
Ratios and Proportions



Ratio

Proportion

Ratios
and proportion properties

Direct proportion

Cross product, means and extremes






Ratio 
A ratio is a comparison of two similar quantities obtained by dividing
one quantity by the other. 
A ratio can be written as,
a
:
b
or as a fraction a/b
or by the phrase ' a to
b '. 
A ratio is a way in which
quantities can be divided or shared. It shows how much bigger one
thing is than
another. 
Make
the numbers in ratios smaller so that they are easier to
compare. Do this by dividing each side of the ratio
by the same number, the highest common factor. 

Proportion 
A proportion is
a statement of the equality of two ratios. If the fractions both reduce
to the same value, the proportion is true. 
Example: 

9
: 6 = 3/2
and, 21
: 14 = 3/2,
follows,
9 :
6 = 21 : 14. 


Ratios and proportion properties

A ratio's value is not altered if both the first and second term are
multiplied or divided by the same number different from zero. 

a
:
b =
(a · c)
:
(b ·
c) 








Two quantities are in
direct proportion when they increase or decrease in the same ratio. 

When two ratios are equal, then the
cross products of the ratios are equal. 

That is, 
a
:
b = c
:
d 
or 



the
product of the means is equal to the product of the extremes.

The
first and last term in a proportion are called the extremes, the
second and third terms are called the means.

If any three terms in
a proportion are given, the fourth may be found. 






the
extremes 

the
means 



Examples: 
a)
2
:
x =
6 :
15 

b)
8
:
(x

1)
= 2 :
7 

c)
(7

x)
:
3 =
4x :
9 





9 · (7

x) =
3 ·
4x 



63

9x
= 12x 

x = 5 

x = 29 

21x = 63
 ¸
21 





x = 3 


The first and third terms, and the second and the fourth terms in a
proportion are the corresponding terms. 







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