1. What is Ratio?
A ratio is a numerical comparison between two or more things of the same kind.
Ratios are generally written as ⟶ a:b or a⁄b
For example:
The number of boys and girls in the class of 10 students is 4 and 6 respectively.
So the ratio of the number of boys to the number of girls will be 4 : 6 (or 4/6).
First term of the ratio (here 4) is called antecedent and the second term (here 6) is called subsequent.
1.1 Different forms of Ratios
Ratio of the simplest form:
When we have a ratio which has bigger numbers, then if we divide each number of the ratio by the highest common factors we get the ratio of the simplest form.
For example, the simplest form of the previous example’s answer.
Equivalent ratio:
Equivalent ratios are such ratios all of which have the same simplified ratio.
For example, the ratios from previous example are equivalent ratios
Part to Part or Part to Whole:
The ratios can be, broadly speaking, written down in two different ways. It's either part to part or part to whole.
For example:
Arya has 10 pairs of shoes, 4 of them are pink and 6 of them are white.
The ratio of pink shoes = 4 : 10 or 2 : 5, is a part to whole ratio.
The ratio of pink to white shoes = 4 : 6 = 2 : 3, is a part to part ratio.
1.2 Types of questions asked in GCSE
Work out the ratio:
In such questions you will be calculating the ratio from given informations
Example:
Anna has a box of marbles which contains 20 marbles out of which 5 are blue and others are red. Write the ratio of red marbles to blue marbles.
Simplify the ratio:
In these types of questions you need to divide each number of the ratio with their highest common factor.
Example:
Simplify : 15 : 3 : 12
Dividing into a ratio:
In these types of questions you will need to use the ratio to divide things.
Example:
Divide 10 chocolates between Joey and Rebecca into the ratio of 1 : 4.
Convert ratio into fraction:
In these types of questions you need to convert the ratio into fraction using the given information.
Example:
The ratio of the number of boys to the number of girls was 4:5 at a party. What fraction of children were boys at the party?
Convert ratio to percentage:
In these types of questions you need to convert the ratio into percentage, which is nothing but an extension of conversion of ratio into fraction but here you need to multiply that fraction with 100.
Example:
A coin collector has 10p coins and 20p coins in the ratio of 13:7. What percentage of coins are 10p in his collection?
Calculating the scale factor or ratio in 1:n (or n:1) format
A sketch of a tower with a length of 100 m is to be drawn on a sheet of 20 cm in length. Find out the ratio of scale which could be used to draw the tower on the sheet?
