The DAV Class 6 Maths Book Solutions Pdf and DAV Class 6 Maths Chapter 1 Worksheet 5 Solutions of Natural Numbers and Whole Numbers offer comprehensive answers to textbook questions.
DAV Class 6 Maths Ch 1 WS 5 Solutions
Question 1.
Fill in the following blanks by using different properties of multiplication.
(a) 52 × (63 + 37) = (52 × _____) + (_____ × 37)
Solution:
63, 52
(b) 297 × (_____ + 43) = (297 × 88) + (297 × _____)
Solution:
88, 43
(c) _____ × (84 + 16) = 36 × 84 + 36 × _____
Solution:
36, 16
(d) 218 × 94 = (218 × _____) – (218 × 6)
Solution:
100
(e) 778 × 994 = (778 × 1000) – (778 × _____) – 778
Solution:
5
Question 2.
Re-arrange the numbers and then multiply them.
(a) 125 × 488 × 8
Solution:
125 × 488 × 8 = (125 × 8) × 488
= 100 × 488
= 48800
(b) 625 × 25 × 20 × 4
Solution:
625 × 25 × 20 × 4 = 625 × 20 × (25 × 4)
= 625 × (20 × 100)
= 625 × 2000
= 1250000
(c) 16 × 125 × 8 × 625
Solution:
16 × 125 × 8 × 625 = (16 × 125) × (8 × 625)
= 2000 × 5000
= 1,00,00,000
(d) 20 × 1975 × 5
Solution:
20 × 1975 × 5 = 1975 × (20 × 5)
= 1975 × 100
= 197500
(e) 8 × 25 × 125 × 40
Solution:
8 × 25 × 125 × 40 = (8 × 25) × (125 × 40)
= 200 × 5000
= 10,00,000
(f) 200 × 625 × 16 × 50
Solution:
200 × 625 × 16 × 50 = 625 × 16 × (200 × 50)
= (625 × 16) × 10000
= 10000 × 10000
= 10,00,00,000
Question 3.
Find the product by using distributive property.
(a) 241 × 107
Solution:
241 × 107 = 241 × (100 + 7)
= 241 × 100 + 7 × 241
= 24100 + 1687
= 25787
(b) 685 × 94
Solution:
685 × 94 = 685 × (100 – 6)
= 685 × 100 – 685 × 6
= 68500 – 4110
= 64390
(c) 439 × 995
Solution:
439 × 995 = 439 × (1000 – 5)
= 439 × 1000 – 5 × 439
= 439000 – 2195
= 436905
(d) 1009 × 1392
Solution:
1009 × 1392 = (1000 + 9) × 1392
= 1000 ×1392 + 9 × 1392
= 1392000 + 12528
= 1404528
(e) 98 × 553
Solution:
98 × 553 = (100 – 2) × 553
= 100 × 553 – 2 × 553
= 55300 – 1066
= 54234
(f) 999 × 399
Solution:
999 × 399 = (1000 – 1) × 399
= 1000 × 399 – 1 × 399
= 399000 – 399
= 298601
Question 4.
Find the value by using distributive property.
(a) 1562 × 62 + 1562 × 38
Solution:
1562 × 62 + 1562 × 38
= 1562 × (62 + 38)
= 1562 × 100
= 156200
(b) 638 × 176 – 638 × 75 – 638
Solution:
638 × 176 – 638 × 75 – 638
= 638 (176 – 75 – 1)
= 638 (176 – 76)
= 638 × 100
= 63800
(c) 85 × 15 + 15 × 15
Solution:
85 × 15 + 15 × 15
= 15 × (85 + 15)
= 15 × 100
= 1500
(d) 688 × 10 × 437 – 6880 × 337
Solution:
688 × 10 × 437 – 6880 x 337
= 6880 × 437 – 6880 × 337
= 6880 × (437 – 337)
= 6880 × 100
= 688000
(e) 125 × 8 × 883 + 117 × 25 × 40
Solution:
125 × 8 × 883 + 117 × 25 × 40
= (125 × 8) × 883 + 117 × (25 × 40)
= 1000 × 883 + 117 × 1000
= 1000 × (883 + 117)
= 1000 × 1000
= 1,00,00,00
(f) 750 × 17 + 750 × 38 + 27 × 750 + 18 × 750
Solution:
750 × 17 + 750 × 38 + 27 × 750 + 18 × 750
= 750 (17 + 38 + 27 + 18)
= 750 × 100
= 75000
Question 5.
Rohan buys 12 computers and 12 printers. If the cost of one computer and one printer is ₹ 56233 and ₹ 7867 respectively, find the total cost incurred by Rohan (Use distributive property of multiplication).
Solution:
Cost of 12 computers = ₹ (12 × 56233)
Cost of 12 printers = ₹ (12 × 7867)
∴ Total cost of 12 computers and 12 printers
= 12 × 56233 + 12 × 7867
= 12 × (56233 + 7867)
= 12 × 64100
= ₹ 769200
Question 6.
In a school, the monthly fee of a child is ₹ 497. If there are 2983 students in the school, find the total fee collected in a month. (Use distributive property of multiplication)
Solution:
Fee of one child = ₹ 497
Number of students = 2983
∴ Total collection of fee = ₹ (2983 × 497)
= 2983 × (500 – 3)
= 2983 × 500 – 2983 × 3
= 1491500 – 8949
= 1482551
Hence, total fee collected = ₹ 1482551