Fractions: Suppose you choose a Circle

Solving Fractions

Now In the above Circle, is divided into 6 parts and then it is shaded with 2 parts, so we say that fraction of the shaded part is 2 out of 6 that is $\frac{2}{6}$.

I think now you got an idea about fractions, Lets define a fraction

Fraction: Fraction is of the form $\frac{Numerator}{denominator}$; here denominator is never equal to zero.

Example: $\frac{3}{5}$, $\frac{9}{8}$

Example: $\frac{4}{0}$ cannot be a fraction since you can never select 4 items out of zero number of things.

Types of Fractions

Now we shall define Different types of fractions:

1. Proper Fraction : Here numerator is less than the denominator. Example $\frac{2}{5}$ that is 2 is less than 5.

2. Improper Fraction : Here numerator is greater than the denominator Example $\frac{5}{4}$ that is 5 is greater than 4.

3. Mixed fraction : An improper fraction converted to a whole number and a proper fraction is called a mixed fraction Example: 3$\frac{5}{6}$, 4$\frac{3}{2}$.


Solving Fractions

In this section we will try to do some operations on the Fractions.

Addition of fractions:

Consider two fractions $\frac{3}{4}$ and $\frac{5}{4}$

$\frac{3}{4}$ + $\frac{5}{4}$

Since they have common denominator we can add up the numerators freely like this

3 + $\frac{5}{4}$ = $\frac{8}{4}$ = 2.

Subtraction of fractions:

Consider two fractions $\frac{9}{4}$ and $\frac{1}{2}$ let us try to subtract it

$\frac{9}{4}$ - $\frac{1}{2}$ = 9$\frac{-1}{4}$ = $\frac{8}{4}$ = 2 [Here also we come across same denominator, so we can subtract freely the numerator and divide it by 4].

Multiplication of fraction: Consider two fractions such as $\frac{2}{4}$ and $\frac{6}{8}$ now multiply these two

$\frac{2}{4}$ $\times$ $\frac{6}{8}$ = $\frac{12}{32}$ = $\frac{6}{16}$ = $\frac{3}{8}$ [you can simplify the answer by 2 table].

Division of a fraction: Let us consider the above two fractions only and try to divide it

$\frac{\frac{2}{4}}{\frac{6}{8}}$. Here you need to invert the Denominator Like this

$\frac{2}{4} \times \frac{8}{6}$ then cancel 8 goes in 4, 2 times and 6 goes in 2, 3 times So our answer is $\frac{2}{3}$.

Next Chapters

Number Theory Linear Equation Set Theory Math Fractions
Math Functions Pyramid Calculus Cone
Cylinder Chain Rule Limits and Continuity Prime Factorization
Square Roots and Cube Roots Parabola Distance Formula Definite Integrals
Interest Simple Interest Compound Interest Area of Irregular Figures

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