Page 25 - WCS - Electrical

WORKSHOP CALCULATION & SCIENCE - CITS

EXERCISE 2 : Ratio & Proportion

Square root, Ratio and Proportions, Percentage -

Ratio and proportion

Ratio
Introduction
It is the relation between two quantities of the same kind and is expressed as a fraction.

Expression
a

a, b two quantities of the same kind. or a:b or a ÷ b or a in b is the ratio.
a b

Ratio is always reduced to the lowest terms.
b a
Example 7 : 14 = 7 = 1 = : 1 2
a b
a a 7 1 14 2
7 : =b = : 1 2
14 =
a b b 14 2
7 : 14 = 7 = 1 = : 1 2 a c
a
b
7
Proportion 14 1 2 =
14:
a a 7 17 7 c = = = : 1 2 b d
1
b
= =
= 14 : 1
: 1 2
2 2
7 14
:
: =
= =
a 14 =
a
7 It is the equality between the ratios, a : b is a ratio and c : d is another ratio. Both ratios are equal. Then
b
b 7 14 24
1
1 2
d a
14 =
7 a :b :: c : d or = = : 1 2 c a
:
=
b b

14
=
7
:
= =
Example 7 a ca 14 = 7 2 a b 1 c d : 1 2 = b
1 c
1 1 db
7 14: = = 7 14 b = 2 : 2 c d
a = = 17
=
7 7 : 14: 14 = ca b db = 14 = 2 d == 2 2 = : 1 : 1 2 2
250 : 2000 :: 1 : 8

=
14
c 14
d a
b
c
ad
b
Proportion fundamentals b d
=
a c = a c b d =
b
a= a ba a b c c b d d = a c
= = =
c
b
d=
If then d
=
b a c d db = a d b d c b d
c
ad
b
• c ad = bc b = d a + b = c + d and a + b = c + d

a b db b = a = c b c a c
d
a + c b = c + d c a + b c + d
b
d

a== ba
a
=
• c b a ca = = dd c and =
c
b
c
c
c = d d a + b c + d a a + b c + d
a bc a + b = c + d and a + b = a − b c − d
d
d
c +
=
=
b c +
a + b a + cb b d + c + d b d a + c a + and c + d a d = c =
b
a
• b= a − d band= d b c c − and = a c b d
b
d c =
=
a + b a b b = = c c + c = d c a + a b a c + c d c
=
a= b c c and b c − d
a
d
a −
b a + b c c + d a = a + b c c + d a + b a c
• = a − and cb − d = = =
a + b c + d b a + b d c + d

=
a + a ba − b + a and dc − dc − c a + b= cb a c + + d d c b + d c d
b
c
d d
c + b−
a + cb
a +
b=
a +
=
= =
= and
= c
b a − b = c − d and b a = d = c
b
b
d d
c
=
• b b b + d c c a + b d a a a c c c 3
b a − b d c − = d a = c = 6
b
a +
b + =
d
b a
a − b
a + a + 3 b= b + dcb b c − c d = c = d 4 8
a
c
b
d
d
6 c − d −
a
a − = −
= =
=
• a + b + db + b b d a c dc = = = d c d c d
d
b = b 4 = 8 3 d 6
b + a + bc ad 3 = c 6 3 4
d
a + b + d = 6 c 4 = d 8 6 = 8
=
3:4::6:8 or cab 3 63
b
3 a= ca
a +
b=
4 c 4
a + =
=
= = =
b + d 3 4 84 = = c 6 8 d 8
6 c c
8 d d
d =
b + db +
• 3 x 8 = 6 x 4 3 4
4 38 6 = 4 8
=
3 3 4 6 6 4 8 3 6 = 4 8 3 = 6

3= 3 43
6
=
4 =
• 3 6 4 6 8 8 8 8 6 8
= =
8
4
=
4
8
4
3
4
6 = 38 6 4 = 8 3 + 4 6 + 8
3 3 + 43= 4 84 6 4 = 8 8 4 3 = 8 6 4 = 8

3
6 +
=
= =
6 = 8 4 4 = 3 + 3 8 6
8
4 8 63 6
4 3
8
6 6
8
6 +
3 = 46 3 + 4 4 = 6 + 8 8
8
=
3 4 3 + 64+ 8 + 6 + 8 4 8 = 8 12
4
6

4== 84 3 8 = 4 8
8
3 + 4 = = 66 + 8
8
34 4
3
3 = 6 6
4 3 + 4 8 6 + 8
=
3 + 4 6 + 8
3 + + 4= 64 4 6 + + 8 8 8
3
4 = = 8
4 4 8 8