# Fractions

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A fraction is a part of a group or a whole object. It always has a numerator and a denominator. A part of a whole (fraction) can be represent by the diagram.

To represent a Fraction on the number line, first divide the whole part (numerator) into number of equal parts as the number given in denominator.

Proper fractions are always less than 1, so their numerator is always less than the denominator.

The fractions, where the numerator is greater than the denominator are called improper fractions.

Mixed fraction is another form of improper fraction which has a combination of a whole number and a proper fraction.

To convert an improper fraction into mixed fraction, first divide the numerator by its denominator and then find a whole number with a proper fraction. To convert a mixed number into improper fraction first multiply the denominator by the whole number and then add the numerator in the product. Now keep the sum in the numerator of the same denominator which is the required improper fraction.

A fraction is said to be in the simplest (or lowest) form if its numerator and denominator have no common factor except 1.

Equivalent fractions have the same value (or same denominator in their simplest form) and represent the same part of an object. For writing equivalent fractions for a given fraction, always multiply both numerator and denominator of the fraction by the same number.

Conversion of a fraction into its lowest form:
• Find HCF of numerator and denominator.
• Divide both numerator and denominator by HCF.

Fractions with same denominators are called like fractions.

Fractions with different denominators are called unlike fractions.
Like fractions have same denominator, hence in like fractions, the fraction with greater numerator is greater.

If fractions have different denominator as in unlike fractions, then take LCM of denominators and make each denominator equal to the LCM. Then, fraction with greater numerator is greater.

Addition of like fractions:
In like fractions, denominators of fractions are same, so add only the numerators and copy the denominator. Write the sum in numerator and copy the denominator in denominator.

Subtraction of like fractions:
Subtract smaller numerator from bigger one and write the answer in numerator. Copy the denominator in denominator.

Addition and subtraction of unlike fractions:
Find the LCM of denominators.

Find equivalent fraction with the same denominator by having its denominator equal to LCM.

Add and subtract the fractions in the similar way as is done in case of like fractions.

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