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Fractions Class 6 Chapter 7 Maths Notes

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:

4/12

where,

4 is the numerator
12 is the denominator
It is read as four-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.

Improper fractions – It is a type of fraction where the denominator is always less than the numerator.

Mixed fractions – It is a type of fraction which consists of a whole number and a proper fraction.

Like fractions – The type of fractions which have same denominators are called, like fractions.

Unlike fractions – The type of fractions which have different denominators are called, unlike fractions.

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.

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.

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.

Let’s Add Fractions

Addition of 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.

Let’s Subtract Fractions

Subtraction of fractions

Many Many Many Fractions Together

Multiplication of fractions

Let’s Divide Fractions

Reciprocals of fractions

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

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

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.

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Fractions: Class 6 Chapter 7 Maths Notes