Lesson video

Hi everyone, my name is Ms. Ku, and today I'm really excited to be learning with you as we'll be looking at the wonderful unit Ratio.

I hope you enjoy the lesson.

So let's make a start.

Hi everyone and welcome to this lesson on checking and securing understanding of converting between ratios, percentages, and fractions, and it's under the unit Ratio.

And by the end of the lesson, you'll be able to move fluently between a ratio, percentage and fractions as well as compare these.

Let's have a look at the keyword proportion.

Now, proportion is a part to whole, sometimes part to part comparison, and if two things are proportional, then the ratio of part to whole is maintained and the multiplicative relationship between parts is also maintained.

Today's lesson will be broken into two parts.

Firstly, we'll be working with fractions, percentages and ratios, and then we'll be looking at problems with fractions, percentages and ratios.

So let's make a start.

Now, percentages, fractions, ratio and decimals all show proportions, and as such it allows us to interchange between them.

So I want you to have a look at this image and tell me what do you think the ratio of shaded to unshaded is? And hopefully you spotted it's 11:14, but what fraction is shaded? Same again, I'm hoping you spotted it'll 11/25.

And from here, can you identify what percentage is shaded? Well, hopefully you've spotted looking at percentage, we need to convert the denominator 100 if possible.

So that gives us the equivalent fraction of 44/100, which is 44%.

But now I'm going to remove the image.

Can you spot how did we get the fraction shaded to be 11/25 using the ratio of shaded to unshaded? Have a little think.

Well, hopefully you've spotted the numerator of the fraction is the part of the ratio showing the shaded, and the denominator of the fraction is the total part of the ratio.

If you add 11 and 14, it gives our denominator, which is 25.

Now, let's have a look at identifying what the percentage shaded would be without the image.

Well, same again, converted to a fraction first as it makes it easier.

Then using our knowledge on equivalent fractions, we can change the denominator into 100, thus giving us our fraction into a percentage, which is 44%.

Now what I want you to do is I'd like you to complete the table showing the equivalence.

I've done the first one for you.

So you can see our bar model shows cats to dogs and the ratio of 2:3.

The fraction of cats is 2/5.

And working out the percentage, I've simply converted my fraction into a percentage using my knowledge on equivalent fractions.

See if you can give this a go.

Press pause if you need more time.

Well done.

Let's see how you got on.

Well, hopefully you spotted the ratio of stars to moon is 1:3.

That means the fraction of stars is 1/4, giving me a percentage of 25% are stars.

For the next question, the ratio of dresses to hats is 3:5.

This gives us the fraction of dresses to be 3/8.

Converting this into a percentage gives me 12.

5% are dresses.

And lastly, cat to hat to bat is 1:1:1.

The fraction of bats is 1/3.

Converting this into a percentage gives me 33 and 1/3 percent.

Really well done if you've got this.

So now let's convert percentages into a ratio.

So in a grid we know 34% of the squares are shaded.

What is the ratio of shaded to unshaded? Well, given the fact that we know the whole is always represented as 100%, therefore we know the proportion which is unshaded, 34% shaded, therefore 66% unshaded.

From here, given that both have been percentages, we can remove that percentage sign, so we have the ratio of 34:66, and then we can simply simplify the ratio to give 17 to 33.

Now let's convert fractions into a ratio.

Let's say on a grid we know 7/10 are shaded, and what we're asked to do is write the ratio of shaded to unshaded.

Well, to do this, we know that there are 7 parts shaded, but how do we find the unshaded? Well, we know the total parts is 10, as this is our denominator, so therefore we can work out this unshaded to be 10 subtract 7, which is 3.

So now we have the ratio of shaded to unshaded.

Alternatively, drawing a bar model can also help if you are unsure.

Here are 7 parts shaded out of the 10, and you can see we have 3 unshaded.

Now it's time for your check.

There are only white and red sweets in a bag.

The ratio of white to red is 3:5.

