of toast.

Underneath we've got three equal parts.

They're thirds and one of those has been subtracted.

Here it is as an equation revealing the solution.

One, subtract one third is equal to two thirds.

Here are all three equations and bar models so far.

What do you notice? Have a look at all three of those.

Look carefully and see what's the same.

What's different? What do you notice? Sam says, "The numerator change." "The denominators in each calculation stay the same." Okay, let's check your understanding of that.

True or false.

When subtracting fractions with the same denominator, the denominator doesn't change.

Pause the video and decide whether you think that that statement is true or false.

(no audio) Welcome back.

Which did you think? That was true.

When subtracting fractions with the same denominator, the denominator doesn't change, but as good mathematicians, we need to try to justify our answer as well.

Here's two justifications.

A, the denominator is the unit for calculation.

The numerator tells us how many there are of the unit, or B, because you are taking away the denominator and that means that it can't change.

Now, which of those justifications do you think is the most apt? Which is the most appropriate? Which one is the best? Pause the video and discuss.

(no audio) Welcome back.

Which justification did you think best? Well, actually, A was the best one here.

The denominator is the unit for calculation.

The numerator tells us how many there are of the unit.

Okay, ready to move on? Izzy looks again at the toast cut into two equal parts.

You can see there we've got the toast that's been divided up.

We've got the equation and we've got the bar model.

I think that this could be thought about differently.

Instead of one whole slice, we could have two lots of one half.

Two lots of one half is equivalent to two halves.

Can you see that Izzy has changed the representation, the bar model and the equation? Sam thinks about other fractions equal to one whole.

When the numerator and denominator are the same, the fraction is equal to one whole.

Five fifths is equal to one whole.

Sam's used a pizza here to show that, to represent that.

10 10ths is equal to one whole.

The pack of colouring pencils that you can see there contains 10.

10 make a complete pack, so each one is one 10th and there are 10 tenths altogether making one whole pack.

15 15ths is equal to one whole.

There's an egg box there and it's completely full.

There are 15 eggs altogether, so 15 15ths is equal to one whole.

Izzy changes all three equations and bar models by converting the whole to a fraction instead.

She's used four quarters in the first one.

She's used three thirds in the second and just like we did before, two halves in this third representation and equation.

What do you notice this time? So have a look.

Same representations with a little bit of difference.

What do you notice? The denominators are still the same, including the converted holes.

The numerators form a subtraction.

Okay, let's check your understanding again.

True or false.

When the numerator and denominator are the same, the fraction is equivalent to one.

What do you think? Pause the video and discuss it if you need to.

(no audio) Welcome back, what did you think? True or false? Well, let's see.

That was true, but again, we need to justify our answer here.

Here are two justifications.

You've got to choose the one that you think is best.

A, one whole has a value of one and one whole is formed where the numerator and denominator are the same, or B, if all the parts of the hole are shaded, then the numerator and denominator are equal.

Which of those justifications is best? Pause the video and I'll be back in a moment to reveal which one is correct.

(no audio) Welcome back.

A was the correct justification here.

One whole has a value of one and one whole is formed when the numerator and denominator are the same.

For B, if all the parts of the whole are shaded, then the numerator and denominator are equal.

This is true, but it doesn't talk about the equivalence with one.

It's not a justification for our statement above.

Sam has a go at finding the missing number in a fractions equation.

One, subtract four sixths is equal to, well, we don't know yet.

That's an unknown.

"I will start by converting one into a fraction." That's good thinking, Sam.

"I'll use sixths." I wonder why Sam has chosen to use sixths.

"One is equal to six sixths.

Now I will look at the numerators.

I know that six, subtract four is equal to two, so the numerator is two.

It's two sixths." Okay, it's time for your first practise task.

For number one, I'd like you to find the missing fractions by converting the whole, so remember every time you see one, you can write in the equivalent fraction that equals one and try using the same denominator that you can see elsewhere in the expression because you'll find that will help you to get a solution.

For number two, I'd like you to rewrite the bar models as an equation, replacing the minuend with a whole.

Have a go at these.

Enjoy the challenge.

Pause the video here and I'll be back in a little while for some feedback.

(no audio) Welcome back.

Let's see how you got on.

We'll go through each very carefully.

So for A, you can see that the hole was converted into four quarters.

Four quarters, subtract three quarters is equal to one quarter.

For B, the whole was converted to six sixths.

