# 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:

** Fractions Addition**
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__Addition of 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

** Fractions Subtraction**
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__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

** Fractions Multiplication**
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__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

** Fractions Division**
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__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.