 Back to Math

# Math Fractions

Given two numbers i and j.
A fraction is of the form, i / j.
i is called Numerator of the fraction.
j is called Denominator of the fraction.
Example: Say we have two numbers 3 and 4. Fraction is 3/4.

Mixed fraction:
Consider three numbers i, j and k.
A mixed fraction is of the form k (i / j).
Where numerator will be k x j + i.

Operations on fractions:

Consider two fractions i / j and a / b.

The addition of the two fractions is:
i/j + a/b = (i+a)/(j+b)
So the numerator of the addition is the sum of numerators of the operands.
The denominator of the addition is the sum of denomimators of the operands.
Example: 3/4 + 1/7 = (3+1)/(4+7) = 4 / 11

Subtraction of Fractions:
The subtraction of two fractions is:
i/j - a/b = (i-a)/(j-b)
So, the numerator is the subtraction of numerators of the operands.
The denominator is the subtraction of denominators of the operands.
Example: 7/10 - 1/3 = (7-1)/(10-3) = 6/7

Multiplication of Fractions:
Multiply fraction with whole number:
Multiplication of fraction with whole number is repeated addition as many times are the number.
Consider a number m and fraction i/j.
m x (i / j) = i/j + i/j ... m times.
Example: 2 x (1 / 3) = 1/3 + 1/3 = 2/3

Multiplication of fraction with another fraction:
Consider two fractions: i/j and a/b.
i/j x a/b = (i x a) / (j x b)
Example: 3/4 x 7/5 = (3 x 7) / (4 x 5) = 21/20

Division of Fractions:
Before we understand division of a fraction, we should familiarize ourselves with the concept of reciprocal of a fraction.

Reciprocal of a fraction:
Reciprocal of a fraction is switching of numerator with denomiator, and denominator with numerator.

Consider a fraction i / j. Reciprocal of fraction is j / i.
Example: Consider a fraction 2 / 3. Reciprocal of fraction is 3 / 2.

Divide fraction with whole number:
Division of a fraction with a whole number is multiplying the denominator with that number. Consider a fraction i/j and whole number m.

(i / j) / m = 1 / (j x m)
Example: (1 / 4) / 2 = 1 / (4 x 2) = 1 / 8.

Divide fraction with another fraction:
Division of a fraction with another fraction is multiplication of fraction with reciprocal of the second fraction.
Consider two fractions: i / j and a / b.
(i / j) / (a / b) = i / j x b / a = (i x b) / (i x a)
Example: (3 / 4) / (7 / 8) = 3/4 x 8/7 = (3 x 8) / (4 x 7) = 24 / 28. Back to Math