I want you to read the statements from Aisha, Izzy, Sofia, and Alex and explain who is correct and explain why the others are incorrect.

See if you can give it a go.

Press pause for more time.

Well done.

Let's see how you got on.

Well, hopefully you spotted Aisha is incorrect.

This is because the denominator should be 8 as the sum of parts is 8.

Izzy is unfortunately incorrect as well as she has given the fraction of white.

Sofia is correct and Alex is incorrect because the denominator should be 8, as the sum of parts is 8.

Really well done if you've got this and you've explained why the others are incorrect too.

Let's have a look at another check.

In a dining room, there are either pupils or teachers.

24% of the people are teachers.

Write the ratio of pupils to teachers in their simplest form.

So you can give it a go.

Press pause for more time.

Well done.

Well, hopefully you spotted all of these ratios are equivalent, but writing the simplified ratio gives us 76:24.

Remember the whole percentage is 100%, so that means we know 76% had to be pupils.

But the question wanted us to write it in its simplest form.

So simplifying gives the answer D.

Very well done if you got this.

Let's have a look at another check.

There are only red, yellow, and green marbles in a bag.

We know 2/5 are red and 1/2 are yellow.

We're asked to write the ratio of red to yellow to green.

Take your time with this one.

Great question.

Well done.

Let's see how you got on.

Well, there are a few different ways in which you can do this question.

Using fractions we can convert them all to the same denominator as it allows us to compare more easily.

So identifying the lowest common multiple of 2 and 5 is 10, I can convert the fraction of red into 4/10 and I can convert the fraction of yellow into 5/10.

So that means I know the fraction of green has to be 10/10 subtract 4/10 subtract 5/10, which is 1/10, therefore, so writing the ratio in its simplest form gives us 4:5:1.

Great work everybody.

Now it's time for your task.

What I want you to do is fill in the table and convert between fractions, percentages and ratios.

Press pause as you'll need more time.

Question two is a great question here.

Take your time.

You've got fractions and you need to write the answer as a ratio.

Well done.

For question three, there are 3 bags containing red, green, and/or blue marbles.

You know bag A has 24 red and 16 green, bag B has a percentage which are red, and bag C gives a ratio of red, green and blue.

Read the question carefully and show your working out.

Great work everybody.

Let's go through these answers.

Here are the answers.

Press pause if you need more time to mark them.

Massive well done if you've got any of these.

Question two was a great question.

So there are a few different ways to work this out as long as you've shown that the final ratio apple to orange to lemon is 24:15:1.

Press pause if you want to see my working out.

Well done.

So let's move on to question three.

Now there are a few different ways to do this.

I've chosen to use percentages to show the proportions.

Hopefully you've spotted bag A shows 60% are red, bag B shows 60% are red, and bag C also shows 60% are red, so therefore Aisha is correct.

Very well done.

And you remember you can represent the proportions in different ways as long as you identify that the proportions of red in each bag is the same.

Great work everybody.

So let's move on to problems with fractions, percentages and ratios.

Now, ratio questions can involve knowledge of other proportions, such as percentage of amounts and fractions of an amount.

So therefore it's important to know how to calculate a fraction of an amount and a percentage of an amount.

For example, Lucas and Andeep have 20 cards in the ratio of 2:3.

Lucas gives 1/4 of his cards to Jun, and Andeep gives 50% of his cards to Jun, and Jun had none to start with.

Write the proportion of cards now in the ratio of Lucas to Andeep to Jun.

Well, let's look at this question carefully.

To work out the number of cards each pupil gave away, we need to work out how many cards each person had to begin with.

So we know that Lucas to Andeep was in the ratio of 2:3.

So I've written my ratio table showing the ratio of Lucas to Andeep, giving a total of 5 parts.

Now we know originally they had 20 cards.

So that means using that multiplicative relationship, we can work out how many cards Lucas had and how many cards Andeep had.

