# CLASS-10RATIO & PROPORTION - INTRODUCTION OF RATIO

RATIO

If a & b are two non zero (a ≠ 0 & b ≠ 0) quantities of the same kind and in the same units, then the

a

fraction ------ is considered the ratio between a & b, written as a : b

b

[should be read as “a is to b”]

Terms of a Ratio

In the ratio a : b, we call a, the first term or antecedent and b, the second term or consequent.

Example.1) Richard is 20 years old and his sister Pamela is 25. We can say that the ages of Richard & Pamela are in the ratio 20 : 25

Example.2) The cost of a pencil is \$ 2 and that of an eraser is \$ 1. We say that the cost of a pencil and that of an eraser are in the ratio 2 : 1

Example.3) There is no ratio between 8 km and 15 kg, as these quantities are not of the same kind and have different units, which are not inter-convertible.

An Important Property

The value of a ratio remain unchanged, if both of its terms are multiplied or divided by the same non-zero number.

Proof:- Let a : b be the given ratio and let ‘n’ be a non-zero number.

a

Then we may write, a : b as ------

b

a          na

(i) Clearly we have ------ = -------

b          nb

above equation shows that, a : b is the same as na : nb

a         (a/n)

(ii) We may write, ------ = -------

b         (b/n)

a          b

This shows that a : b is the same as ------ : ------

n          n

A ratios in its lowest terms

What a & b have no common factor, other than 1, we say that a : b is in its lowest terms.

a) To convert an ordinary ratio into its lowest terms, we divide both the terms by their H.C.F.

45        27

Thus, 45 : 27 = ------ : ------ =  5 : 3    (in lowest term)                                                                                                                      9         9

70         40

70 : 40 = ------- : ------- = 7 : 4       (in lowest term)

10         10

b) If the terms of a given ratio are fraction, then we convert them into whole numbers by multiplying each term by the L.C.M. of their denominators.

1          1          1              1

Thus, ------ : ------ = (----- X 6) : (----- X 6)

2          3          2              3

=      3 : 2        (Ans.)