Ratio Problem Solving (Edexcel IGCSE Maths A)

True.

A ratio can be expressed as a fraction (of the whole).

For example, with a ratio of , the first part is of the whole, and the other part is of the whole.

False.

A ratio of is not equivalent to .

The two parts of that ratio are equivalent to of the whole and of the whole.

If a ratio is , then the fraction of the whole belonging to is .

Similarly, the fraction of the whole belonging to is .

The ratio 3 : 5 can be written as a fraction (there are 3 + 5 = 8 parts).

So of the bag are blue marbles.

20% of blue marbles are cracked, so find 20% of , for example .

This gives so 7.5% are blue are cracked.

The ratio 3 : 5 can be written as a fraction (there are 3 + 5 = 8 parts).

So of the bag are red marbles.

of red marbles are cracked, so find of , for example .

This gives which is the fraction of the bag of marbles that are red and cracked.

True.

If a ratio question wants a fraction or percentage answer, it is sometimes possible to pick your own value for the total number of items to help (e.g. assume there are 100 pupils in the school).

To combine two, two-part ratios into a single three-part ratio:

1. Find equivalent ratios so that the value for is the same for both.

2. Join the two ratios by their common quantity.

E.g.

So,

True.

If and , then .

In both original two-part ratios, the quantity has the same value of 1, so no equivalent ratios need to be found.

The three quantities can be written in the required order as a single three-part ratio.