Fractions (like Percentages and Decimals) are always present in the Numerical Aptitude section of the Civil Service Exam so better be acquainted with the basics of it before you take the test.
What is a FRACTION? A fraction is simply a part of a whole number. It is also a number you get from dividing one whole number by another.
HOW TO PERFORM THE BASIC MATH OPERATIONS ON FRACTIONS
ADDING or SUBTRACTING FRACTIONS: Before you can add or subtract fractions, you have to make sure that they are LIKE fractions. Like fractions are fractions which have the same DENOMINATORS (The numbers below the bar line). If you are adding or subtracting like fractions, you simply keep the denominator and then add or subtract the NUMERATORS (The numbers above the bar line):
- 1/5 + 2/5 = (1+2)/5 = 3/5
- 6/15 — 3/15 = (6—3)/15 = 3/15
If the fractions you need to add or subtract are UNLIKE fractions (Meaning, they have different denominators), we need to make them like fractions first before we can add or subtract them.
How to Convert Unlike Fractions to Like Fractions
To do that, we need to find the least common multiple (LCM) of the denominators and work on each of the fractions separately. Divide the LCM with the denominator and multiply the quotient with the numerator. The result will be the new numerator, and the LCM will be the new denominator. For example:
- 3/5 + 2/8 =
STEP 1: Find the LCM of the denominators 5 and 8
The LCM is 40.
STEP 2: Divide the LCM with the denominators
STEP 3: Multiply the quotient with the numerators:
40 ÷ 5 (denominator) = 8 x 3 (numerator) = 24
>>> 3/5 = 24/40
40 ÷ 8 (denominator) = 5 x 2 (numerator) = 10
>>> 2/8 = 10/40
So, 3/5 + 2/8 = 24/40 +10/40 = 34/40 or 17/20 (lowest term)
MULTIPLYING FRACTIONS: Simply multiply the numerators to get the new numerator and multiply the denominators to get the new denominator:
- 2/3 x 4/7 = (2×4)/(3×7) = 8/21
DIVIDING FRACTIONS: To divide fractions, get the reciprocal of the divisor and multiply it with the dividend:
- 3/7 ÷ 2/3 = 3/7 x 3/2 (the reciprocal of 2/3) = (3 x 3)/ (7 x 2) = 9/14
How to Reduce Fractions to Lowest Terms
To reduce a fraction to its lowest terms, divide both the numerator and denominator by their greatest common factor
8/10 = Find the factors of 8 and 10:
Factors of 8 = 1, 2, 4, 8
Factors of 10 = 1, 2, 5, 10
GCF = 2. Now divide the numerator and denominator:
(8 ÷ 2) / (10 ÷ 2) = 4/5 is the lowest term of 8/10