Fractions, Decimals And Percentages JSS2 Mathematics Lesson Note

 FRACTIONS (TYPES OF FRACTIONS), RATIO AND PERCENTAGES

A fraction is a small part or item forming a piece of a whole. It is the quotient of the rational numbers.

Types of Fractions

EQUIVALENT FRACTIONS: Examples are 2/5 = 4/10 = 8/20 = 16/40

IMPROPER FRACTIONS: Examples are 13/2, 100/7, 67/5,102/5

MIXED FRACTIONS: 72/3, 91/8, 1421/2 etc.

RATIOS, DECIMALS, AND PERCENTAGE

RATIO is the relative magnitudes of two quantities (usually expressed as a quotient).

Example 1: In a bus station, the ratio of men to women is 2:5 (a) what fraction of the people are men (b) what fraction of the people

Solution:

2:5 = 2+5 = 7

The fraction of men = 2/7 (i.e. the fraction of men over the total fraction)

The fraction of women = 5/7 (i.e. the fraction of women over the total fraction)

Example 2: The population of a country is estimated to be 12 million people. The last survey reveals that 40% were boys, 30% were girls, 10% were men and 20% were women. Express the composition in ratio and evaluate the estimated number of people in each category.

Solution:

40% (boys)           30% (girls)              20% (women)          10% (men)

Step 1: eliminate the % first = 40                30                20                10

Step 2: divide through by 10 to reduce the value = 4       3        2          1

Therefore we have 4:3:2:1 = 4 + 3 + 2 + 1 = 10

Step 3: find the people for each category.

MEN = 1/10 * 12 000 000 = 1 200 000 (ZERO CANCEL ZERO)

WOMEN = 2/10 * 12 000 000 = 2 400 000 (ZERO CANCEL ZERO)

GIRLS = 3/10* 12 000 000 = 3 600 000 (ZERO CANCEL ZERO)

BOYS = 4/10 * 12 000 000 = 4 800 000 (ZERO CANCEL ZERO)

THEREFORE: 4 800 000 + 3 600 000 + 2 400 000 + 1 200 000 = 12 000 000.

FRACTION AND DECIMALS TO PERCENTAGES 

Example 1: Express the following fraction to percentage (a) 5/12 (b) 120/500 (c) 0.009

Solution:

5/12 * 100 = 500/ 12 = 412/3

120/500 * 100 = 24%

0.009 = 9/1000 * 100 = 0.9%