Six sixths subtract four sixths is equal to two sixths.

For C, the whole was converted to three thirds and even though the expressions had switched round, in a sense, two thirds is equal to three thirds subtract one third.

That still works as an equation.

For D, eight eighths, subtract five eighths is equal to three eighths.

For E, five sevenths is equal to seven sevenths subtract two sevenths.

And for F nine ninths subtract five ninths is equal to four ninths.

You can really see from this question how converting one into a fraction where the numerator and denominator are the same and crucially where the denominator matches other fractions in the question can be really, really useful.

Okay, let's look at number two then.

We had some bar models that we needed to rewrite as an equation, replacing the minuend with a whole, so for A, we had one subtract one quarter is equal to three quarters, which is the same as four quarters subtract one quarter is equal to three quarters.

For B, we had one subtract two fifths is equal to three fifths, which is the same as five fifths subtract two fifths is equal to three fifths.

For C, it was one, subtract one third is equal to two thirds, which was the same as three thirds subtract one third is equal to two thirds, and for D we have one subtract four sixths is equal to two sixths which was the same as six sixths subtract four sixths is equal to two sixths.

Okay, let's move on to the second part of the lesson, applying the concept to new contexts.

Ready to go? Let's do this.

Izzy has a multipack of eight yoghourts.

She eats a yoghourt on Monday, Tuesday, and Wednesday.

What fraction of the multipack is left? What do you think? Have a reread of that question and consider it carefully.

Let's see what Sam and Izzy came up with.

"The multipack is the whole and we are subtracting from it." "Let's convert the whole." What is one multipack as a fraction? "A multipack is made up of eight yoghourts.

Each yoghourt is one eighth." "That means that one multi-pack is eight eighths." They've written it down because they're starting an equation to make sense of this problem.

"You've eaten three, Monday, Tuesday, and Wednesday.

That's three eighths." So they've subtracted three eighths from eight eighths.

"I know that eight, subtract three is equal to five.

The answer is five eighths of a multi-pack." So look closely there.

It's another really good example of the fact that the denominator has stayed the same, but that the numerator has formed a subtraction.

If you just look at the numerator, you can see eight, subtract three is equal to five.

Here's another one.

Sam has a full bottle of bubble mixture.

She uses some of the mixture to blow some bubbles.

Now she has less than a whole bottle of bubble mixture.

What fraction of the bubble mixture remains? "Right then, let's convert the whole to help with this subtraction," a crucial tool.

"I don't think we can do that yet." What do you think? Can they convert that whole yet? "We don't know what denominator to use.

I'll look more closely at the bottle." She peers in.

She peels off the label and looks more closely at the bottle.

She spies a scale.

You can see there we've got an empty part and then we've got the rest where there's bubble mixture.

"I think I can estimate what fraction I've already used.

The empty part fits into the bottle five times.

1, 2, 3, 4, 5." Oh yeah, I can see that, Izzy.

So then she's drawn a bar model of that.

The whole is the bubble mixture at the top and it's been split into five equal parts.

"The whole can be converted into five fifths." There we go.

We've got five fifths replacing the words, bubble mixture, and then each of those parts is one fifth and at the top you can see five fifths has been written on its own.

That's where Izzy's decided to start writing an equation as well.

The empty part is one fifth, which is the subtrahend.

She's crossed it out on the bar model and she's got her expression now at the top that reads five fifths subtract one, fifth.

"Five fifths subtract one fifth is equal to four fifths." There's the completed equation.

Okay, your turn.

Let's check your understanding so far.

Sam has a full bottle of bubble mixture.

She uses one 10th of the mixture to blow some bubbles.

Now she has less than a whole bottle of bubble mixture.

What fraction of the bubble mixture remains? Pause the video here and have a go at that question.

You might like to turn it into an equation to make sense of it.

Don't forget about trying to convert the whole so that the numerator and denominator are equal.

Good luck.

Pause the video here.

(no audio) Welcome back.

Here's how your equation may have looked.

10 10ths subtract one 10th is equal to nine 10ths, so the answer was nine 10ths.

How did you get on? Alright, let's move on.

Izzy and Sam look at an equation with missing numbers.

One, subtract and you've got a fraction there with two missing parts.

The numerator and the denominator, is equal to three 11ths.

Let's convert the one into 11 11ths to start with.

Again, think about why Sam might have chosen 11ths.