Lucas had 8, Andeep had 12.

Knowing that Lucas had 8 cards and Andeep had 12 cards, we can work out how many cards were given to Jun.

So I'm going to draw a new ratio table to show this new ratio.

Now the question says Lucas gives 1/4 of his cards to Jun, so 1/4 of 8 is 2.

So that means I know Lucas now has 6 cards and Jun has two cards, as Lucas has given 1/4 to Jun.

Andeep gives 50% of his cards to Jun.

So that means Andeep originally had 12 cards, 50% is 6, so that means Andeep given 6 to Jun, so now Andeep only has 6 cards left.

From here we can work out the ratio.

The ratio for Lucas to Andeep to Jun is 6:6:8, which can be simplified to 3:3:4.

Very nice of Lucas and Andeep to give Jun some cards.

Now let's move on to a check.

Izzy, Alex and Jacob have 48 sweets between them in the ratio of 5:4:3.

Izzy gives 1/4 of their sweets to Jacob, and Alex gives 3 of his sweets to Jacob.

What is the new ratio for each person? Take your time with this one.

Draw ratio tables if it helps.

Well done.

Let's see how you got on.

Well, first of all, before any sweets were given, we know the ratio of Izzy to Alex to Jacob was 5:4:3.

This gave us a total of 12 parts, but we know that there were 48 sweets in total.

So identifying that multiplicative relationship, Izzy has 20 sweets, Alex has 16 sweets and Jacob has 12 sweets.

So knowing this, let's construct our new ratio table.

Well, we know that Izzy gave 1/4 of her sweets to Jacob, and 1/4 of 20 is 5.

So that means given the fact that Jacob had 12 to begin with, and then Izzy gave him another 5, Izzy has 15 and Jacob has 5 extra sweets.

Now, Alex gave 3 of his sweets to Jacob, so that means Alex now has 13 and Jacob has 3 more.

So we can work out how many sweets Jacob has now.

Jacob has 20 sweets because he originally started with 12, he got 5 from Izzy and then he got 3 from Alex.

So that means the new ratio is 15:13:20.

Really well done if you've got this.

Once again careful attention must be paid to the correct sharing of parts to the correct amount.

What I want you to do is identify the differences between these two questions.

The one on the left says a box of chocolates has 30 chocolates and are either milk, dark or contain nuts.

1/2 are milk, 20% are dark, and we need to work out how many chocolates contain nuts.

The next question says a box of chocolates has 30 chocolates.

The ratio of milk to dark is in the ratio of 2:3.

25% of the milk contain nuts.

1/3 of the dark contain nuts.

How many chocolates contain nuts? Can you spot the difference between these two questions? Well, let's have a look at the question on the left.

Hopefully you spotted this question states that the number of chocolates containing nuts is the remaining amount after 1/2 of 30 and 20% of 30 has been calculated.

But the question on the right states that the number of chocolates containing nuts is calculated by working out the milk first, and then working out 25% of that will have nuts.

Then you work out the number of dark chocolate and work out a third of that, and that gives you the number of dark chocolates containing nuts.

So they are two very different questions.

So let's see if we can work out how many chocolates contain nuts now we know these two questions are very different.

Take your time, show your working out.

Well done.

Let's see how you got on.

Well, the question on the left, hopefully you spotted 1/2 of 30 are 15.

So that means we know 15 are milk chocolates.

We know 20% of 30 are 6, so that means we know 6 are dark chocolate, therefore the remaining chocolates have nuts, so we know 9 have nuts.

For the second question, let's draw a ratio table.

We know the ratio to milk to dark is in the ratio of 2:3.

Now remember we know there are 30 chocolates.

So spotting that multiplicative relationship again, we know we're multiplying by 6 to give us 12 milk chocolates to 18 dark chocolates.

Now remember 25% of the milk, in other words, 25% of the 12 have nuts, so that means 25% of 12 is 3.

3 of the milk chocolates have nuts.

