# Ratio and Percentage

Topics in this chapter:
**Ratio**
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Let us say there was a mathematics examination, and three candidates Susan, Carla and Ryan gave the exam.

Susan scored 100 marks.

Carla scored 80 marks.

Ryan scored 70 marks.

The ratio of their scores can be recorded as 100:80:70.

Since 10 is common factor among the numbers, it can be further simplified to - 10:8:7.

Therefore the ratio of scores of Susan, Carla and Ryan are 10:8:7.

Note: To compare quantities as ratios, their units must be the same.

__Ratio and Proportions:__Ratios are very useful to expressing proportions of quantities.

For instance, let us say we draw a diagram of a rectangle for a construction site.

We can use the following to scale the diagram.

Say,

Actual width of rectangle = Wa

Actual Height of Rectangle = Wh

Width of rectangle in drawing = Wd

Height of rectangle in drawing = Hd

Wa / Wh = Wd / Hd

**Percentage**
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Percentage is useful tool for comparing quantities.

Percentage is represented by the symbol %, and it can be represented in fraction and decimal forms.

Example:

Percentage format: 3%

Fraction format: 3/100

Decimal format: 0.03

Example:

Consider three students, Carla, Susan and Ryan. They scored the following in Mathematics examination out of 150 marks.

Carla: 120 marks.

Susan: 78 marks.

Ryan: 89 marks.

Percentages:

Carla: (120 / 150) x 100 = 80%

Susan: (78 / 150) x 100 = 52%

Ryan: (89 / 150) x 100 = 59.33%