Equivalent Fractions
Let us  take some pictorial representation of fraction.

These fractions are  representing the parts taken from the total number of parts. If we place the pictorial representation of one over the other they are found to be equal.
These fractions are called equivalent fractions.

Understanding equivalent fractions

They represent the same part of a whole.
There are  two ways of obtaining equivalent fractions.

(a)     By multiplying its numerator and denominator by the same number.

(b)     By dividing its numerator and denominator by the same number.

Sol.:     We know 2 × 3 = 6. This means we need to multiply both the numerator and the denominator by 3 to get the equivalent fraction.

Simplest Form of a Fraction
A fraction is said to be in the simplest (or lowest) form if its numerator and denominator have no common factor except 1.
The shortest way
The shortest way to find the equivalent fraction in the simplest form is to find the HCF of the numerator and denominator, and then divide both of them by the HCF.

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In case of like fractions, the denominator is same so we can add them fluently.

Leave the common denominator same. (Do not add the denominator).

Example

Solutions:

Subtracting like fractions

Steps to subtract the like fractions-

Subtract the small numerator from the bigger one.

Leave the common denominator same.

Example:

Solution:

Still, first we have to find the Equivalent bit of the given fractions with the same denominator then add them, if we have to add the unalike fractions.

Take the LCM of the denominator of the given fractions.

Find the Equivalent fractions of both fractions with LCM as the denominator.

Add them as such like fractions.

Example

Take the LCM of 5 and 8, which are 40.

Subtracting unlike Fractions

Steps to subtract unlike fractions-

Take the LCM of the denominator of the given fractions.

Find the Equivalent fractions of both fractions with LCM as the denominator.

Subtract them as such like fractions.

Example

LCM of 4 and 5 is 20.

Comment:  To add or abate the mixed fractions, simply convert them in the improper bit then add and abate them directly

Mixed fraction,

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