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# Fractions

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A fraction is a part of a group or a region.

A fraction has two parts- top part is numerator and bottom one is denominator.

The numerator is the portion of whole being considered and denominator is number of parts the whole is divided.

Examples:

a) In this fraction 5 / 12

5 is the top number (Numerator)

12 is the bottom number (Denominator)

b) In 15 / 33,

15 is the top number (Numerator)

33 is the bottom number (Denominator)

c) For the numerator 8 and denominator 27, the fraction is 8 / 27

In this topic, we are going to learn.

## Fractions, Types of Fractions

Students can learn about the various Types of Fractions, How to do fractions step by step and the differences between them.

In types of fractions, we discuss

• Proper fraction

• Improper fractions

• Mixed fractions

• Equivalent fractions

• Like and Unlike fractions

## Comparing Fractions

Fractions are compared to know which is greater or which is smaller among a group of fractions.

Here, we discuss

• Comparing of like fractions

• Comparing of unlike fractions

• Decimal method of comparing

• Common denominator method of comparing and

• Some Useful short-cuts

## Addition and Subtraction of Fractions

Addition of fractions and subtraction of Fraction can be done only when fraction have same denominators.

Learn how to add fractions with different denominators with our online expert tutor.

When fractions have different denominators they can be added or subtracted in their equivalent fractions with common denominator.

(i) 4/5 + 9/5 = 13 / 5

(ii) 3/7 + 8/7 = 11 / 7

(iii) $\frac{5}{7}$ - $\frac{1}{7}$

=$\frac{5-1}{7}$

$\frac{4}{7}$

## Multiplication and Division of Fractions

Under this heading, we discuss the various steps to multiply and divide the fractions.

Also, Multiplication and division of Mixed Fractions and Multiplication and division of Algebraic expressions are also discussed in detail.

$\frac{1}{3}$ x $\frac{2}{5}$

• Multiply the numerators first, say 1 x 2 = 2
• Multiply the denominators , say 3 x 5 = 15
• Write them as fraction, $\frac{2}{15}$
• Look if 2 and 15 have any GCD.
• They do not have any GCD.

$\frac{1}{3}$ x $\frac{2}{5}$ = $\frac{2}{15}$
Divide 5 into halves or $$5\div\frac12$$
We see that we have 10 parts. Therefore, $$5\div\frac12=10$$