Ratio Ratio is a way of comparing amounts of something. It shows how much bigger one thing is than another. There are two aspects that we will look at in relation to ratio: 1. Using a ratio to calculate parts and scale up and down as necessary 2. Simplify numbers in to a more useful ratio

Ratio Example: I would like to make some light orange paint to paint a room in my house. I need to mix red and yellow paint in the ratio 1:2. To paint the room I need 21 litres of light orange paint. How many litres of red and yellow paint do I need?

Ratio Answer: R Y Add the parts of the ratio together:1 + 2 = 3 parts altogether Divide the total amount required (21 litres) by the number of parts to find what 1 part is:21 ÷ 3 = 7 litres The original ratio was 1:2 I know that 1 part is 7 litres so I need 7 litres of red paint. Yellow was 2 parts so 2 x 7 = 14 litres To check, add the two amounts back up and they should equal the original amount:7 red + 14 yellow = 21 litres

Ratio There are a lot of similarities to fractions with ratio. If we take the previous paint example where the ratio was 1:2 there were 3 parts altogether. So, we can also say that in the final mixture: 1/3 was red and 2/3 were yellow.

Ratio Another example: The instructions in a bottle of plant food say ‘dilute 1 part plant food with 3 parts water’ I put 250ml plant food in a watering can, how much water do I need to add?

Ratio Answer: The ratio is 1:3, plant food to water The 250ml of plant food is 1 part Water is 3 times that of plant food So, 250 x 3 = 750ml Adding the two together gives the total mixture 250 = 750 = 1000ml = 1litre

Ratio Simplifying ratio Sometimes we are given large numbers and we need to make sense of them by simplifying them. This is done in the same way as simplifying fractions. Example: The ratio of supporters at a match is 24,000:8,000 ÷ by :8 ÷ by 83:1 The ratio in its simplest form is 3:1 Keep dividing both sides by the same number until you have the smallest possible numbers

Ratio Another example: The recipe for a children’s cocktail says, ‘Mix 75ml of strawberry syrup with 100ml of apple juice and 150ml of mango juice’ How much mango juice and apple juice should you mix with 120ml strawberry syrup?

Ratio Answer: First simplify the ratio of ingredients: We had 120ml of strawberry syrup = 3 parts To find 1 part divide 120ml by 3 = 40ml We can then work our how much of mango and apple we need by multiplying their parts by 40ml: Mango 4 parts x 40ml = 160ml Apple 6 parts x 40ml = 240ml S M AS:M:A 75:100:150÷ 25 3:4:6