Fraction

Exercise 2.2

Question 1: Which of the drawings (a) to (d) show:

`2xx1/5`, `2xx1/2`, `3xx1/3`, `3xx1/4`

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Answer: (i) → d, (ii) → b, (iii) → a, (iv) → c


Question 2: Some pictures (a) to (c) are given below. Tell which of them show:

`3xx1/5=3/5`, `2xx1/3=2/3`, `3xx3/4=2\1/4`

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Answer: (i) → c, (ii) → a, (iii) → b

Question 3: Multiply and reduce to lowest form and convert into a mixed fraction:

(a) `7 xx 3/5`

Solution: `7xx3/5=(21)/(5)=4\1/5`

(b) `4 xx 1/3`

Solution: `4xx1/3=4/3=1\1/3`

(c) `2 xx 6/7`

Solution: `2xx6/7=(12)/(7)=1\5/7`

(d) `5 xx 2/9`

Solution: `5xx2/9=(10)/(9)=1\1/9`

(e) `2/3 xx 4`

Solution: `2/3xx4=8/3=2\2/3`

(f) `5/2 xx 6`

Solution: `5/2xx6=5xx3=15`

(g) `11 xx 4/7`

Solution: `11xx4/7=(44)/(7)=6\2/7`

(h) `20 xx 4/5`

Solution: `20xx4/5=4xx4=16`

(i) `13 xx 1/3`

Solution: `13xx1/3=(13)/(3)=4\1/3`

(j) `15 xx 3/5`

Solution: `15xx3/5=3xx3=9`


Question 4: Shade (i) ½ of the circles in box (a) (ii) 2/3 of the triangles in box (b) and (ii) 3/5 of the squares in box (c).

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Answer:

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Question 5: Find the following:

(a) Find the value of following: `1/2` of (i) 24 (ii) 46

Solution: `1/2` of 24 `=1/2xx24=12`

`1/2` of 46 `=1/2xx46=23`

(b) Find the value of following: `2/3` of (i) 18 (ii) 27

Solution: `2/3` of 18 `=2/3xx18=12`

`2/3` of 27 `=2/3xx27=18`

(c) Find the value of following: `3/4` of (i) 16 (ii) 36

Solution: `3/4` of 16 `=3/4xx16=12`

`3/4` of 36 `=3/4xx36=27`

(d) Find the value of following: `4/5` of (i) 20 (ii) 35

Solution: `4/5` of 20 `=4/5xx20=16`

`4/5` of 35 `=4/5xx35=28`


Question 6: Multiply and express as mixed fraction:

(a) `3xx5\1/5`

Answer: `3xx5\1/5=3xx(26)/(5)`

`=(78)/(5)=25\3/5`

(b) `5xx6\3/4`

Answer: `5xx6\3/4=5xx(27)/(4)`

`=(135)/(4)=33\3/4`

(c) `7xx2\1/4`

Answer: `7xx2\1/4=7xx9/4`

`=(63)/(4)=15\3/4`

(d) `4xx6\1/3`

Answer: `4xx6\1/3=4xx(19)/(3)`

`=(76)/(3)=25\1/3`

(e) `3\1/4xx6`

Answer: `3\1/4xx6=(13)/(4)xx6`

`=(13xx3)/(2)=(39)/(2)=19\1/2`

(f) `3\2/5xx8`

Answer: `3\2/5xx8=(17)/(5)xx8`

`=(136)/(5)=27\1/5`

Question 7: Find the following

(a) `1/2` of (i) `2\3/4` (ii) `4\2/9`

Answer: `1/2` of `2\3/4`

`=1/2xx(11)/(4)=(11)/(8)=1\3/8`

`1/2` of `4\2/9`

`=1/2xx(38)/(9)=(19)/(9)=2\1/9`

(b) `5/8` of (i) `3\5/6` (ii) `9\2/3`

Answer: `5/8` of `3\5/6`

`=5/8xx(23)/(6)=(115)/(48)=2\(19)/(48)`

`5/8` of `9\2/3`

`=5/8xx(29)/(3)=(145)/(24)=6\(1)/(24)`

Question 8: Vidya and Pratap went for a picnic. Their mother gave them a water bottle that contained 5 litres of water. Vidya consumed 2/5 of the water. Pratap consumed the remaining water.

(a) How much water did Vidya drink?

Answer: Quantity of water used by Vidya

`2/5` of `5l=2/5xx5=2l`

(b) What fraction of the total quantity of water did Pratap drink?

Answer: Fraction of total water consumed by Pratap:

`=1-2/5=(5-2)/(5)=3/5`



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