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Ratio and Proportion (Part I)

The document explains the concepts of ratio and proportion, defining ratio as a comparison of two quantities of the same kind and proportion as an equation stating that two ratios are equivalent. It emphasizes the importance of having similar units when comparing ratios and provides examples and exercises for solving and equating ratios. Additionally, it discusses the impact of arithmetic operations on ratios and includes various problems for practice.

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Suyog Chandelkar
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17 views15 pages

Ratio and Proportion (Part I)

The document explains the concepts of ratio and proportion, defining ratio as a comparison of two quantities of the same kind and proportion as an equation stating that two ratios are equivalent. It emphasizes the importance of having similar units when comparing ratios and provides examples and exercises for solving and equating ratios. Additionally, it discusses the impact of arithmetic operations on ratios and includes various problems for practice.

Uploaded by

Suyog Chandelkar
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Ratio : - Comparison or simplified form of two quantities of the same kind is

referred to as ratio.
This relation gives us how many times one quantity is equal to the other quantity. In
simple words, the ratio is the number which can be used to express one quantity as a
fraction of other ones.
The two numbers in a ratio can only be compared when they have the same unit. We
make use of ratio s to compare two things. The sign used to denote a ratio is ‘:’.
2
A ratio can be written as a fraction also like .
5
Key points to remember
- The ratio should exist between the quantities of the same kind
- While comparing two things, the units should be similar
Example : - A : B = 3 : 4
Here if the total amount is 7, then the value of A will be 3 and the value of B will be
4
Note - A is also called as antecedent and B is also called consequent.
Proportion : - Proportion is an equation which defines that the two given ratios
are equivalent to each other. In other words, the proportion states the equality of
the two fractions or ratios.
When two ratios are equal in value, then they are said to be in proportion. In
simple words, it compares two ratios. Proportions are denoted by the symbol
‘: :’ or ‘=‘.
if a, b, c, and d are proportional a : b : : c : d Then a × d = b × c Here, two terms
b & c are called “ Means”/ Mean term whereas the terms ‘a’ & ‘d’ are known as
extremes or extreme terms.
Ratio is an expression whereas proportion is an equation.
Impact of Addition, Subtraction, Multiplication & Division on Ratio
Total Quantity Ratio 1st Part 2nd Part 3rd Part
100 2:3 40 60 -
200 3:5 -
300 1:2:3
400 2:3:5
150 200 150
600 7:3:2
11 : 12 : 12 220
800 4:7:? 160
11 : ? : 7 480 280
1400 9:4:? 750
Total
Ratio Boys Girls Difference
Students
13 : 7 120
56 63
91 169
11 : 8 32
35 (B > G) 105
19 : 13 30
20 (B < G) 80
13 : ? 4 100
Solving Ratios

1. If 2a = 3b, then a : b = ?

2. If 11a = 7b, then a : b = ?

3. If 4a = 6b = 5c, then a : b : c will be


equal to:
4. If 5A = 13B = 7C, then find the value
of A : B : C.

1 3 5
5. If a = b =
3 4 7
c then a : b : c will be
equation to:
4 7 11
6. If a = b = c then a : b : c will be
3 5 2
equation to.

7. 62.5% of a = 15b then a : b will be


equal to.

8. If 12.5% of B = 11A then A : B will be


equal to.
2
9. If of A = 75% of B = 0.6 of C then
3
A : B : C is.

10. If 0.7A = 1.2B = 0.3C then A: B: C = ?


11. If 0.5A = 0.07B = 1.2 C then A:B:C = ?

1 1
12. If x = 3 y and y = 2 z then x : y : z = ?

2 3
13. If A = B and B = C then A : C will
3 4
be ?
Equating Ratios
1. If a : b = 7 : 9 , b : c = 3 : 5 then the
value of a : b : c is.

A 5 B 11
2. If = & = then A : B : C is.
B 7 C 7

3. If a : b = 7 : 9 and b : c = 5 : 7 then
what is a : c
4. If A : B = 3 : 4, B : C = 5 : 7 and
C : D = 8 : 9 then A : B : C : D is equal to.

5. If A : B = 3 : 4, B : C = 5 : 6 and
C : D = 2 : 3 then A : B : C : D will be equal
to.
2 1 2 5
6. If a : b = ∶ , b : c = ∶ and
9 3 7 14
7 3
d:c= ∶ then a : b : c : d is.
10 5

a) 4 : 6 : 7 : 9

b) 16 : 24 : 30 : 35

c) 8 : 12 : 15 : 17

d) 30 : 35 : 24 : 16

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