**Ratio and Proportion 7th grade :**

In this section, we will learn ratio and proportion.

**What is ratio ?**

The comparison of 2 quantities of the same kind by means of division is termed as ratio.

Ratio is a way to compare two or more quantities of the same kind

- The ratio of two non-zero quantities a and b is written as a : b. It is read as “a is to b”
- The ratio is represented by the symbol “ : “
- a and b are called as the terms of the ratio. "a" is called as the antecedent and "b" is called as the consequent
- The ratio is represented in numbers and it does not have any unit.
- Order in a ratio is important. a : b is different from b : a.

**What is proportion ?**

An equality of two ratios is called a proportion.

Four quantities a, b, c, d are said to be in proportion,

if a : b = c : d (also written as a : b :: c : d).

That is, a/b = c/d.

The quantities a, b, c, d are called terms of the proportion; a, b, c and d are called its first, second, third and fourth terms respectively.

First and fourth terms are called extremes (or extreme terms). Second and third terms are called means (or middle terms).

**Cross product rule :**

In a proportion,

product of extremes = product of means.

If a : b = c : d are in proportion, ad = bc.

This is called cross product rule.

**Example 1 :**

Express the following ratios in the lowest form :

1 kg to 500 g

**Solution :**

To represent the above two quantities using ratio, we have to convert both quantities of same kind.

1 kg = 1000 gram

1000 : 500 = 1000/500

= 2 / 1

= 2 : 1

**Example 2 :**

Express the following ratios in the lowest form :

45 minutes to 2 hours

**Solution :**

To represent the above two quantities using ratio, we have to convert both quantities of same kind.

1 hour = 60 minutes

45 : 60 = 45/60

= 9 / 12

= 3 : 4

After having gone through the stuff given above, we hope that the students would have understood ratio and proportion.

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