Division in a given ratio

Question

Dave and Lisa win \pounds{500} between them. They agree to divide the money in the ratio 2:3.

How much does each person receive?

The ratio 2:3 tells us that for every \pounds{2} that Dave receives, Lisa will receive \pounds{3}.

In other words, this tells us that, of the total amount, Dave will receive {2} parts and Lisa will receive {3} parts. This means that there are {5} parts in total.

\pounds{500} represents {5} parts. Therefore, \pounds{100} represents {1} part.

Dave receives {2} parts: 2 \times \pounds{100} = \pounds{200}

Lisa receives {3} parts: 3 \times \pounds{100} = \pounds{300}

Order

It's important to notice what order the parts of the ratio are written in. 2:3 is not the same as 3:2.

In the example, the ratio of Dave's money to Lisa's was 2:3. If we swap the order to 3:2 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 3:2.

Question

Q1. Amelia and Shabana win a sum of money, which they agree to share in the ratio 5:3.

If Amelia receives \pounds{150}, how much will Shabana receive?

Q2. A necklace is made using gold and silver beads in the ratio 3:2. If there are {80} beads in the necklace:

a) How many are gold?

b) How many are silver?

Necklace with some gold and some silver pearls

A1. Amelia receives {5} parts, which is equivalent to \pounds{150}. Therefore, \pounds{150} represents {5} parts.

\pounds{150} \div 5 represents one part, so one part is \pounds{30}.

Shabana receives {3} parts: 3 \times \pounds{30} = \pounds{90}.

A2. Gold : Silver = 3:2, so there are {5} parts altogether.

80 \div 5 = 16, so {1} part represents {16} beads.

a) Gold = 3 \times 16 = 48 beads.

b) Silver  = 2 \times 16 = 32 beads.