RS Aggarwal Solutions: Integers (Exercise 2B) | Mathematics (Maths) Class 7 PDF Download

Q.1. Find the product:
(i) 3/5×7/11
(ii) 5/8×4/7
(iii) 4/9×15/16
(iv) 2/5×15
(v) 8/15×20
(vi) 5/8×1000
(vii)×16
(viii) ×12
(ix) ×
(x) ×
(xi)
(xii)
Ans. (i) 3/5×7/11 = (3×7) / (5×11) = 21/55
(ii) 5/8×4/7 = (5×4) / (8×7) = (5×1) / (2×7) =5/14
(iii) 4/9×15/16 = (4×15) / (9×16) = (1×5) / (3×4) = 5/12
(iv) 2/5×15 = 2/5×15/1 = (2×15) / (5×1) = (2×3) / (1×1) =6
(v) 8/15×20 = 8/15×20/1 = (8×20)/(15×1) = (8×4) / (3×1) = 32/3 =
(vi)  5/8×1000 = 5/8×1000/1 = (5×1000) / (8 × 1) = (5×125) / (1×1) = 625
(vii) ×16 = 25/8 × 16/1 = (25×16) / (8×1) = (25×2) / (1×1) = 50
(viii)× 12 = 34/15 × 12/1 = (34×12) / (15×1) = (34×4) / (5×1) = 136/5 =
(ix) ×= 27/7 × 14/3 = (27×14) / (7×3) = (9×2) / (1×1) =18
(x)= 19/2 × 28/19 = (19×28) / (2×19) = (1×14) / (1×1) = 14
(xi) = 33/8×32/11 = (33×32) / (8×11) = (3×4) / (1×1) =12
(xii)= 35/6×12/7 = (35×12) / (6×7) = (5×2) / (1×1) =10

Q.2. Simplify:
(i) 2/3×5/44×33/35
(ii) 12/25×15/28×35/36
(iii) 10/27×28/65×39/56
(iv)
(v)
(vi)
Ans. We have the following:
(i) 2/3×5/44×33/35 = (2×5×33) / (3×44×35)
= (1×1×11) / (1×22×7) = (1×1×1) / (1×2×7) =1/14
(ii)12/25 × 15/28 × 35/36 = (1×3×5) / (5×4×3) = (1×1×1) / (1×4×1) = 1/4
(iii) 10/27 × 28/65 × 39/56 = (10×1×3) / (27×5×2) = (1×1×3) / (27×1×1) = 3/27 = 1/9
(iv)= 11/7 × 35/22 × 16/15 = (11×35×16) / (7×22×15) = (1×5×16) / (1×2×15) = (1×1×8) / (1×1×3) = 8/3 =
(v)= 36/17 × 65/9 × 85/52 = (36×65×85) / (17×9×52) = (4×5×5) / (1×1×4) =(1×5×5) / (1×1×1) = 25
(vi)= 49/16 × 52/7 × 64/39 = (7×4×4) / (1×1×3) = 112/3 =

Q.3. Find:
(i) 1/3 of 24
(ii) 3/4 of 32
(iii) 5/9 of 45
(iv) 7/50 of 1000
(v) 3/20 of 1020
(vi) 5/11 of Rs 220
(vii) 4/9 of 54 metres
(viii) 6/7 of 35 litres
(ix) 1/6 of an hour
(x) 5/6 of an year
(xi) 7/20 of a kg
(xii) 9/20 of a metre
(xiii) 7/8 of a day
(xiv) 3/7 of a week
(xv) 7/50 of a litre
Ans. We have the following:
(i) 1/3 of 24 = 24×1/3 = 24/1 × 1/3 = 24 × 1 / 1×3 =8
(ii) 3/4 of 32 = 32 × 3/4 = 32/1×3/4= (32×3) / (1×4) = (8×3) / (1×1)=24
(iii) 5/9 of 45 = 45×5/9 = 45/1 × 5/9 = (45×5) / (1×9) = (5×5) / (1×1)=25
(iv) 7/50 of 1000 = 1000 × 7/50 = 1000/1×7/50 = (20×7) / (1×1)=140
(v) 3/20 of 1020 = 1020×3/20 = 1020/1×3/20 = (51×3)/(1×1)=153
(vi) 5/11 of Rs 220 = Rs (220×5/11) = Rs (20 × 5 ) = Rs 100
(vii) 4/9 of 54 m = (4/9×54)m = (4 × 6)m = 24 m
(viii) 6/7 of 35 L = (6/7×35)L = (6 × 5) L = 30 L
(ix) 1/6 of 1 h = 1/6 of 60 min = (60×1/6) min = 10 min
(x) 5/6 of an year = 5/6 of 12 months = (12×5/6) months = (2 × 5) months = 10 months
(xi) 7/20 of a kg = 7/20 of 1000 g = (1000×7/20) g = (50 × 7) gm = 350 g
(xii) 9/20 of 1 m = 9/20 of 100 cm = (100×9/20) cm = (5 × 9) cm = 45 cm
(xiii) 7/8 of a day = 7/8 of 24 h = (24×7/8) h = (3 × 7) = 21 h
(xiv) 3/7 of a week = 3/7 of 7 days = (7×3/7) days = 3 days
(xv) 7/50 of 1 L = 7/50 of 1000 ml = (1000×7/50) ml = (20 × 7) ml = 140 ml

