8. Simplify.
(i) (21.6 ÷ 1.2) × 3.9
(ii) (2.8 × 1.6) ÷ 12.8
(iii) (12.8 ÷ 0.125) ÷ 3.2
9. The product of two decimals is 0.252. If one of them is 0.72, find the other.
10. A bar of chocolate costs ₹10.50 and a packet of chips costs ₹6.75. What will be the total cost of 8 bars of chocolate and 5 packets of chips?
11. Eight copies of a book cost ₹523.60. What is the cost of a copy of the book?
12. If 40 vessels of equal capacity can be filled with 186 litres of water, find the capacity of each vessel.
13. A certain sum of money is distributed among 26 people. If each person receives ₹6.45 and ₹2.30 is left in the end, what was the initial sum of money?
Answer (2)
The answers to the simplification problems are 70.2, 0.35, and 32 respectively. The other decimal is approximately 0.35, and the total cost of items is ₹117.75. The cost of one book is ₹65.45, each vessel holds 4.65 liters, and the initial sum of money is ₹170.00.
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Let's go through each part of the question step by step.
Simplify:
(i) ( 21.6 ÷ 1.2 ) × 3.9
First, divide:
21.6 ÷ 1.2 = 18
Then, multiply the result by 3.9:
18 × 3.9 = 70.2
(ii) ( 2.8 × 1.6 ) ÷ 12.8
First, multiply:
2.8 × 1.6 = 4.48
Then, divide the result by 12.8:
4.48 ÷ 12.8 ≈ 0.35
(iii) ( 12.8 ÷ 0.125 ) ÷ 3
First, divide:
12.8 ÷ 0.125 = 102.4
Then, divide the result by 3:
102.4 ÷ 3 ≈ 34.1333 or 34.13 rounded to two decimal places.
Find the other decimal:
The product of two decimals is 0.252. If one of them is 0.72, find the other.
Let's denote the unknown decimal by x . We have:
0.72 × x = 0.252
Solve for x :
x = 0.72 0.252 ≈ 0.35
Total cost of chocolates and chips:
The cost of a bar of chocolate is ₹10.50 and a packet of chips is ₹6.75.
For 8 bars of chocolate:
8 × 10.50 = ₹84.00
For 5 packets of chips:
5 × 6.75 = ₹33.75
Total cost:
₹84.00 + ₹33.75 = ₹117.75
Cost of a copy of the book:
Eight copies of a book cost ₹523.60.
To find the cost of one copy:
₹523.60 ÷ 8 = ₹65.45
Capacity of each vessel:
If 40 vessels can be filled with 186 liters of water, then the capacity of each vessel is:
186 ÷ 40 = 4.65 liters.
Initial sum of money:
Each of the 26 people receives ₹6.45, and ₹2.30 is left over.
Amount distributed:
26 × 6.45 = ₹167.70
Adding the leftover:
₹167.70 + ₹2.30 = ₹170.00
The initial sum of money was ₹170.00.
