Lesson video

Hi, I'm Miss Kidd-Rossiter and I'm going to be taking you through today's lesson on ratio problem solving, where we're going to look at some problems that involve ratios with fractions and percentages.

And we're also going to look at combining ratios too.

It's a really great topic and I hope you're really going to enjoy it.

Before we get started, please make sure that you're in a nice, quiet area if you're able to be, and you're free from all distractions.

You're going to need something to write with and something to write on.

So if you need to, pause the video now to get yourself sorted.

If not, let's get going! So, for today try this activity then.

You've got Zaki and Binh, and they've collected some seashells.

Which of the statements on the right are correct? Can you improve or add to any of the statements? And, can you write any statements of your own that we haven't covered already? So, pause the video here and have a go at this task.

What did you think? Did you agree? Did you disagree? Are any of them wrong? Let's go through it then.

For every shell Zaki has, Binh has three.

Do you agree with this one or not? Let me know.

Excellent.

I agree as well.

For every shell that Zaki has, Binh has three.

We can say that one's correct.

Zaki has one quarter of the total number of shells.

Well how many shells does Zaki have? Tell me now.

Excellent.

He has three, doesn't he? Out of a total of how many? Tell me now.

Excellent, 12.

So, he has three shells out of 12 shells which does simplify to 1/4.

So this one is correct as well.

Zaki has 3/9 of the shells.

Well, we know this one's wrong, don't we? Because we've just worked out that Zaki has 1/4 of the shells.

And 3/9, does that simplify to 1/4? Let's just double check.

So 3/9, simplifies to what? Tell me now.

Excellent, 1/3.

So that one cannot be right.

Binh has three times as many shells as Zaki.

So, we know Zaki has three and Binh has nine.

So, does she have three times as many? Tell me now.

Excellent.

Yes, she does, so that one's correct.

And the ratio of Zaki to Binh's shells is 3:9.

Well, we know that's correct, don't we? Cause we've already worked out how many each of them have.

Could we make this statement even better? Could we simplify this ratio? What would it be? Tell me now.

Excellent.

We could say that this ratio is 1:3 and that links in with our very first statement, doesn't it? Excellent.

So that one is correct.

Well done on that.

So we've got a question on the screen here.

The ratio of roses to violets is 5:4 and the ratio of violets to daisies is 3:2.

You are asked, what is the ratio of roses to violets to daisies? Now, before I can get started on a question like this, I find it really, really helpful to draw myself a diagram.

So I'm going to represent the roses to violets like this, where the roses are, the five pink parts on the left hand side, and the violets are the four purple parts on the right hand side.

And then I'm going to do the same for violets to daisies and show it like this.

So violets to daisies.

The three parts on the left hand side of the bottom bar are my violets and the two parts on the right hand side of my bottom bar are my daisies.

Now I've got the same amount of violets in both ratios.

So that's why I've overlapped those there.

I need to find common, multiple here that I can use to compare these ratios, to get the ratio of roses to violets to daisies.

So, first of all, can you think of a common multiple of four and three, pause the video now and tell me.

Excellent, 12.

So we've gotten from 5:4 and 3:2.

So we've got roses to violets and violets to daisies.

And you told me that the common multiple of both four and three is 12, which is correct.

So I'm going to change these four parts here to 12 parts.

What have I multiplied four by to get 12? What's my constant of proportionality? Tell me now.

Excellent, three.

And what would I multiply my three by to get 12? Tell me now.

Excellent, four.

And so I'm going to multiply my violets here by four to get my 12 parts there.

But I know that if I scale one side of my ratio, I have to do the same to the other, don't I? So I'm also going to multiply my five by three and get what? Excellent, 15.

And here I'm also going to multiply my two by four.

And what will I get? Tell me now.

Excellent, eight.

So now I have a ratio that I can compare all of these, can't I? Because these now, the parts in both ratios are an equal size.

So that means that roses to violets to daisies will be 15:12:8.

In a moment, you're going to have a go at doing a question like this.

So my face is going to disappear and you need to pause the screen and have a go at the question.

When you're ready to go through an answer, resume the video.

So you can see we've got the same question on the screen here.

The first thing I did was I wrote out my two ratios.

So I had them clearly in front of me.

So peas to tomatoes, 5:3.

And tomatoes to carrots, 6:5.

Then I looked for the common part of both ratios.

So here, our common part is the tomatoes.

So I'm looking for a common multiple of three and six.

What's a common multiple of three and six? Tell me now.

Excellent, I'm sure you all shouted different things.

I'm going to use the lowest common multiple, which in this case is six.

So I'm going to change my tomatoes to be six in both ratios.

You'll notice that for the tomatoes to carrots ratio, that means I don't need to change it because I've already got six parts that are tomatoes.

So for my peas to tomatoes, I need to change my tomatoes to be six.

So what would my constant of proportionality be here? Tell me now.

Excellent, two.

And if I multiply one part of my ratio by two, I also need to multiply the other part of my ratio by two, well done.

So that will become 10:6.

Now I have parts of my ratio that are equal.

I can write my final ratio of peas to tomatoes to carrots as 10:6:5.

Look at that ratio on the screen help me with the next part.

And I'm told that there are 50 carrots grown.

So I know that that part of my ratio will be 50.

And I'm looking for my constant of proportionality here.

So what do I multiplied five by to get 50? Tell me now.

Excellent, 10.

And I'm looking for how many peas are grown.

