# Direct proportion - currency problems

## Home learning focus

Learn how to use direct proportion to solve currency problems.

This lesson includes:

- two videos
- two interactive activities

# Learn

**Calculating amounts using proportions**

Proportion calculations can be used to calculate values when one relationship is known.

Example: 8 pencils cost £2.16. Calculate how much 7 pencils cost.

To find out the cost of one item, divide the cost by how many items have been bought. Any amount can be calculated when the value of 1 is known.

8 pencils cost £2.16.

Divide both numbers by 8:

8 pencils ÷ 8 = 1 pencil

£2.16 ÷ 8 = £0.27

Multiply both numbers by 7:

1 pencil × 7 = 7 pencils

£0.27 × 7 = £1.89

So 7 pencils cost £1.89.

**Comparing best buys**

Proportion calculations can be used to decide which items in a shop offer the best value. Many items sold in supermarkets have a price per item and a price per 100g or per kg. This lets people compare products and get the best value for money.

It is generally easier to make the size of the items the same but how this is done can vary depending on the numbers that are used.

**Example**

If 2 kg of basmati rice costs £2.68 and 500 g of long grain rice costs £0.95 which one represents the best value for money?

There are many ways to approach this problem, for example:

- calculate the cost of 500 g of basmati rice in the 2 kg bag
- calculate the cost of 2 kg of long grain rice from the 500 g bags

For this solution, the cost of 1 kg for each of the bags will be calculated.

Price per kg for basmati rice:

£2.68 ÷ 2 = £1.34

Price per kg for long grain rice:

£0.95 × 2 = £1.90

This shows that basmati rice is cheaper per kg and better value for money than the long grain rice.

# Practise

## Activity 1

**Proportion questions**

Have a go at the worksheet below from Collins. You can print it out or write the answers on a piece of paper.

## Activity 2

**Converting currency colours**

Print out the worksheet below from Beyond, or use an image editing program to colour in the pieces of the picture. Choose the correct colour by converting the currencies.

# There's more to learn

Have a look at these other resources around the BBC and the web.