Q.4. Apples are sold at Rsper kg. What is the cost of kg of apples?
Ans. Cost of 1 kg apple = = 244/5
Cost of kg apples =× 244/5 = 15/4 × 244/5= 183
Hence, the cost ofapples is 183.

Q.5. Cloth is being sold at Rsper metre. What is the cost of metres of this cloth?
Ans. Cost of 1 m of cloth = Rs= Rs 85/2
∴ Cost ofm 535 m of cloth = Rs (85/2 ×)
= Rs (85/2 × 28/5)=Rs ((85×28) / (2×5))
=Rs (17×14)=Rs 238
Hence, the cost ofof cloth is Rs 238.

Q.6. A car covers a certain distance at a uniform speed ofkm per hour. How much distance will it cover in 9 hours?
Ans. Distance covered by the car in 1h =km
Distance covered by the car in 9h  =(×9) km
=(200/3×9) km =(200×9) / (3×1) km
=(200×3) km=600 km
Hence, the distance covered by the car in 9 h will be 600 km.

Q.7. One tin holdslitres of oil. How many litres of oil can 26 such tins hold?
Ans. Capacity of 1 tin =L= 51/4 L
∴ Capacity of 26 such tins =(26×51/4) L
= (26/1×51/4) L =(26×51) / (1×4) L
= (13×51) / (1×2) L = (663/2) L
=L
Hence, 26 such tins can holdL of oil.

Q.8. For a particular show in a circus, each ticket costs Rs 35123512. If 308 tickets are sold for the  show, how much amount has been collected?
Ans. Cost of 1 ticket = Rs= Rs 7/12
∴ Cost of 308 tickets = Rs (7/12×308) =Rs (7/12×308/1)
=Rs (71×154)
=Rs 1093
Hence, 308 tickets were sold for Rs 10,934.

Q.9. Nine boards are stacked on the top of each other. The thickness of each board iscm. How high is the stack?
Ans. Thickness of 1 board =cm
∴ Thickness of 9 boards = (9×) cm
=(9/1×11/3) cm
= (3 × 11) cm
= 33 cm
Hence, the height of the stack is 33 cm.

Q.10. Rohit takesminutes to make complete round of a circular park. How much time will he take to make 15 rounds?
Ans. Time taken by Rohit to complete one round of the circular park =min = 24/5 min
∴ Time taken to complete 15 rounds =(15×24/5) min
= (3 × 24) min
= 72 min
= 1 h 12 min [∵ 1 hr = 60 min]
Hence, Rohit will take 1 h 12 min to make 15 complete rounds of the circular park.

Q.11. Amit weighs 35 kg. His sister Kavita's weight is 3/5 of Amit's weight. How much does Kavita weigh?
Ans. Weight of Amit = 35 kg
Weight of Kavita = 3/5 of Amit's weight
= 35 kg x 3/5
= (35×3/5)kg
=(7×3) kg=21 kg
Hence, Kavita's weight is 21 kg.

Q.12. There are 42 students in a class and 5/7 of the students are boys. How many girls are there in the class?
Ans. Number of boys in the class = 5/7 of the total no. of students
=5/7 × 42 = (5×42) / 7
=5×6=30
∴ Number of girls in the class = 42 − 30 = 12
Hence, there are 12 girls in the class.

Q.13. Sapna earns Rs 24000 per month. She spends 7/8 of her income and deposits rest of the money in a bank. How much money does she deposit in the bank each month?
Ans. Total monthly income = 24000
Monthly expenditure = 7/8 of 24000
=24000×7/8
=21000
Monthly savings =24000−21000
= 3000

Q.14. Each side of a square field ism. Find its area.
Ans. Side of the square field =m
∴ Area of the square = (side)²
= (m)²
= (14/3 m)²
= 14/3 m ×14/3 m
= (14×14) / (3×3) m²
= 196/9 m²
=m²
Hence, the area of the square field ism².

Q.15. Find the area of a rectangular park which ism long andm broad.
Ans. Length of the rectangular park =m = 125/3 m
Its breadth =m = 93/5 m
∴ Its area = length × breadth
= (125/3 × 93/5) m²
= (25 × 31) m = 775 m²
Hence, the area of the rectangular park is 775 m².