2.FRACTIONS AND DECIMALS

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Review Exercise

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Fraction is a part of the whole.
Like fractions have same denominator.
Example: `1/5,2/5,6/5,13/5`
Unlike fractions have different denominators.
Example:`7/5,5/3,2/5,7/3`

1. Write the following fractions in ascending order .

i) `3/2,5/2,1/2,17/2,9/2`

Given fractions are like fractions so we compare numerator,
ascending order:`1/2,3/2,5/2,9/2,17/2`

ii) `6/5,11/10,19/5,7/10,5/10`

Given fractions are unlike fractions so first we have to change them into like fractions
`6/5=(6×2)/(5×2)=12/10 , 19/5=(19×2)/(5×2)=38/10`

ascending order: `5/10,7/10,11/10,6/5,19/5`

iii) `8/3,7/6`,3`1/4,5/3,11/4`

Given fractions have different denominators so they are unlike fractions.We have to change them to like fractions.
LCM of 3,4,6 is 12.
`8/3= (8×4)/(3×4)=32/12`

`7/6= (7×2)/(6×2)=14/12`

3`1/4 =13/4= (13×3)/(4×3)=39/12`

`5/3= (5×4)/(3×4)=20/12`

`11/4= (11×3)/(4×3)=33/12`

ascending order: `14/12,20/12,32/12,33/12,39/12`

=`7/6,5/3,8/3,11/4`,3`1/4`

2.Calculate the following

i)`3/4+7/4`

Solution:

`3/4+7/4 = (3+7)/4 = 10/4=5/2`

ii)`5/6+7/12`

Solution:

LCM of 6,12 is 12.
`(5×2)/(6×2)=10/12`

`5/6+7/12 = 10/12+7/12`

` = (10+7)/12 = 17/12 =`1`5/12`

iii)1`7/8-1/5`

Solution:

1`7/8-1/5 = 15/8 - 1/5`

L.C.M of 8,5 is 40
`(15×5)/(8×5)=75/40`

`(1×8)/(5×8)=8/40`

`15/8 - 1/5 = 75/40-8/40= (75-8)/40`

`=67/40=`1`27/40`

iv) 4`1/2-`3`1/3`

Solution:

4`1/2-`3`1/3 = 9/2 - 10/3`
L.C.M of 2,3 is 6
`(9×3)/(2×3)=27/6`

`(10×2)/(3×2)=20/6`

`9/2 - 10/3 = 27/6-20/6= (27-20)/6`

`=7/6=`1`1/6`

v) 4`1/2+`3`1/3`

Solution:

4`1/2+`3`1/3 = 9/2 + 10/3`
L.C.M of 2,3 is 6
`(9×3)/(2×3)=27/6`

`(10×2)/(3×2)=20/6`

`9/2 + 10/3 = 27/6+20/6= (27+20)/6`

`=47/6=`7`5/6`

3.Simplify the following

i) `1/4`of 3

`1/4`of 3 = `1/4`× 3 =`3/4`

ii) `5/8`of `2/3`

`5/8`of `2/3` = `5/8× 2/3 =10/24 = 5/12`

iii) `15/4`of 2`1/7`

`15/4`of 2`1/7` = `15/4× 15/7 =225/28 =`8 `1/28`

iv) 3`1/3`of 2`2/5`

3`1/3`of 2`2/5`= `10/3× 12/5 =120/15 =`8

4.calculate the following

i)`3/4÷3`

`3/4÷3 = `3/4× 1/3 = 1/4`

ii) 8 ÷ 2`1/7`

8 ÷ 2`1/7 = 8 ÷ 15/7 `
`=8× 7/15 = 56/15=`3`11/15`

iii) `12/7 ÷ 2/7`

`12/7 ÷ 2/7 = 12/7 × 7/2 = 6`

iv)5`1/2`÷ 2 `9/11`

5`1/2`÷ 2 `9/11 = 11/2 ÷ 31/11`

`=11/2 × 11/31 = 121/62=`1`59/62`

Example : Raju used 3`1/2` litres of milk in the morning and 2`1/2`litres of milk in the evening to prepare tea in his hotel. What was the total quanitity of milk he used?

Solution :
Milk used in the morning =3`1/2 = 7/2`
Milk used in the evening =2`1/2=5/2`
Total quantity of milk he used in the hotel =`7/ 5 +5/2= (7+ 5)/2 =12/2=`6 liters

Example : Subtract `3/5` from `7/2`.

Solution : `7/2 , 3/5` have different denominators. So, they are unlike fractions.
we have to change them into like fractions. LCM of 2 and 5 is 10.
`7/2=(7×5)/(2×5)=35/10`

`3/5=(3×2)/(5×2)=6/10`

`7/2-3/5 = 35/10 - 6/10 = (35-6)/10 = 29/10`

Exercise 1 >