Ratios are usually written in the form a:b and can be used on maps to show the scale in relation to real life. Two quantities are in direct proportion when they increase or decrease in the same ratio.

Part of

- Question
Dave and Lisa win between them. They agree to divide the money in the ratio .

How much does each person receive?

The ratio tells us that for every that Dave receives, Lisa will receive .

In other words, this tells us that, of the total amount, Dave will receive parts and Lisa will receive parts. This means that there are parts in total.

represents parts. Therefore, represents part.

Dave receives parts:

Lisa receives parts:

It's important to notice what order the parts of the ratio are written in. is not the same as .

In the example, the ratio of Dave's money to Lisa's was . If we swap the order to then Dave would get more than Lisa.

To keep it the same as in the example we could say that the ratio of Lisa's money to Dave's would be .

- Question
Q1. Amelia and Shabana win a sum of money, which they agree to share in the ratio .

If Amelia receives , how much will Shabana receive?

Q2. A necklace is made using gold and silver beads in the ratio . If there are beads in the necklace:

a) How many are gold?

b) How many are silver?

A1. Amelia receives parts, which is equivalent to . Therefore, represents parts.

represents one part, so one part is .

Shabana receives parts: .

A2. Gold : Silver , so there are parts altogether.

, so part represents beads.

a) Gold beads.

b) Silver beads.