Is it because it's elsewhere? Yes, I think it is.

The denominator of the subtrahend will also be 11.

That's because the denominator stays the same.

"I know that three plus eight is equal to 11, which is the inverse.

So I also know 11 subtract eight is equal to three, meaning that the numerator is eight." Izzy and Sam look at another equation with missing numbers.

One, subtract six 15ths, subtract something, an unknown is equal to zero.

The one can be converted into 15 15ths.

"The denominator of the second subtrahend will be 15 too." "I know that six plus nine is equal to 15, which is the inverse, so I also know 15, subtract six, subtract nine is equal to zero, meaning that the numerator is nine." Izzy and Sam look at an inequality statement with a missing numerator.

One subtract two ninths is greater than something ninths.

"Let's start by working out the value of the first expression." "The one can be converted into nine ninths." "I know that nine subtract two is equal to seven, so it's seven ninths." Now it's starting to look a bit simpler, isn't it? "The denominators are the same in both expressions, so the numerator could be zero, 1, 2, 3, 4, 5, or six." Okay, it's time for your second task.

For number one, we've got a worded problem.

Izzy has a multipack of 12 Juice Blast drinks.

She drinks one on Sunday, Tuesday, Wednesday, and Friday.

What fraction of the multipack is left? For number two, another worded problem.

Sam drinks two 10ths of a bottle of Juice Blast and then pours out four 10ths for Izzy to drink.

What fraction remains in the bottle? For number three, you've got to find the missing numerators and denominators in these questions and for number four, how many ways can you complete these inequality statements? Okay, have a good go at those.

Pause the video here and I'll be back for some feedback in a little while.

(no audio) Welcome back.

Let's look at number one to begin with.

Sam's gonna talk us through some of it.

One multi-pack as a fraction will be 12 12ths because there are 12 bottles altogether.

Altogether Izzy has drunk four bottles because there are four days.

You can see in the question Sunday, Tuesday, Wednesday, and Friday.

"I know that 12 subtract four is equal to eight, so there are eight bottles left.

As a fraction, that will be eight 12ths." So that's the answer.

Let's look at number two then.

So we start with a whole bottle, but we need to convert this to a fraction to help us to understand the question.

We know that in the question we've got 10ths, so we'll convert the whole to 10 10ths.

Then we'll subtract two 10ths because that's what Sam has drunk to begin with.

Then we're gonna take away four 10ths because that's been poured into the glass for Izzy to drink.

Altogether you can see we've got, the denominators are the same, but 10 subtract two, subtract four is equal to four.

That's the numerators.

The answer is four 10ths.

Okay, let's look at these missing numerators and denominators.

For A, we've got three sixths is equal to six sixths subtract three sixths.

For B two 14ths is equal to 14 14ths, subtract 12 14ths.

For C, we've got four ninths is equal to nine ninths, subtract three ninths, subtract two ninths.

For D, we've got five fifths, subtract three fifths, subtract two fifths is equal to zero.

for E, zero is equal to three thirds, subtract two thirds, subtract one third.

For F, we've got zero is equal to nine ninths, subtract eight ninths, subtract one ninth.

For each of these, we chose to convert one into a fraction, but the question didn't ask you to do that, so if you were able to complete it anyway without converting one into a fraction, then that's absolutely fine.

Alright, pause the video here if you need more time to mark and I'll be back with the feedback for four in a moment.

Let's look at number four.

We had to complete some inequality statements, so for A, 10 13ths is less than one, subtract something 13ths.

You could have had one or two.

10 13ths is less than one, subtract one 13th or 10 13ths is less than one, subtract two 13ths.

For B, you could have had one to 12.

Any of those.

One subtract seven 20ths is greater than something 20ths.

If I convert the one to 20 20ths, I can say 20 20ths, subtract seven 20ths.

That is equal to 13 20ths, so I had to make sure that I used any numerators where they were less than 13 20ths.

The other one that could have been included here was of course zero.

Okay, we've come to the end of the lesson.

Here's a summary of what we've learned today.

When subtracting a fraction from a whole, the whole must firstly be converted to a fraction where the numerator and denominator are the same and the denominator matches the denominator in the subtrahend.

This can be done by substituting the fraction into an equation which features one.

My name is Mr. Tazzyman.

I've really enjoyed the lesson today and I hope you have as well.

I'll see you again soon.

Bye-Bye.