1. Knowing Our Numbers Worksheet With Answers Page 20
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253. Estimate each of the following sum to its nearest thousands:
(a) 56,784 + 76,834
(b) 43,829 + 34,784
(c) 24,568 + 54,118
(d) 21,384 + 45,379
4. Estimate each of the following difference to its nearest tens:
(a) 67 – 43
(b) 689 – 432
(c) 564 – 321
(d) 856 – 672
5. Estimate each of the following difference to its nearest hundreds:
(a) 674 – 432
(b) 689 – 532
(c) 764 – 321
(d) 956 – 572
6. Estimate each of the following difference to its nearest thousands:
(a) 7,674 – 3,432
(b) 3,689 – 2,532
(c) 6,764 – 5,321
(d) 8,956 – 7,572
7. Estimate the following products by rounding off each number to its nearest tens:
(a) 58 × 45
(b) 67 × 33
(c) 78 × 32
(d) 23 × 98
8. Estimate the following products by rounding off each number to its nearest hundreds:
(a) 581 × 456
(b) 167 × 233
(c) 478 × 132
(d) 223 × 198
9. Estimate the following products using general rule:
(a) 345 × 46
(b) 3,427 × 456 (c) 2,192 × 479 (d) 9,876 × 32
10. Find the estimated quotient for each of the following:
(a) 567 ÷ 24
(b) 861 ÷ 29
(c) 347 ÷ 13
(d) 691 ÷ 18
Brackets
<
Vani bought 5 sketch pens from a stationery shop for
3 each. Vani’s brother Nikhil bought 7 sketch
<
pens for
3 each. Vani calculated that the total money spent by them is 5 × 3 + 7 × 3 =
<
15 + 21 = 36, i.e.,
36. Nikhil calculated it by a different method but got the same amount, i.e.,
<
(5 + 7) × 3 = 12 × 3 = 36, i.e.,
36. Nikhil combined the total number of pens, i.e., 5 + 7 and treated
<
it as a single number by putting brackets and then multiplied it by the cost of 1 pen, i.e.,
3. The
rule is to first simplify everything in the bracket to a single number and then perform the other
operations outside.
Expanding Brackets
We will now see how the use of brackets allows us to make calculations simple and systematic.
(i) 13 × 1,013 = 13 × (1,000 + 13)
= 13 × 1,000 + 13 × 13
= 13,000 + 169 = 13,169
(ii) 102 × 105 = 102 × (100 + 5)
= 102 × 100 + 102 × 5
= (100 + 2) × 100 + (100 + 2) × 5
= 100 × 100 + 2 × 100 + 100 × 5 + 2 × 5
= 10,000 + 200 + 500 + 10 = 10,710
Roman Numerals
We are well aware of the numerals 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. These numerals are used in Hindu-
Arabic numeral system. However, one of the old systems of numeration developed by Romans is
also in common use. This system is called Roman system of numeration. There are seven distinct
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