Class 6 – Arithmetic
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Introduction: In daily life, there are different situations to compare quantities such as heights, weights, distance or time. Two quantities of the same kind are compared in two ways by subtracting the smaller from the bigger or by dividing one by the other.
Ratio: The comparison between two quantities in terms of magnitude is called ratio i.e. it tells us “one quantity is how many times that of other quantity.” We denote ratio using symbol ‘:’. Read as “is to”.
Example: Amit has 5 pens and Saritha has 3 pens it means the ratio of number of pens with Amit and Saritha is 5 is to 3. It can be expressed as ‘5 : 3’. So the ratio of any two quantities is expressed as or a : b. In a : b the numerator ‘a’ is called first term or antecedent and denominator ‘b’ is called second term or consequent. Simplest form of a ratio: In a : b, a and b have only one as the common factor (coprimes), then a : b is called simplest form of the ratio.

Example: Write the simplest form of 18 : 6. Solution: 18 : 6 The HCF of 18 and 6 = 6. The comparison of two quantities is meaningless if they are not of the same kind or in same units. Example: It is meaningless to compare 8 boys with 6 cows or 15 litre with 5 toys. The quantities to be compared, should be expressed in same units. Example: If container A has 125 ml of juice and container B has The ratio of quantity of juice in container A to container B is 1:16 
Example:Consider a ratio 4 : 8
Multiply numerator and denominator by say 12 then
If we divide numerator and denominator by 12 then
∴ The ratio does not change in either case.
Example: Express 36 minutes : 1 hour in the simplest form
Solution: 36 minutes : 1 hour
Example: If ` 1250is divided between Mayank and Istha in the ratio 3 : 2 then find the share of each.
Solution: Total money = `1250
Given ratio = 3 : 2
Sum of terms in the ratio =(3 + 2) = 5
Mayank’s share ` 750
Istha’s share ` 500
Example: Shukla earns `14000 per month and Mishra earns ` 18000 per month. Calculate the ratio of Shukla’s salary to Mishra’s salary.
Solution:
Example: Total number of boys and girls in a school is 1056. The number of girls is equal to 480. Find the ratio of number of boys to girls.
Solution: Total number of boys and girls = 1056
Number of girls = 480
Number of boys = 1056 – 480 = 576
Comparison of ratio: Two ratios can be compared by expressing them with a common denominator. i.e.,
To compare and , wewrite them with a common denominator as respectively.
Example: Compare and .
Solution: and
L.C.M of 4 and 9 = 36
Compound ratio: If two or more ratios are multiplied corresponding term wise, the ratio thus obtained is called their compound ratio.
The compound ratio of a :b and c : d is ac : bd
Example: Find the compound ratio of 2 : 3 and5 : 7
Solution:= (2 × 5): (3 × 7) = 10 : 21
Example: Express in its simplest form
Solution:
L.C.M. of 4, 2, 6 = 12
Example: Which ratio is greater?
13 :24 (or) 17 : 32
Solution:
LCM of 24, 32
Clearly,
Hence,
Example: Compare and .
Solution: and
LCM of 3 and 21 = 21
Here, both ratios are equal.
1. Ratio has no units.
2. The ratio does not change if the numerator and denominator is multiplied or divided by the same nonzero number.
In the following diagram
what is the ratio of shaded squares to unshaded squares?
There are 5 shade squares and 11 plane squares, so the ratio is 5 : 11.