Fraction
Exercise 2.2
Question 1: Which of the drawings (a) to (d) show:
`2xx1/5`, `2xx1/2`, `3xx1/3`, `3xx1/4`
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`
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).
Answer:
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`