What is Fraction?

Fractions and Decimals 7th Math

What is Fraction?

Fraction can be defined as part of whole.

Example:

`1/2, 2/3, 3/4` etc.

In the fraction of `1/2` means 1 part of total 2 parts.

Similarly, in the fraction of `2/3` means 2 parts of total 3 parts.

Similarly, in fraction `3/4` means 3 parts of total 4 parts.

Types of Fractions

Fractions can be divided into three parts. These are Proper Fraction, Improper Fraction and Mixed Fraction

(a) Proper Fraction

Fractions in which numerator is smaller than denominator, are called a Proper Fraction.

Example:

`1/2, 2/3, 3/4` etc.

(b) Improper Fraction

Fractions in which numerator is bigger than denominator, are called Improper Fractions.

Example:

`4/3, 5/4, 6/5` etc.

(c) Mixed Fraction

Mixed fraction is a combination of whole and a proper fraction.

Example:

`1 2/3, 2 4/5, 3 2/3` etc.

Solution of NCERT Exercise 2.1

Question (1) Solve:

(i) `2-3/5`

Solution :

Given, `2-3/5`

`=2/1-3/5`

Now, to solve the given question based on fraction, first LCM of denominators are taken. Here LCM of denominators of given fractions = 5

`=((2xx5)-(3xx1))/5`

`=(10-3)/5`

`=7/5`

`=1 2/5` Answer

(ii) `4+7/8`

Solution :

Given, `4+7/8`

`=4/1+7/8`

Now, to solve the given question based on fraction, first LCM of denominators are taken. Here LCM of denominators of given fractions = 8

`=((4xx8)+(7xx1))/8`

`=(32+7)/8`

`=39/8`

`=4 7/8` Answer

(iii) `3/5+2/7`

Solution :

Given, `3/5+2/7`

Now, to solve the given question based on fraction, first LCM of denominators are taken. Here LCM of denominators of given fractions = 5 × 7 = 35

`=((3xx7)+(2xx5))/35`

`=(21+10)/35`

`=31/35` Answer

(iv) `9/11-4/15`

Solution :

Given, `9/11-4/15`

Now, to solve the given question based on fraction, first LCM of denominators are taken. Here LCM of denominators of given fractions = 11 × 15 = 165

`=((9xx15)-(4xx11))/165`

`=(135-44)165`

`=91/165` Answer

(v) `7/10+2/5+3/2`

Solution :

Given, `7/10+2/5+3/2`

Now, to solve the given question based on fraction, first LCM of denominators are taken. Here LCM of denominators of given fractions = 10

`=(7+(2xx2)+(3xx5))/10`

`=(7+4+15)/10`

`=26/10`

`=(13xxcancel2)/(5xxcancel2)`

`=13/5`

`=2 3/5` Answer

(vi) `2 2/3+3 1/2`

Solution :

Given, `2 2/3+3 1/2`

`=8/3+7/2`

Now, to solve the given question based on fraction, first LCM of denominators are taken. Here LCM of denominators of given fractions = 3 × 2 = 6

`=((8xx2)+(7xx3))/6`

`=(16+21)/6`

`=37/6`

`=6 1/6` Answer

(vii) `8 1/2-3 5/8`

Solution :

Given, `8 1/2-3 5/8`

`=17/2-29/8`

Now, to solve the given question based on fraction, first LCM of denominators are taken. Here LCM of denominators of given fractions = 8

`=((17xx4)-29)/8`

`=(68-29)/8`

`=39/8`

`=4 7/8` Answer

Question (2) Arrange the following the descending order :

(i) `2/9, 2/3, 8/21`

Solution :

Given, `2/9, 2/3, 8/21`

To compare or arrange the fractions, first we have to make their denominators equal by multiplying their numerators and denominators with suitable numbers.

Here, the LCM of given fractions = 63

`=(2xx7)/(9xx7), (2xx21)/(3xx21)` and `(8xx3)/(21xx3)`

`=14/63 , 42/63, 24/63`

Now, their descending order is clearly

`42/63 > 24/63 > 14/63`

Thus, the descending order of given fractions is clearly

`2/3 > 8/3 > 2/9` Answer

(ii) `1/5, 3/7, 7/10`

Solution :

Given, `1/5, 3/7, 7/10`

To compare or arrange the fractions, first we have to make their denominators equal by multiplying their numerators and denominators with suitable numbers.

Here, the LCM of given fractions = 70

`=(1xx14)/(5xx14), (3xx10)/(7xx10)` and `(7xx7)/(10xx7)`

`=14/70, 30/70, 49/70`

Now, their descending order is clearly

`=49/70 > 30/70 > 14/70`

Thus, the descending order of given fractions is clearly

`7/10 > 3/7 > 1/5` Answer

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