Proportion
Exercise 1 (Page 1, & 2) - Example
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Tom travelled
60
miles in
1
hour and
120
miles in
2
hours.
The ratio of time is 1 hour to 2 hour = 1:2
The ratio of distance is 60 miles to 120 miles = 60:120
1:2 and 60:120 are equivalent ratios.
1:2 = 60:120 (or) 1:2 :: 60:120 (or) 1/2 = 60/120
A proportion can be written as = or ::
In 1:2 :: 60:120 ==> 1 and 120 are EXTREMES & 2 and 60 are MEANS.
IN A PROPORTION,
PRODUCT OF EXTREMES (1 X 120 = 120)
=
PRODUCT OF MEANS (2 X 60 =120)
.
To test for proportion either use equal ratio or cross product.
1. Is 2:12 = 5:30 a proportion.
2/
12
=
5
/30 check for cross products (products of extremes and means).
2 x 30 = 60 &
5 x 12
= 60
60 = 60 hence 2:12 = 5:30 is a proportion.
2. Find the value of y in: 1:9 = y:54
1/9 = y/54
1 x 54 = y x 9
54 = y x 9
54/9 = y
6 = y
3. The ratio of father to son age is 5:1, if dad is 40 years old, how old is the son?
(Father age is 5 parts and Son age is 1 part.
5 parts = 40 ==> 1 part = 40/5 = 8)
5:1 = 40:X
5/1 = 40/X
X = 40 x 1/5 = 8
8 years old.
4. The ratio of father to son income is 5:2, if the total income is 14,000 dollars, find their individual income?
Father income is 5 parts and Son income is 2 parts.
Total = 5 + 2 = 7 parts
7 parts = 14,000
1 part = 2,000
Father income = 5 parts = 5 x 2000 = 10,000 dollars
Son income = 2 parts = 2 x 2000 = 4,000 dollars
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