- Fraction Definition
- Types of Fractions
- Proper Fraction
- Mixed Fraction
- Improper Fraction
- Mixed Fractions to Improper Fractions
- Improper Fractions to Mixed Fraction
- How to Represent Fraction on Number Line?
- Simplest form of Fraction
- Equivalent Fractions
- Like and Unlike Fractions
- Comparing Fractions
- How to add Fractions
- How to Subtract Fractions
- Comparison, Addition and Subtraction of Mixed Fractions

Suppose Ramesh has a chocolate and we want to equally share with his Friend Amit. He will divide the chocolate into two pieces and keep one piece with him and give another piece to Amit. So basically they each have got 1 part out of 2 parts i.e 1/2 of the chocolate. Similarly if they have another suresh also, then they will divide chocolate in three equal parts,then each of them will have 1 out of 3 parts i.e 1/3 of the chocolate

$\frac {3}{11}$

3 out of 11 parts

3 -> Called Numerator

11 -> Called Denominator

When expressing a situation of counting parts to write a fraction, it must be ensured that all parts are equal

Identify the Numerator and Denominator from below fraction

a. $\frac {2}{15}$

b. $\frac {11}{13}$

c. $\frac {3}{2}$

d. $\frac {1}{8}$

a. $\frac {2}{15}$

b. $\frac {11}{13}$

c. $\frac {3}{2}$

d. $\frac {1}{8}$

a. Proper Fraction

b. Improper Fraction

c. Mixed Fraction.

Let dive into each of them in detail in below

Here the Denominator shows the part whole has been divided and numerator shows the part which has been considered.

This is the same fraction which we discussed with fraction definition

Example

$\frac {1}{3}$

$\frac {2}{3}$

$\frac {4}{5}$

$\frac {1}{3}$

$\frac {2}{3}$

$\frac {4}{5}$

Lets understand this with example . Suresh has 5 chocolates and he has to divide those chocolate among four friends.We can divide each chocolate into fours parts and each one can have one-quarter part of the each chocolate. So Each friend will be having 5 parts of the one-quarter part.Now 4 parts make one whole. So basically each one of them is getting 1 whole and 1 part. So this can be written as 5/4

Here numerator is more than denominator

$\frac {11}{5}$

$\frac {5}{4}$

$\frac {10}{9}$

$8 \frac {4}{9}$

Lets the example of improper fraction only. The division can made in another way. We give one chocolate to each of them and divide the fifth chocolate into four pieces. So each of them got 1 full chocolate and one-quarter part of last chocolate. So this can written as

$1 + \frac {1}{4} =1 \frac {1}{4}$

This is mixed fraction.

Also $1 + \frac {1}{4} =1 \frac {1}{4} = \frac {5}{4}$

$2 \frac {1}{5}$

$1 \frac {3}{4}$

$1 \frac {1}{9}$

Step 1 |
Obtain the mixed fraction. Let the mixed fraction be 5^{2}/_{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}$ =$\frac {32}{6}$ |

$ 1\frac {1}{3}$

Apply the formula

$\frac {(Whole \times Denominator) + Numerator}{Denominator}$

So $1\frac {1}{3}=\frac {4}{3}$

- $ 1 \frac {1}{4}$
- 5$\frac {2}{3}$
- 3$\frac {5}{11}$
- 2$\frac {17}{44}$
- 1$\frac {3}{7}$
- 3$\frac {5}{9}$

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 $Quotient \frac {Reminder}{denominator}$ |

$\frac {11}{3}$

Here Numerator is greater than denominator, So Improper fraction

Now dividing 11 by 3, we get reminder as 2

So $\frac {11}{3}=3 \frac {2}{3}$

- $\frac {9}{4}$
- $\frac {11}{2}$
- $\frac {37}{18}$
- $\frac {99}{44}$
- $\frac {103}{9}$
- $\frac {17}{3}$

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

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.

$\frac {1}{3}$

$\frac {2}{3}$

Equivalent fractions are fractions that have the same value in its simplest form.

$\frac {2}{6} \;,\; \frac {1}{3} \;,\; \frac {6}{18}$ are equivalent fractions as they have same value

Checkout Equivalent Fraction calculator

$\frac {2}{3}$

Equivalent Fraction can be obtained by multiplying both the numerator and the denominator of the given fraction by the same number.