1/3 of the dark chocolates have nuts, so 1/3 of the 18 is 6, so that means we know 6 of the dark chocolates have nuts, thus meaning we know 9 have nuts.

They are two very different questions and two completely different strategies.

Really well done if you got the answer to these.

So in some problem solving questions, only proportions are given.

For example, the Oak teacher has some sweet and sour chews.

We know 3/5 of the chews are sweet.

Now Lucas and Alex shared the sour chews in the ratio of 1:3, and we're asked what fraction of the chew did Alex receive? So we know 2/5 are sour and we also know the ratio of Lucas to Alex is 1:3, which means 3/4 of the sour chews go to Alex.

So we need to work out 3/4 of the 2/5, because 3/4 of the sour chews go to Alex, and we know 2/5 of the entire chews are sour.

Working this out, it's simply 3/4 multiplied by 2/5, which is 6/20, which simplifies to 3/10.

So therefore we know Alex received 3/10 of the chews from the Oak teacher.

This is a great question as you were only given proportions.

Now let's have a look at a check.

Sofia and Jun received some money from a prize competition in the ratio of 4:5.

Jun gives 1/4 of his money to charity.

What proportion of the prize money went to the charity? See if you can give it a go.

Press pause if you need more time.

Well done.

Let's see how you got on.

Well, hopefully you spotted the ratio of Sofia to Jun is 4:5, which means Jun gets 5/9 of the prize money.

Given the fact that he gives 1/4 of his prize money to charity, that means we need to find 1/4 of the 5/9.

Working this out, it's 1/4 times 5/9, which is 5/36, which means 5/36 of the prize money went to the charity.

Really well done.

Great work everybody.

So now it's time for your task.

Question one states a bag of sweets contains red, yellow, pink, and green sweets.

There are 48 sweets in the bag, 25% red, 3/8 of them yellow.

The rest are pink and green in the ratio of 7:2.

The question wants you to work out how many of each colour there are.

See if you can give it a go.

Press pause if you need more time.

Well done.

Let's move on to question two.

There are red and green sweets in a bag.

The ratio of red to green in a bag is 4:5, and there are 36 sweets in total.

Laura takes 25% of the red sweets.

Aisha takes 1/5 of the green sweets.

What is the new ratio of red to green sweets in the bag? Well done.

Question 3 says the Oak teacher makes 240 cupcakes, so that chocolate to vanilla to orange is 5:1:2.

2/5 of the chocolate have icing, 30% of the vanilla have icing, and none of the orange have icing.

What fraction of the cupcakes have icing? And I want you to give your answer in its simplest form.

Great question.

So you can give it a go.

Well done.

Let's have a look at question four.

Jacob, Andeep and Lucas receive some prize money.

Now, Jacob gets 3/8 of the prize money, Andeep and Lucas share the rest in the ratio 4:5.

The question asks, what proportion of the prize money does Andeep receive? See if you can give it a go.

Press pause for more time.

Well done.

Let's move on to these answers.

For question one, here's my working out.

Lots of different ways you could have showed this working out.

But you should have got the answer of 12 red, 18 yellow, 14 pink, and 4 green in the bag.

Press pause if you need more time to have a look at the working out.

Question two, here's my working out, press pause if you need.

But the new ratio should be 3:4 simplified.

Well done if you got this.

For question three, press pause if you need more time to mark.

But the fraction with icing should be 23:80 as a simplified fraction.

Well done.

And for question four, great question.

Here's my working out stating that Andeep receives 25/72.

Well done.

Great work everybody.

So in summary, percentages, fractions, and ratio all show proportions, and as such we can interchange between them.

This allows us to make comparisons or to efficiently calculate problem solving questions.

And it's important to read these problem solving questions carefully, so that you know which amount needs sharing according to a specified proportion.

Finally, for more complex problems, you may be required to work out a proportion of a proportion.

Really well done everybody.

It was great learning with you.