# CBSE Notes for Class 6 Maths Chapter 7: Fractions

## What is Fraction

A fraction is a number representing a part of a whole. The whole may be a single object or a group of objects.
Example
$\frac {3}{11}$
3 out of 11 parts
3 -> Called Numerator
11 -> Called Denominator

## What is proper Fraction

Proper Fraction is the fraction which is less than 1 or where Numerator is less than Denominator
Example
$\frac {1}{3}$
$\frac {2}{3}$
$\frac {4}{5}$

## What is Mixed Fraction

It is combination of whole number and proper fraction
$8 \frac {4}{9}$

## What is Improper Fraction

Improper Fraction is the fraction which is greater than 1 or where Numerator is greater than Denominator
Example
$\frac {11}{5}$
$\frac {5}{4}$
$\frac {10}{9}$

## How to convert Mixed Fractions to Improper Fractions

 Step1 Obtain the mixed fraction. Let the mixed fraction be 52/6 Step 2 Identify the whole number and the numerator (top) and denominator (bottom) of the proper fraction. Whole Number=5 Numerator=2 Denominator=6 Step 3 Apply the formula $\frac {(Whole \times Denominator) + Numerator}{Denominator}$ Example $5\frac {2}{6}$ =$\frac {32}{6}$

## How to convert Improper Fractions to Mixed Fraction

 Step 1 Obtain the improper fraction. Step 2 Divide the numerator by the denominator and obtain the quotient and remainder. Step 3 Write the mixed fraction as $Quotient \frac {Reminder}{denominator}$
Example
$\frac {11}{3}$
Here Numerator is greater than denominator, So Improper fraction
Now dividing 11 by 3, we get reminder as 2
So $\frac {11}{3}=3 \frac {2}{3}$
Practice Questions
• $\frac {9}{4}$
• $\frac {11}{2}$
• $\frac {37}{18}$
• $\frac {99}{44}$
• $\frac {103}{9}$
• $\frac {17}{3}$

## How to Represent Fraction on Number Line?

We can show fractions on a number line. In order to represent 1/2 on the number line, draw the number line and look for the portion between 0 and 1
Now, divide the gap between 0 and 1 into two equal parts. The point of division represents 1/2.

To represent 1/4 on a number line, we divide the gap between 0 and 1 into 4 equal parts
First point will represent ½
Second point will represent 2/4 =1/2
Third point will represent 3/4

More points about Fraction
1) If the numerator and the denominator of a fraction have no common factor except, then it is said to be in its simplest form or lowest form.
Example
$\frac {1}{3}$
$\frac {2}{3}$

2) Equivalent fractions are fractions that have the same value in its simplest form.
Example
$\frac {2}{6} \;,\; \frac {1}{3} \;,\; \frac {6}{18}$ are equivalent fractions as they have same value
3) The equivalent fraction of a given fraction is obtained by multiplying both the numerator and the denominator of the given fraction by the same number.
Example
$\frac {2}{3}$
Equivalent Fraction can be obtained by multiplying both the numerator and the denominator of the given fraction by the same number.
$\frac {2}{3} = \frac {2 \times 3}{3 \times 3}= \frac {6}{9}$
$\frac {2}{3} = \frac {2 \times 5}{3 \times 5}= \frac {10}{15}$
$\frac {2}{3} = \frac {2 \times 7}{3 \times 7}= \frac {14}{21}$

## Comparison, Addition and subtraction of Fraction

Important definition
 Like Fractions Fractions with the same denominators are called like fractions. Example $\frac {1}{3}$, $\frac {2}{3}$ are Like Fractions $\frac {1}{4}$ ,$\frac {3}{4}$ are like Fractions Unlike Fraction Fractions with different denominators are called unlike fractions. Example $\frac {1}{3}$ , $\frac {2}{5}$ are Unlike Fractions

### Comparison, addition and subtraction of Like Fraction

Comparison: The numerator value decides the larger value.
$\frac {5}{6} > \frac {2}{6}$
$\frac {3}{6} > 0$
$\frac {1}{6} < \frac {6}{6}$
$\frac {8}{6} < \frac {5}{6}$
Addition: The numerator adds to provide the final fraction value.
$\frac {1}{5} + \frac {1}{5} = \frac {2}{5}$
$\frac {1}{6} + \frac {4}{6} = \frac {5}{6}$
$\frac {9}{11} + \frac {1}{11} = \frac {10}{11}$
Subtraction: The Numerator subtract to provide the final fraction value.
$\frac {4}{5} - \frac {1}{5} = \frac {3}{5}$
$\frac {5}{6} - \frac {4}{6} = \frac {1}{6}$
$\frac {9}{11} - \frac {1}{11} = \frac {8}{11}$

