 # RATIO, PERCENTAGE AND POPULATION ISSUES

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Percentages are used to indicate fractions. When a fraction is written with 100 as the denominator it is called a percentage. It has the symbol %. So, 25% means 25 out of every 100.

Percentages often indicate proportions. For example, labels in clothes indicate proportions of different yarns in the fabric. 100% is the same as the whole, or one hundred per hundred.

40/100 (or 0.4) is polyester.

Example:

1. A building society offers 90% mortgages to first-time buyers. How much would the Smiths get on a house valued at N150,000?

Solution:

They want to find 90% of N150 000. 90% =90/100  = 0.9.

0.9 × 150 000 = 135, 000

So, the Smiths would get N135,000

ACTIVITY

1. Express each of the following percentages as fractions:
• (a) 40%
• (b) 8%
• (c) 70%
• (d) 5 1/2%
1. Express each of the following percentages as decimals:
• (a) 50%
• (b) 85%
• (c) 7%
• (d) 7  1/2%

Converting to a percentage

Fe converted to percentages, by multiplying by 100%.

So, for example, 0.17, 0.3 and can be expressed as percentages as follows:

0.17 × 100% = 17%;

0.3 × 100% = 30%;

Decimals or fractions bigger than 1 correspond to percentages greater than 100%. For example,

= 1.75, which as a percentage is 1.75 × 100% = 175%.

ACTIVITY

1. Convert each of the following to percentages. Round off the percentages to whole numbers.
• (i) 0.8
• (ii) 0.21
• (iii) 0.70
• (iv) 2.4

(b) (i)      1/2     (ii)     1/8     (iii)      1/9       (iv) 1 1/7

1. Express each of the following percent as a ratio:

(i) 12 % (ii) 11/2 % (iii) 4/5 % (iv) 6.5 % (v) 0.28%

1. Convert each of the following percent as ratio:

(i) 25 % (ii) 115 % (iii) 62/5 % (iv) 0.8 % (v) 6.72 %

Word Problem on Percentages

Example: In a basket of apples, 12% of them are rotten and 66 are in good condition. Find the total number of apples in the basket.

Solution:

Let the total number of apples in the basket be m

12 % of the apples are rotten, and apples in good condition are 66

Therefore, according to the question,

88% of m = 66

88/100 × m = 66

m = (66 × 100)/88

m = 3 × 25

m = 75.      Therefore, total number of apples in the basket is 75.

ACTIVITIES

1. In an examination, 300 students appeared. Out of these students; 28 % got first division, 54 % got second division and the remaining just passed. Assuming that no student failed; find the number of students who just passed.
2. An alloy contains 26 % of copper. What quantity of alloy is required to get 260 g of copper?
3. In an exam Ashley secured 332 marks. If she secured 83 % makes, find the maximum marks.

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