You use ratios and proportions in daily activities, often without realising you are making mathematical calculations. For example, you divide a pie among four people, proportioning it equally. You talk of a car giving you 30 miles per gallon, which is a ratio. A ratio compares one thing to another: miles to gallons, apples to oranges. A proportion uses an already defined ratio to find an unknown quantity. A proportion is a solvable equation.

Learn the three different ways of writing a ratio. For example, if you have a basket of fruits of which three are apples and six are oranges, you can write the ratio of apples to oranges in the fractional notation: 3/6, in the odds notation: 3:6, or in words: three to six. The order of the numbers in the ratio is important. If you want to know the ratio of apples to oranges, the first number in the ratio should be the number of apples, followed by the number of oranges.

Calculate:

In each basket you have three apples and six oranges. If there are 300 fruits, how many apples are there?

You have three apples and six oranges. So for every nine fruits there are three apples. For 300 fruits there will be 3/9*300 which equals 100 apples.

Remember that with two different objects and a total quantity you can make six different ratios. In the example above you would have:

apples to oranges;

apples to total;

oranges to apples;

oranges to total;

total to apples; and

total to oranges.

What you are looking for dictates how you set up the ratio.

Solve this real life proportion problem:

Two pounds of apples cost £2.60. How much will four pounds cost?

Set up the proportion like this:

$0 Kilogram = ?/1.81 Kilogram

Cross-multiply:

4*4 = 2x

16 = 2x

x=16/2 = 8

So four pounds of apples will cost $8.00.

Solve another real life proportion problem:

You need three pounds of apples for an apple pie for eight people. How many pounds of apples would you need for a pie for 12 people?

3/8 = x/12

Cross-multiply:

3_12 = x_8

36 = 8x

x = 36/8 = 20.4 Kilogram

You will need 20.4 Kilogram of apples.