$\frac {2}{3} = \frac {2 \times 3}{3 \times 3}= \frac {6}{9}$

$\frac {2}{3} = \frac {2 \times 5}{3 \times 5}= \frac {10}{15}$

$\frac {2}{3} = \frac {2 \times 7}{3 \times 7}= \frac {14}{21}$

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 |

Identify which ones are like fractions and unlike fractions

a. $\frac {2}{3}$ and $\frac {4}{3}$

b. $\frac {2}{5}$ and $\frac {1}{3}$

c. $\frac {11}{5}$ and $\frac {17}{4}$

d. $\frac {2}{5}$ and $\frac {9}{5}$

a. These are like fractions

b. These are unlike fractions

c. These are unlike fractions

d. These are like fractions

$ \frac {5}{6} > \frac {2}{6}$

$ \frac {3}{6} > 0 $

$ \frac {1}{6} < \frac {6}{6} $

$ \frac {8}{6} < \frac {5}{6} $

So, $ \frac {1}{10} < \frac {2}{10} < \frac {3}{10} < \frac {4}{10} $

a. Comparing fractions with same numerator

For fractions having same numerator, the fraction with the lowest denominator is the greater number

Example

2/5 and 2/7

Here 5 < 7

So 2/5 > 2/7

b. Comparing fractions with different denominator and numerator

Here we would be using the technique of equivalent fractions. We would convert each of the fraction into equivalent fraction such that they become like fractions.Then comparison is simple. So here are the steps

1. Find the LCM of the denominators

2. Convert each fraction into equivalent fraction such that denominator is the LCM.

3. Now both the fraction are converted into Like fraction,so we can do the comparison easily

Let us check few example to make it clear

1)Compare $\frac {2}{3}$ and $\frac {2}{7}$

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)Compare $\frac {5}{6}$ and $\frac {13}{15}$

LCM of denominator is 6 and 15 is 30

So converting them equivalent Like fractions

$\frac {5}{6} = \frac {5 \times 5}{6 \times 5} = \frac {25}{30}$

$\frac {13}{15} = \frac {13 \times 2}{15 \times 2} = \frac {26}{30}$

Now $\frac {26}{30} > \frac {25}{30}$

So $\frac {13}{15} > \frac {5}{6}$

$\frac {1}{5} + \frac {1}{5} = \frac {2}{5}$

$\frac {1}{6} + \frac {4}{6} = \frac {5}{6}$

$\frac {9}{11} + \frac {1}{11} = \frac {10}{11}$

And then it works like “like” Fraction

Let us check few example to make it clear

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

$\frac {1}{2} + \frac {1}{3} = \frac {3}{6} + \frac {2}{6} =\frac {5}{6}$

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

$\frac {4}{5} - \frac {1}{5} = \frac {3}{5}$

$\frac {5}{6} - \frac {4}{6} = \frac {1}{6}$

$\frac {9}{11} - \frac {1}{11} = \frac {8}{11}$

And then it works like “like” Fraction

Let us check few example to make it clear

Perform the below Subtraction

$\frac {1}{2} - \frac {1}{3}$ 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

$\frac {1}{2} - \frac {1}{3} = \frac {3}{6} - \frac {2}{6} =\frac {1}{6}$

- $\frac {1}{5} - \frac {1}{6}$
- $\frac {1}{7} - \frac {1}{8}$
- $\frac {2}{11} - \frac {1}{12}$

- Two mixed fractions 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.

1)Perform the below Addition

$1\frac {1}{2} + 2\frac {1}{3}$

Solution

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

=$3+ \frac {1}{2} + \frac {1}{3} = 3 + \frac {3}{6} + \frac {2}{6} =3 +\frac {5}{6} =3\frac {5}{6}$

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

=$\frac {9}{6} + \frac {14}{6}$

=$\frac {23}{6} =3\frac {5}{6}$

- 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$\frac {1}{3} + 5\frac {1}{4} + 6\frac {1}{5}$

**Notes****Assignments & NCERT solutions**

Class 6 Maths Class 6 Science