Ratio and Proportion

Ratio and Proportion

A Ratio tells us how much of one thing there is compared to another

What do we use Ratios for?

• Recipes (100ml flour to 1 part salt)

• Building (4 parts sand to 1 part cement)

• Maps (1cm to 1km/mile)

• Plans (scale drawings)

• Mixing drinks (1 part cordial to 6 parts water)

• Infection Rates (1 person may infect 1.5 other people, etc)

Sharing Ratios (for example, how do we split £24 in the ratio 3:1)?

• Add the Ratio Numbers up (3:1 3+1 = 4)

• Divide £24 by 4 = £6

• Multiply each part of the ratio by £6

• 3 x 6 = 18, and 1 x 6 = 6

• Check the amounts add up correctly (£18 + £6 = £24)

Multiple Choice

Bob and Ben win £100 and agree to split the winnings in the ratio 2:3 How much does Ben get?

• £30

• £40

• £50

• £60

Multiple Choice

Kate and Gill's meal comes to £35 and they agree to split in the ratio 1:4 How much does Gill pay?

• £7

• £14

• £21

• £28

Open Ended

A baker makes 1 white sandwich for every 4 brown sandwiches. Today he has mad 350 sandwiches; how many were white?

Proportion

You can use Proportion to scale up and down

Direct Proportion

• If an amount is directly proportional to another, it means that as one amount increases, the other amount increases at the same rate

• To calculate Direct Proportion, find the value of ONE UNIT (by dividing) and then MULTIPLY using that value

Multiple Choice

A photocopier can copy 16 pages per minute.

How many pages can copied in 7.5 minutes ?

• 100 pages

• 120 pages

• 160 pages

• 175 pages

Multiple Choice

Every 30 seconds, you can text 35 words. How many words can you type in 5 mins?

• 1200

• 350

• 1000

• 1,800

Inverse Proportion

(the opposite of Direct Proportion)

• If an amount is inversely proportional to another, it means that as one amount increases, the other amount decreases at the same rate

• To calculate Inverse Proportion, find the value of ONE UNIT (by multiplying) and then DIVIDE using that value

Multiple Choice

3 workers build a wall in 12 hours. How long would it have taken for 6 equally productive workers?

• 6

• 12

• 36

• 48

Multiple Select

12 men can dig a pond in 8 days. How many men can dig it in 6 days?

• 20

• 15

• 16

• 24

Multiple Choice

The number of hours to paint a house varies inversely with the number of painters working. A 2400-square foot house can be painted in 27 hours by 6 painters. How many painters would need to work in order to paint the house in 18 hours?

• 8 painters

• 10 painters

• 9 painters

• 11 painters