Mathematical reasoning class 6 chapter 1 knowing our numbers ans
Answers
Answer:
Exercise 1.1 PAGE NO: 12
1. Fill in the blanks:
(a) 1 lakh = ………….. ten thousand.
(b) 1 million = ………… hundred thousand.
(c) 1 crore = ………… ten lakh.
(d) 1 crore = ………… million.
(e) 1 million = ………… lakh.
Solutions:
(a) 1 lakh = 10 ten thousand
= 1,00,000
(b) 1 million = 10 hundred thousand
= 10,00,000
(c) 1 crore = 10 ten lakh
= 1,00,00,000
(d) 1 crore = 10 million
= 1,00,00,000
(e) 1 million = 10 lakh
= 1,000,000
Difference between the two numbers = 76432 – 23467 = 52965
∴ The difference between the two numbers is 52965
6. A machine, on an average, manufactures 2,825 screws a day. How many screws did it produce in the month of January 2006?
Solutions:
Number of screws manufactured in a day = 2825
Since January month has 31 days
Hence, number of screws manufactured in January = 31 × 2825 = 87575
Hence, machine produce 87575 screws in the month of January 2006
7. A merchant had Rs 78,592 with her. She placed an order for purchasing 40 radio sets at Rs 1200 each. How much money will remain with her after the purchase?
Solutions:
Total money the merchant had = Rs 78592
Number of radio sets she placed an order for purchasing = 40 radio sets
Cost of each radio set = Rs 1200
So, cost of 40 radio sets = Rs 1200 × 40 = Rs 48000
Money left with the merchant = Rs 78592 – Rs 48000 = Rs 30592
Hence, money left with the merchant after purchasing radio sets is Rs 30592
8. A student multiplied 7236 by 65 instead of multiplying by 56. By how much was his answer greater than the correct answer?
Solutions:
Difference between 65 and 56 i.e (65 – 56) = 9
The difference between the correct and incorrect answer = 7236 × 9 = 65124
Hence, by 65124, the answer was greater than the correct answer
9. To stitch a shirt, 2 m 15 cm cloth is needed. Out of 40 m cloth, how many shirts can be stitched and how much cloth will remain?
Solutions:
Given
Total length of the cloth = 40 m
= 40 × 100 cm = 4000 cm
Cloth required to stitch one shirt = 2 m 15 cm
= 2 × 100 + 15 cm = 215 cm
Number of shirts that can be stitched out of 4000 cm = 4000 / 215 = 18 shirts
Hence 18 shirts can be stitched out of 40 m and 1m 30 cm of cloth is left out
10. Medicine is packed in boxes, each weighing 4 kg 500g. How many such boxes can be loaded in a van which cannot carry beyond 800 kg?
Solutions:
Weight of one box = 4 kg 500 g = 4 × 1000 + 500
= 4500 g
Maximum weight carried by the van = 800 kg = 800 × 1000
= 800000 g
Hence, number of boxes that can be loaded in the van = 800000 / 4500 = 177 boxes
11. The distance between the school and a student’s house is 1 km 875 m. Everyday she walks both ways. Find the total distance covered by her in six days.
Solutions:
Distance covered between school and house = 1 km 875 m = 1000 + 875 = 1875 m
Since, the student walk both ways.
Hence, distance travelled by the student in one day = 2 × 1875 = 3750 m
Distance travelled by the student in 6 days = 3750 m × 6 = 22500 m = 22 km 500 m
∴ Total distance covered by the student in six days is 22 km and 500 m
12. A vessel has 4 litres and 500 ml of curd. In how many glasses, each of 25 ml capacity, can it be filled?
Solutions:
Quantity of curd in the vessel = 4 l 500 ml = 4 × 1000 + 500 = 4500 ml
Capacity of 1 glass = 25 ml
∴ Number of glasses that can be filled with curd = 4500 / 25 = 180 glasses
Hence, 180 glasses can be filled with curd.
Exercise 1.3 Page NO: 23
1. Estimate each of the following using general rule:
(a) 730 + 998 (b) 796 – 314 (c) 12904 + 2888 (d) 28292 – 21496
Make ten more such examples of addition, subtraction and estimation of their outcome.
Solutions:
(a) 730 + 998
Round off to hundreds
730 rounds off to 700
998 rounds off to 1000
Hence, 730 + 998 = 700 + 1000 = 1700
(b) 796 – 314
Round off to hundreds
796 rounds off to 800
314 rounds off to 300
Hence, 796 – 314 = 800 – 300 = 500
(c) 12904 + 2888
Round off to thousands
12904 rounds off to 13000
2888 rounds off to 3000
Hence, 12904 + 2888 = 13000 + 3000 = 16000
(d) 28292 – 21496
Round off to thousands
28292 round off to 28000
21496 round off to 21000
Hence, 28292 – 21496 = 28000 – 21000 = 7000
Ten more such examples are
(i) 330 + 280 = 300 + 300 = 600
(ii) 3937 + 5990 = 4000 + 6000 = 10000
(iii) 6392 – 3772 = 6000 – 4000 = 2000
(iv) 5440 – 2972 = 5000 – 3000 = 2000
(v) 2175 + 1206 = 2000 + 1000 = 3000
(vi) 1110 – 1292 = 1000 – 1000 = 0
(vii) 910 + 575 = 900 + 600 = 1500
(viii) 6400 – 4900 = 6000 – 5000 = 1000
(ix) 3731 + 1300 = 4000 + 1000 = 5000
(x) 6485 – 4319 = 6000 – 4000 = 2000
2. Give a rough estimate (by rounding off to nearest hundreds) and also a closer estimate (by rounding off to nearest tens):
(a) 439 + 334 + 4317 (b) 108734 – 47599 (c) 8325 – 491 (d) 489348 – 48365
Make four more such examples.
Solutions:
(a) 439 + 334 + 4317
Rounding off to nearest hundreds
439 + 334 + 4317 = 400 + 300 + 4300
= 5000