So I have to also multiply this by the same constant of proportionality to get 100.

I don't need to do the middle part of my ratio here because the question hasn't asked it, but I will do it anyway.

And that will give me 60 tomatoes.

And then my final answer to the question will be a lovely sentence that says, 100 peas are grown, well done on that.

So moving onto the second connect part of the lesson today, then.

There are only yellow, blue, and purple counters in a bag.

20% of the counters are yellow, 9/20 of the counters are blue.

And you're asked to write down the ratio of yellow counters to blue counters to purple counters.

So here we're going to have to move quite flexibly between percentages, fractions, and ratios.

So first of all, we know that yellow is 20%.

I'm going to convert everything to percentages here before I write my ratio.

You could choose to do everything as fractions first.

That's absolutely fine.

And then I know that blue is 9/20.

And I know to convert that to a percentage, I first need to convert it to an equivalent fraction out of a hundred.

What would I multiply 20 by to get a hundred? Tell me now.

Excellent, five.

So that means I also need to multiply my nine by five to get 45/100.

So that means that my blue counters are 45%.

Therefore my purple counters will be 100% take away the other two percentages added together.

Well then say 20%, add the 45%.

What's 20% add 45%? Tell me now.

Excellent, 65%.

So I've got 100% take away 65%.

And that gives me what? Tell me now.

Excellent, 35%.

So that means my ratio of yellow to blue to purple would be 20%:45%:35%.

And then I can simplify this ratio, can't I? So this would be 4:9:7.

Can we see that? Excellent, well done.

So now I've got some questions for you to try in the independent task that involve working with percentages and fractions and ratios.

So pause the video here, navigate to the independent task.

And when you're ready to go through responses, resumed the video.

Good luck.

Excellent work, well done.

So first question then, I'm not going to go through in full, but your answer is 52%.

The second one then, the ratio of that age is Antoni:Binh:Calala is 12:4:1.

And the fraction of the total ages that Binh represents is 4/17 because her part is four parts of a total of 17 parts.

Let's go through this one then.

I love this question, there's so much in it.

It's really exciting for me, right? So the first thing we have to do is write down the ratio of Antoni to Cala and Xavier.

So we know if they get 150% of the amount that Antoni gets, that means they get 1 1/2 times as much.

So in our ratio, if we write it as one for Antoni, that means that Cala and Xaier will get 1.

5.

And you can see if I've written that as an equivalent ratio, there 2:3:3, where my constant of proportionality is 2, just so that I've avoided the decimals.

And also it's going to help me again in a little bit.

Now we need to look at Antoni and Binh.

So I'm going to write the ratio, Antoni to Binh.

If Antoni gets 2/7 of the amount that Binh gets, then the ratio must be 2:7, because two is 2/7 of seven.

Now we can see that in all of our ratios that we've written so far here and here, this two represents Antoni.

And because that two is the same in both ratios, it means that our ratios must be the same size.

The parts of the ratio must be the same size, I'm sorry.

So that means we can write a final ratio of Antoni to Binh to Cala to Xavier as 2:7:3:3.

Now we've got to divide this 1,440 pounds into this ratio.

So I've drawn a bar model for it where we've got Antoni at the top, Binh here, Cala here, and Xavier here.

And we know that this bar model represents in total 1,440 pounds.

So let's work out what one part of our ratio is.

Tell me how many parts of the ratio there are in total now, please.

Excellent, there are 15.

So we're dividing our 1,440 pounds by 15 to find out what one part will be.

And what's the answer to that.

Pause the video and work it out.

Excellent, it's 96 pounds.

So that means that each part of our ratio is 96 pounds.

I'm not going to write them all in, but you understand that every one of these boxes represents 96 pounds.

We then need to work out how much money each one of them get before we can work out how much more money Binh gets.

So I've done these all already for you.

So I'm just going to tell you those answers now.

So Antoni gets 192 pounds.

Binh gets 672 pounds and Cala and Xavier get the same amount.

Don't know if we can see that here.

And they both get 288 pounds.

Now, of course you didn't have to work this out first.

You could have seen how many more parts it was than each of them and work it out that way.

That would be absolutely fine.

So Binh, how much more money does she get than Antoni? Tell me now.

Excellent, 480 pounds, more than Antoni.

And it's really nice to write these in full sentences.

And then Binh gets how much more than Cala and Xavier? Tell me now.

Excellent, she gets 384 pounds more than Cala and Xavier.

Excellent work on that one.

There was so many steps there.

So I'm super impressed if you managed to get all the way through to the end, well done.

Moving on to the explore task now then.

A jar contains red, yellow, and green jelly beans.

20% of the beans are green.

The ratio of red beans to yellow beans is 5:3.

Write down everything, you know, based on this information about the jar of jelly beans.

There's loads here that you could write down.

So good luck with that activity.

What did you say? Did you figure it out anything here? Did you figure out the ratio of red to yellow to green? Did you figure out the percentage of red? Did you figure out the percentage of yellow? Did you figure out what fraction of the full amount they were? There's some prompts there if you didn't manage to get started I'm not actually going to go through this at all, because I want to know what you worked out.

Well done on this task.

That's the end of today's lesson on ratio problems. We crumb loads in there, so well done for making it all the way through to the end.

I'm really, really impressed.

Thank you so much for all your hard work.

Please don't forget to go and take the end of lesson quiz so that you can show me what you've learned and hopefully I'll see you again soon.

Bye.