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Encapsulate
math

RATIO AND PROPORTION

Ratio Proportion

A comparison of two quantities a and b of same The equality of two ratios is called proportion.
kind by division is called a ratio. It is denoted by the symbol (‘: :’) or (‘=’).
a ← Antecedent
It is denoted by a : b or , If a : b and c : d are in proportion,
b ← Consequent
where b ≠ 0. then a = c or a : b : : c : d
Properties: b d
• It has no unit. ⇒ a × d = b × c
• It can be expressed in the simplest form. i.e., product of extremes = product of means
E.g., 5 : 15 = 1 : 3
• The order of terms is obligatory i.e., 3 : 4 ≠ 4 : 3

Continued Proportion
Equivalent Ratio
If three numbers a, b, and c are in continued
If a ratio is multiplied and divided by the same
non-zero number, the resultant remains same. proportion,
×
×
3 32 6 3 33 9 then, a : b : : b : c
E.g., = = , = = E.g., If 4, 20, and 100 are in continued
×
×
8 82 16 8 83 24
Here, 3 : 8, 6 : 16 and 9 : 24 are the equivalent proportion, then
ratios. 4 : 20 : : 20 : 100
Comparing Ratios
Mean Proportion
• Write ratios in fraction form.
• Make denominators equal by taking LCM of If b is the mean proportional of a and c,
denominators of fraction. then b = ac
2
• Fraction with greater numerator is greater.
E.g. Consider, 4 : 7 and 5 : 9 E.g., 6 is the mean proportional of 18 and 2
2
(LCM of 7 and 9 is 63) as 6 = 18 × 2
4 49 36 5 57 35
×
×
So, = = and = =
×
×
7 79 63 9 97 63
Q 36 > 35
4 5 Third Proportion
\ > . So, 4 : 7 > 5 : 9
7 9 If three numbers a, b, and c are in continued
proportion, then c is called the third
Simplest Form of Ratio proportion.
E.g., In the proportion 5 : 10 :: 10 : 20, 20 is
The ratios are reduced into the simplest form
by dividing the numbers on both terms of the the third proportion.
ratio by their highest common factor.
E.g., The simplest form of 14 : 18 is 7 : 9 as the
HCF of 14 and 18 is 2.

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