### Comparison, addition and subtraction of Unlike Fraction

First we need to convert the unlike fraction to like fraction using the LCM of the denominators and convert each fraction into like fraction using the LCM
And then it works like “like” Fraction
Let us check few example to make it clear
Example
1)Compare $\frac {2}{3}$ and $\frac {5}{7}$
Solution
LCM of denominator is 3 and 7 is 21
So converting them equivalent Like fractions
$\frac {2}{3} = \frac {2 \times 7}{3 \times 7} = \frac {14}{21}$
$\frac {5}{7} = \frac {5 \times 3}{7 \times 3} = \frac {15}{21}$
Now $\frac {15}{21} > \frac {14}{21}$
So $\frac {5}{7} > \frac {2}{3}$
2)Perform the below Addition
$\frac {1}{2} + \frac {1}{3}$ Solution
LCM of 2 and 3 is 6
So converting them into equivalent Like Fractions
$\frac {1}{2} =\frac {1 \times 3}{2 \times 3} =\frac {3}{6}$
$\frac {1}{3} =\frac {1 \times 2}{3 \times 2} =\frac {2}{6}$
So
$\frac {1}{2} + \frac {1}{3} = \frac {3}{6} + \frac {2}{6} =\frac {5}{6}$

Practice Questions
• $\frac {1}{5} + \frac {1}{6}$
• $\frac {1}{5} - \frac {1}{6}$
• $\frac {1}{2} + \frac {1}{3} + \frac {1}{4}$
• $\frac {1}{3} + \frac {1}{4} + \frac {1}{5}$

### Comparison, Addition and Subtraction of Mixed Fraction

• Two mixed fraction can be added or subtracted by adding or subtracting the whole number of the two fractions and then adding or subtracting the fractional parts together.
• Two mixed fractions can also be converted into improper fractions and then added or subtracted.
Example
1)Perform the below Addition
$1\frac {1}{2} + 2\frac {1}{3}$ Solution
First way
We add the whole number and add the fractional part
$1\frac {1}{2} + 2\frac {1}{3}$ =$1 + 2+ \frac {1}{2} +\frac {1}{3}$ =$3 +\frac {1}{2} +\frac {1}{3}$ Now LCM of 2 and 3 is 6
So converting them into equivalent Like Fractions
$\frac {1}{2} =\frac {1 \times 3}{2 \times 3} =\frac {3}{6}$
$\frac {1}{3} =\frac {1 \times 2}{3 \times 2} =\frac {2}{6}$
So
=$3+ \frac {1}{2} + \frac {1}{3} = 3 + \frac {3}{6} + \frac {2}{6} =3 +\frac {5}{6} =3\frac {5}{6}$
Second way
We convert them into improper fraction
$1\frac {1}{2} + 2\frac {1}{3}$
=$\frac {3}{2} + \frac {7}{3}$
Now LCM of 2 and 3 is 6

So converting them into equivalent Like Fractions
$\frac {3}{2} =\frac {3 \times 3}{2 \times 3} =\frac {9}{6}$
$\frac {7}{3} =\frac {7 \times 2}{3 \times 2} =\frac {14}{6}$
So
=$\frac {9}{6} + \frac {14}{6}$
=$\frac {23}{6} =3\frac {5}{6}$

Practice Questions
• 1$\frac {1}{5} + 1\frac {1}{6}$
• 3$\frac {1}{5} - 2\frac {1}{6}$
• 1$\frac {1}{2} + 2\frac {1}{3} + 3\frac {1}{4}$
• 4$\frac {1}{3} + 5\frac {1}{4} + 6\frac {1}{5}$

### Quiz Time

Question 1 Which of these fraction is greatest?
A) $\frac {11}{39}$
B)$\frac {10}{39}$
C)$\frac {1}{3}$
D)$\frac {9}{39}$
Question 2 Which of these fraction is lowest?
A)$\frac {13}{24}$
B)$\frac {1}{2}$
C)$\frac {16}{24}$
D)$\frac {17}{39}$
Question 3 which is of these is proper fraction
A)$\frac {10}{3}$
B)$\frac {17}{3}$
C)$\frac {12}{24}$
D)$1\frac {1}{3}$
Question 4 Which of the following is in the lowest form
A) 2/10
B) 11/121
C) 4/76
D) 11/13
Question 5 The sum $\frac {1}{11} + \frac {9}{11}$?
A)$\frac {10}{11}$
B)$\frac {10}{22}$
C)$\frac {8}{11}$
D)$\frac {8}{22}$

Reference Books for class 6

Given below are the links of some of the reference books for class 6 science and class 6 math.

You can use above books for extra knowledge and practicing different questions.