Solve the following and reduce the answer in lowest terms (a)2 3/10 - 1 7/15 (b) 4 7/20 + 3 8/15
Answers
Solve:
(i) 2 – 3/5 (ii) 4 + 7/8 (iii) 3/5 + 2/7 (iv) 9/11 – 4/15 (v) 7/10 + 2/5 + 3/2
(vi) 2 + 3 (vii) 8 - 3
Answer:
(i) 2 – 3/5 = 2/1 – 3/5
= (2 * 5 – 3 * 1)/5 [LCM (1, 5) = 5]
= (10 - 3)/5
= 7/5
= 1
(ii) 4 + 7/8 = 4/1 + 7/8
= (4 * 8 + 7)/8 [LCM (1, 8) = 8]
= (32 + 7)/8
= 39/8
= 4
(iii) 3/5 + 2/7 = (3 * 7 + 2 * 5)/35 [LCM (7, 5) = 35]
= (21 + 10)/35
= 31/35
(iv) 9/11 – 4/15 = (9 * 15 – 4 * 11)/165 [LCM (11, 15) = 165]
= (135 - 44)/165
= 91/165
(v) 7/10 + 2/5 + 3/2 = (7 * 1 + 2 * 2 + 3 * 5)/10
= (7 + 4 + 15)/10
= 26/10 [26 and 10 are divided by 2]
= 13/5
= 2
(vi) 2 + 3 = 8/3 + 7/2
= (8 * 2 + 7 * 3)/6 [LCM (2, 3) = 6]
= (16 + 21)/6
= 37/6
= 6
(vii) 8 - 3 = 17/2 – 29/8
= (17 * 4 – 29 * 1)/8 [LCM (2, 8) = 8]
= (68 - 19)/8
= 39/8
= 4
Time taken by Vaibhav to colour the picture = 3/4 hour
Converting both fractions in like fractions, 7/12 and (3 *3)/(4 * 3) = 9/12
Here, 7/12 < 9/12
=> 7/12 < 3/4
Thus, Vaibhav worked longer time.
Vaibhav worked longer time by 3/4 - 7/12 = 9/12 – 7/12
= (9 - 7)/12
= 2/12 = 1/6 hours
Thus, Vaibhav took 1/6 hour more than Michael.
Exercise 2.2
Question 1:
Which of the drawings (a) to (d) show
(i) 2 * 1/5
(ii) 2 * 1/2
(iii) 3 * 2/3
(iv) 3 * 1/4
Answer:
(i) à (d) Since 2 * 1/5 = 1/5 + 1/5
(ii) à (b) Since 2 * 1/2 = 1/2 + 1/2
(iii) à (a) Since 3 * 2/3 = 2/3 + 2/3 + 2/3
(iv) à (c) Since3 * 1/4 = 1/4 + 1/4 + 1/4
Question 2:
Some pictures (a) to (c) are given below. Tell which of them show:
(i) 3 * 1/5 = 3/5
(ii) 2 * 1/3 = 2/3
(iii) 3 * 3/4 = 2
Answer:
(i) à (c) Since 3 * 1/5 = 1/5 + 1/5 + 1/5
(ii) à (a) Since2 * 1/3 = 1/3 + 1/3
(iii) à (b) Since 3 * 3/4 = 3/4 + 3/4 + 3/4
Question 3:
Multiply and reduce to lowest form and convert into a mixed fraction:
(i) 7 * 3/5 (ii) 4 * 1/3 (iii) 2 * 6/7 (iv) 5 * 2/9 (v) 2/3 * 4
(vi) 5/2 * 6 (vii) 11 * 4/7 (viii) 20 * 4/5 (ix) 13* 1/3 (x) 15 * 3/5
Answer:
(i) 7 * 3/5 = (7 * 3)/5 = 21/5 = 4
(ii) 4 * 1/3 = (4 * 1)/3 = 4/3 = 1
(iii) 2 * 6/7 = (2 * 6)/7 = 12/7 = 1
(iv) 5 * 2/9 = (5 *2)/9 = 10/9 = 1
(v) 2/3 * 4 = (2 * 4)/3 = 8/3 = 2
(vi) 5/2 * 6 = (5 * 6)/2 = 30/2 = 15
(vii) 11 * 4/7 = (11 * 4)/7 = 44/7 = 6
(viii) 20 * 4/5 = (20 *4)/5 = 80/5 = 16
(ix) 13* 1/3 = (13 * 1)/3 = 13/3 = 4
(x) 15 * 3/5 = (15 * 3)/5 = 45/5 = 9
Question 4:
Shade:
(i) 1/2 of the circles in box
(ii) 2/3 of the triangles in box
(ii) 3/5 of the squares in box
Answer:
(i) 1/2 of 12 circles
= (1/2) * 12
= 12/2 = 6 circles
(ii) 2/3 of 9 triangles
= (2/3) * 9
= (2 * 9)/3
= 18/3
= 6 triangles
(ii) 3/5 of 15 squares
= (3/5) * 15
