11. Maths - ratio and proportion

​11. Maths - ratio and proportion

​A proportion is a comparison of two numbers that each represent the parts of a whole.

A proportion says that two fractions are the same, even if the amount is different. For example, 1/2 of 10 marbles is the same proportion as 1/2 of 50 marbles.

​What is proportion?

What do you need to know about Ratios?

• They are a comparison of 2 quantities in a group of things

• They compare 2 or more parts to each other

• Formats: Word form, Colon form

• ORDER MATTERS!

Example

• Equivalent ratios are equal in value - just like equivalent fractions

• You can use multiplication or division to find equivalent ratios - just like equivalent fractions.

• 3:5 is equivalent to 9:15, because we have multiplied both numbers by 3. (finding equivalent ratios in the same way you find equivalent fraction)

Real life example - picture explanation on the next page!

If I had 20 toys I could share them between tom and Sarah in a ratio of 2:3.

The total number of parts I have split my whole pile of toys into is 5 (2+3)

Therefore if I divide my pile of 20 toys by 5. (total number of parts) I have the value of 1 part, which is 4 toys.

Going back to the ratio - Tom recieves 2 parts of the whole (2 x 4 = 8)
Sarah recieves 3 parts of the whole (3 x 4 = 12)

The total number of parts (5) makes up the 20 toys!

Ratio

Ratio Tom and Sarah share 20 toy cars in a ration of 2:3
let's demonstrate how the parts are split!

Practise Tom and Sarah share 20 toy cars in a ration of 1:3 - how many cars does Tom receive?

Practise Tom and Sarah share 20 toy cars in a ration of 3:7 - how many cars does Tom receive?

What are equivalent ratios?

• Equivalent ratios are equal in value - just like equivalent fractions

• You can use multiplication or division to find equivalent ratios - just like equivalent fractions.

• 3:5 is equivalent to 9:15, because we have multiplied both numbers by 3. (finding equivalent ratios in the same way you find equivalent fraction)

Just like fractions - ratios can be simplified by finding the highest common factor of the two numbers and then dividing the two numbers by this common factor.


Example - what is the simplest form of 30:18?

The HCF of 30 and 18 is 6.

Therefore divide both numbers by 6 and we end up with a ratio of
5:3

​Simplifying ratios

Just like fractions - ratios can be simplified by finding the highest common factor of the two numbers and then dividing the two numbers by this common factor.


Practise - what is the simplest form of 63:36?

​Simplifying ratios

Converting from fractions to ratios

Converting from fractions to ratios

Converting from fractions to ratios

Practise question

If a fruit bowl is made of oranges, bananas and grapes in a ratio of 1:2:3 - what fraction of the bowl are grapes?

Converting from fractions to ratios

real life ratios and proportion

If butter cost £1.40 per kg how much does 250 grams cost?

(250g is 1/4 of a kilogram)
Let's work it out together!

real life ratios and proportion