Ratios are seen in everyday life. They can be used when adding ingredients to make a meal, when deciding how much pocket money children get or when reading a map.
Ratios are used to show how things are shared. They can have more than 2 numbers, such as 4:2:1.
Ratios can also be fully simplified just like fractions. To simplify a ratio, divide all of the numbers in the ratio by the same number until they cannot be divided anymore.
A common example of a ratio in everyday life is when mixing paint colours. For example; 2 parts blue to 1 part yellow will make green.
We are looking at ratios in context. I funded my context because we're kind of mainly focusing on the real world applications of ratios. So first look at what our ratios will kind of break them down into our stuff topics and then we'll do a couple of example questions at the end. So what's the point in ratios? Well, if you've ever followed a recipe book, you've probably used ratios.
Often the recipe might say, this makes pancakes for four people and you've got to make pancakes for six people. You probably times all of your values, all of your 200 grammes and 300 grammes by 1.5 to get 300 grammes and 450 grammes. If you've ever been driving down the road and your car is in miles per hour and the road signs are in kilometres per hour, again, you use ratios to work out if you're speeding over the speed limit, right? If we convert between kilometres and miles, that's just using ratios again. So whenever we're doing conversions, or whenever we're doing scaling, or whenever we're sharing things out between groups of people, we're always going to be using ratios.
So that's why that's why they're useful simplifying ratios. So in general, there are kind of two main rules we want to follow when we're writing down ratios. One is we never want to have decimal points in our ratios. We never want to have a ratio that looks like this. Ideally we would just have whole numbers, right?
And so if I want to get this into a whole number, I can double that and that will give me three to eight. And that's much better than that. Like I said, we don't have fractions, right? If I was to write this as let's do another one, let's say we've got four, five to seven. Again, we don't want to have a fraction.
So we can times both sides by five. We end up with four T 35 as our ratio. So that's the kind of first rule, right? No decimals or fractions, just whole numbers. Our second rule is we always want to have the simplest form that we can.
If we've got say, twelve to 18 as a ratio, what I've got a common factor of six on both sides here and so I can divide both sides by six. And in doing so, I massively simplify the ratio and so I end up with two to three. So again, we don't want that. We want that. We want the simplest form that we can have.
So whole numbers and a simple form. That's our aim with ratios, applying ratios. So we can either be kind of given a total amount so we're making pasta bake. Let's say we're given 600 grammes. That's what the recipe tells us, how much we can make.
And we want to work out if we're cooking for boys and girls, we want to work out how much the boys are going to have to eat. Well, in that case, if we've got a boys and girls, let's say we've got three boys and two girls that we're kicking for, and what we can do is we can say, well, in total yes, before girls, that's fine. We'll do two girls, we'll give it a nice factor. Let's say we've got three plates of pasta bake for boys and two plates of pasta bake for girls. Well, in total, we've got five plates that we're going to have to serve up, and we can work out how much pasta bake is going to be on each plate.
Right, we've got 600 total. We just use 600 grammes divided by five. That gives us 120 grammes on each plate. Well, if you want to work out how much the boys are going to eat in total, we just do 120 grammes per plate times three plates. That gives us 360 grammes.
We can also work backwards, right? Sometimes we're told that the boys have demanded that they get 360 grammes of pasta bake to eat between them, and we want to keep things even. We don't want the girls to have less pasta bake. So what we can do is we can say, well, if we've got to make 360 grammes for the boys, well, we can work out how much each boy is going to have on that plate. We can do 360 in total for the boys, divide that by three and that gives us the amount per plate.
That's going to be 120. And if we want to have the same amount of pasta bake on each plate, we need five lots of 120, right? So we can take that 120 grammes, we can times it by five and we know we need to make 600 grammes in total. And so we're kind of working forward in one direction and backwards in the other direction. We can also work with scale factors, right, as I mentioned, with pedometers and things, that's all scale factors.
Quite often, if you see on a map, even on your smartphone, on Google Maps or something, we quite often have a map and there may not be a grid, but there'll be a small scale box in the bottom here. This might be maybe centimetre wide. This could be one centimetre wide on your phone screen or on your map. And it says this is equal to, I don't know, three kilometres.
Well, in this case, if we know we're trying to get from one point to another point, we can measure how many centimetres that is on our map. Let's say that's five centimetres. We can use our scale factor or our ratio to work out how many kilometres that is in real life, right? So if we know that one centimetre is the equivalent to three kilometres, then we know five centimetres is going to be well, what's our scale factor? Right, we've got our scale factor here.
We know it's time to move by five on the left we then put half the times by five on the right and we get 15 kilometres. So we're using ratios and scale factor to work out real world problems. Let's do some exam style questions to finish off with. So Rosa is preparing ingredients for a pizza. She uses cheese, toppings and dough in ratio two to three to five.
So we've got cheese to toppings today, it's going to be the ratio of two to three to five. And we know she uses £70 of day. Again, I'd always encourage you to literally, we've got like, two pairs of cheese, we've got three pairs of toppings and we've got five piles of dough.
And we want to work out how much cheese and how much toppings do actually need, how many grammes of each do we need. And so, ideally, we need to know how many grammes are in one pile. And we can therefore work out how many grammes in total of cheese and toppings. Are there going to be? How many grammes are there in one pile?
Well, we're given this information, right? We know 70 grammes of dough is going to be used. And so this is our dough here. We've got five piles of dough and we know in total, this is equal to 70 grammes. So that's equal to five piles, right?
If you want to just get how many grammes is equal to one pile, when we know we're just dividing by five, that's our scale factor in this case. And so if I'm dividing the right hand side by five, I also have to divide the left hand side by five. So 17 divided by five is going to give us 14. We know each pile is going to contain 14 grammes, and so cheese has two piles in it. If each pile is 14 grammes and we've got two piles, we've got 28 grammes of cheese, and likewise toppings.
We've got three parts of toppings, each part is 14 grammes. Three times 14, that's going to give us 42 grammes. Final question ratio. 20 minutes to 1 hour can be written in the form one to N. Find the value of N.
And so we don't ever want to be comparing minutes and hours or apples to oranges or chalk and cheese. We want to have the same units on both side of our ratio, otherwise it gets quite confusing in a way that we don't know exactly what the ratio actually is. So we can say we could either convert them both to minutes or both hours, it doesn't really matter. Let's say 1 hour is the exact same as 60 minutes. And so we can actually say the ratio we're starting with is 20 minutes to 60 minutes.
We now can basically ignore our units because we're just dealing with time. So even if we're dealing with hours or days or years, it's always going to be in the ratio of 20 to 60. We can simplify this. Now right, we've got a common factor on the left and the right of 20. We can divide both sides by 20 and we can massively simplify this.
We end up with one on the left and three on the right. And so N in this case is going to be three. That's the answer on the scale map on a map is one to 25,000. How many kilometres on the ground is represented by six centimetres on the map. So we've got a ratio of one to 25,000 and we're going from one to six metres.
Well, what's that scale back is going to be? It's going to be times in by six. Right. So whatever you need to the left, we have to do to the right. We have to time that by six as well.
25 gives us 150,000, so we know that six increases on the map gives us 150,000 and that is the end of ratio.
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