A ratio is a way of comparing two values in relation to each other. It shows how much there is of each value.
What is a ratio?
A ratio indicates the relationship of one thing to another or shows that we are comparing the quantity of one thing to the quantity of another. A ratio is usually written as two numbers with a colon separating them (we can also use the word 'to' instead or present it as a fraction).
For example, a household might have four fish and two dogs. As a ratio, this would be expressed as 4:2.
Remember that the order of the numbers in a ratio is important! They must match the order of the objects that you are referring to. We can find examples in all parts of life, from cooking (ingredients) to sports (football match score). We use ratios daily, even if we don't notice.
Let’s have a look at a ratio is action:
Let's say your after-school club has 12 boys and 16 girls. As a ratio, this would be expressed as 12:16. This ratio can then be simplified (in the same way as a fraction) to 3:4. This means that for every 3 boys in the class, there are 4 girls.
(Remember to express the ratio in its simplest form.)
How to work out a ratio
We can also use ratios as a method to share out a total number between two or more people, just like we do with fractions and percentages.
In this example, we will share £100 in a ratio of 2:3.
1. The first step is to find the total number of parts in the ratio.
2 + 3 = 5 parts.
2. Find the value of one part by dividing the total number by the total parts.
£100 ÷ 5 = £20
3. Multiply each part of the ratio by the value of one part.
2:3 = 2 x £20 and 3 x £20 2:3 = £40:£60
The first person would get £40, and the second person would get £60.
Another question involving ratios, could look like this:
The ratio of boys to girls in a dance class is 6:9.
How many boys are there if there are:
27 girls? (Answer: 18 boys)
72 girls? (Answer: 48 boys)
In the two examples above, pupils need to know that the number of girls has been multiplied by three for the first question and by eight for the second question. They must then multiply the number of boys by the same factor to get the correct answer.
Ratios work closely with fractions and percentages. You will often find worded questions that ask the child to provide their answer to the ratio in either a fraction or as a percentage.
Another place we can find ratios are in scales (not the measuring kind, the kind you find on a map). The scale factor is the number that is multiplied by the scale of an object to get another object that looks the same but is a different size; either scaled up or down.
How Do I Enlarge An Object By A Scale Factor?
To enlarge an object by a scale factor, you must measure each side of the object, then multiply that number by the scale factor number.
For example:
You're given a square that is 4x4cm. Increase the square by a scale factor of 2.
To do this, multiply each side by 2.
You then end up with a square that is 8x8cm.
Then we have questions that reflect direct proportion. This is when two quantities are said to be directly proportional if one doubles, the other doubles as well.
What is an Example of Direct Proportion?
The number of dogs being fed will be directly proportional to the amount of food needed (if each dog eats the same amount).
What is the Formula for Direct Proportion?
An equation can be set up to link any two variables which are directly proportional. If x and y are proportional to one another, then y = kx, for some constant value of k.