# Fractions Class 6 Maths Notes - Chapter 7

A fraction is defined as a part of a whole number. It can be expressed as a ratio between two integers separated by a solidus. The number in the upper part of a fraction is termed as numerator whereas the number in the lower part is termed as the denominator. For example, let us consider a fraction $\frac{3}{12}$ where,

• 3 is the numerator
• 12 is the denominator
• It is read as three-twelfths

## Types Of Fractions

Let us understand the different types of fractions. There are five types of fractions. They are proper fractions, improper fractions, mixed fractions, like fractions and unlike fractions.

• Proper fractions – It is a type of fraction where the denominator is always greater than the numerator. Some examples are $\frac{4}{5}$ , $\frac{3}{7}$
• Improper fractions – It is a type of fraction where the denominator is always less than the numerator. Some examples are $\frac{5}{4}$ , $\frac{7}{3}$
• Mixed fractions – It is a type of fraction which consists of a whole number and a proper fraction. Some examples are $16\frac{3}{7}$ , $3\frac{4}{5}$
• Like fractions – The type of fractions which have same denominators are called, like fractions. Some examples are $\frac{1}{15}$ , $\frac{3}{15}$
• Unlike fractions – The type of fractions which have different denominators are called, unlike fractions. Some examples are $\frac{6}{27}$ , $\frac{6}{28}$

## Introduction to Fractions

• A fraction is a number that represents a part of a whole.
• The whole may be a single object or a group of objects.
• Fraction=Numerator/Denominator
• Example: 1/2, 3/7

### Representing fractions

• Fractions can be represented using numbers, figures or words.

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## Avatars of Fractions

### Proper fractions

• If numerator < denominator in a fraction, then it is a proper fraction.
• Example: 2/3 and 4/9

### Improper and Mixed fraction

• If numerator > denominator in a fraction, then it is an improper fraction.
• Example: 4/3 and 8/11
• An improper fraction can be written as a combination of a whole and a part, and is called mixed fractions.

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### Interconversion between Improper and Mixed fraction

Improper to mixed fraction

## Meet the Twin Fractions

### Equivalent fractions

• Each proper or improper fraction has many equivalent fractions.
• Multiply both numerator and denominator by a number, to find an equivalent fraction for the fraction.

Example: 1/2 and 2/4 are equivalent fractions.

• 1/3 + 7/3 = (1+7)/3 = 8/3
• 1/3 + 2/4 = (4+6)/12 = 10/12 = 5/6

### LCM

• Least common multiple of two numbers (LCM) is the smallest number that gets divided by both the numbers.
• Example: LCM of 3 and 4 is 12.

## Many Many Many Fractions Together

### Multiplication of fractions

Proper fraction * Proper fraction

Proper fraction * Improper fraction

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## Let’s Divide Fractions

### Reciprocals of fractions

• Turning the fraction upside down gives the Reciprocal of a fraction.
• Fraction × (Reciprocal of the fraction) = 1

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### Division of fractions

• 1/2 ÷ 1/3
1/2 × Reciprocal of (1/3)
=1/2 × 3 = (1×3)/2
=3/2
• 4/3 ÷ 3/2
=4/3 × Reciprocal of (3/2)
=4/3×2/3=8/9

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## Where do Fractions Live?

### Comparison of fractions

• Comparing like fractions with same denominators

2/3 and 8/3
2 < 8
∴ 2/3 < 8/3

• Comparing unlike fractions with same numerators

1/3 and 1/4
Portion of the whole showing 1/3 > Portion of the whole showing 1/4
∴1/3>1/4

• Comparing unlike fractions with different numerators

5/6 and 13/15
LCM of 6 and 15: 30
(5×5)/(6×5) = 25/30
(13×2)/(15×2)=26/30
⇒ 25/30<26/30
∴ 5/6<13/15

### Fractions on the number line

• The following figure shows how fractions 14, 24 and 34 are represented on a number line.
• Divide the portion from 0 to 1 on the number line into four parts.
• Then each part represents 1/4th portion of the whole.