= (3 * 15)/5
= 45/5
= 9 squares
Question 5:
Find:
(a) 1/2 of (i) 24 (ii) 46 (b) 2/3 of (i) 18 (ii) 27
(c) 3/4 of (i) 16 (ii) 36 (d) 4/5 of (i) 20 (ii) 35
Answer:
(a) (i) 1/2 of 24 = 1/2 * 12 = 12/2 = 6
(ii) 1/2 of 46 = 1/2 * 46 = 46/2 = 23
(b) (i) 2/3 of 18 = 2/3 * 18 = (2 * 18)/3 = 36/3 = 12
(ii) 2/3 of 27 = 2/3 * 27 = (2 * 27)/3 = 54/3 = 18
(c) (i) 3/4 of 16 = 3/4 * 16 = (3 *16)/4 = 48/4 = 12
(ii) 3/4 of 36 = 3/4 * 36 = 3 * 9 = 27
(d) (i) 4/5 of 20 = 4/5 * 20 = 4 * 4 = 16
(ii) 4/5 of 35 = 4/5 * 35 = 4 * 7 = 28
Question 6:
Multiply and express as a mixed fraction:
(a) 3 * 5 (b) 5 * 6 (c) 7 * 2 (d) 4 * 6 (e) 3 * 6 (f) 3 * 8
Answer:
(a) 3 * 5 = 3 * 26/5 = (3 * 26)/5 = 78/5 = 15
(b) 5 * 6 = 5 * 27/4 = (5 * 27)/4 = 135/6 = 33
(c) 7 * 2 = 7 * 9/4 = (7 * 9)/4 = 63/4 = 15
(d) 4 * 6 = 4 * 19/4 = (4 * 19)/3 = 76/3 = 25
(e) 3 * 6 = 13/4 * 6 = (13 * 6)/4 = 78/4 = 39/2 = 19
(f) 3 * 8 = 17/5 * 8 = (17 * 8)/5 = 136/5 = 27
Question 7:
Find:
(a) 1/2 of (i) 2 (ii) 4 (b) 5/8 of (i) 3 (ii) 9
Answer:
(a)
(i) 1/2 of 2 = 1/2 * 11/4 = (1 * 11)/(2 * 4) = 11/8 = 1
(ii) 1/2 of 4 = 1/2 of 38/9 = (1 * 38)/(2 * 9) = 38/18 = 19/9 = 2
(b)
(i) 5/8 of 3 = 5/8 * 23/6 = (5 * 23)/(8 * 6) = 115/48 = 2
(ii) 5/8 of 9 = 5/8 * 29/3 = (5 * 29)/(8 * 3) = 145/24 = 6
Find:
(i) 1/4 of (a) 1/4 (b) 3/5 (c) 4/3
(ii) 1/7 of (a) 2/9 (b) 6/5 (c) 3/10
Answer:
(i)
(a) 1/4 of 1/4 = 1/4 * 1/4 = (1 * 1)/(4 * 4) = 1/16
(b) 1/4 of 3/5 = 1/4 * 3/5 = (1 * 3)/(4 * 5) = 3/20
(c) 1/4 of 4/3 = 1/4 * 4/3 = (1 * 4)/(4 * 3) = 4/12 = 1/3
(ii)
(a) 1/7 of 2/9 = 1/7 * 2/9 = (1 * 2)/(7 * 9) = 2/63
(b) 1/7 of 6/5 = 1/7 * 6/5 = (1 * 6)/(7 * 5) = 6/35
(c) 1/7 of 3/10 = 1/7 * 3/10 = (1 * 3)/(7 * 10) = 3/70
Answer:
(i) The given figure represents 2 shaded parts out of 4 equal parts.
So, the fraction = 2/4
(ii) The given figure represents 8 shaded parts out of 9 equal parts.
So, the fraction = 8/9
(iii) The given figure represents 4 shaded parts out of 8 equal parts.
So, the fraction = 4/8
(iv) The given figure represents 1 shaded part out of 4 equal parts.
So, the fraction = 1/4
(v) The given figure represents 3 shaded parts out of 7 equal parts.
So, the fraction = 3/7
(vi) The given figure represents 3 shaded parts out of 12 equal parts.
So, the fraction = 3/12
(vii) The given figure represents 10 shaded parts out of 10 equal parts.
So, the fraction = 10/10
(viii) The given figure represents 4 shaded parts out of 9 equal parts.
So, the fraction = 4/9
(ix) The given figure represents 4 shaded parts out of 8 equal parts.
So, the fraction = 4/8
(x) The given figure represents 1 shaded part out of 2 equal parts.
So, the fraction = 1/2