- Books Name
- CBSE Class 7 Mathematics Book

- Publication
- Param Publication

- Course
- CBSE Class 7

- Subject
- Mathmatics

** Ratio and Proportion**

**Ratio**

A ratio is the comparison of two or more quantities of same kind using division or we can define ratio of two quantities a and b of the same kind in the same units as a fraction which is written generally as a : b (read as ‘a’ is to ‘b’). In the ratio a : b, ‘a’ is called the first term or antecedent and ‘b’ is called the second term or consequent.

**RATIO IN SIMPLEST FORM OR LOWEST TERM**

A ratio is said to be in its simplest form or lowest terms when its terms do not have common factor except 1.

**Note :**

1. Ratio only exists between quantities of same kind :

(i) There exists no ratio between the height of a child and the weights of a child.

(ii) We cannot write a ratio between the age of a student and the marks obtained by the student.

2. To find a ratio between the quantities of same kind, quantities should be expressed in same units.

3. Ratio has no unit.

**(I) Comparison of Ratio: ** Two ratios can be compared by converting them to like fractions. If the two fractions are equal, we say that two given ratios are equivalent.

** Illustration 1 **

Express the ratio 36 : 81 in the simplest form.

** Solution **

H.C.F. of 36 and 81 is 9

- Books Name
- class 7 Mathematics Book

- Publication
- ReginaTagebücher

- Course
- CBSE Class 7

- Subject
- Mathmatics

**Chapter -8**

**Comparing Quantities**

**The Ratio**

**Introduction to ratio**

Ratios are used to compare quantities.

Symbol ':' is used to denote ratio.

• For a ratio, the two quantities must be in the same unit. If they are not, they should be expressed in the same unit before the ratio is taken.

**Example: ** If there are four girls and seven boys in a class, then the ratio of number of girls to number of boys is **4:7**.

g. Cost of 6 pens is Rs 90. What would be the cost of 10 such pens?

**Solution:** Cost of 6 pens = Rs 90

Cost of 1 pen = 90 ÷ 6 = Rs 15

Hence, cost of 10 pens = 10 × 15 = Rs 150.

**Application of ratios**

Ratios have numerous applications in various fields on a daily basis.

- Used in finance - Current ratio, debt-equity ratio, etc.
- Used in chemistry to know the ratio of quantity of chemicals to be mixed in a chemical reaction.
- Used to solved mathematical problems involving - speed-distance-time, boat and stream problems,etc

**Equivalent ratios**

- By multiplying numerator and denominator of a rational number by a non zero integer, we obtain another rational number equivalent to the given rational number. These are called
**equivalent ratio**.

**Example **

And

**Unitary method**

Unitary method is the method of finding the value of one unit (unit rate) at first and then the value of required number of units

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###### Medha Sharma

Course : CBSE Class 7

Start Date : 06.12.2022

End Date : 18.07.2023

Types of Batch : Classroom