Page 41 - Start Up Mathematics_6

Division Algorithm
If a whole number x is divided by a non-zero whole number y, then there exists a quotient q and
a remainder r such that x = yq + r, where q and r are whole numbers and r < y, i.e.,
q
y x
–qy
r

Thus, Dividend = quotient × divisor + remainder

Let’s divide 14 by 3.
4
3 We have, dividend = 14, divisor = 3, quotient = 4, remainder = 2.
14
–12 Let’s verify, dividend = quotient × divisor + remainder
2 RHS = 4 × 3 + 2 = 14 = dividend = LHS, hence true.

EXERCISE 2.2

1. Fill in the blanks with suitable numbers.
(a) 456 + 567 = 567 + ________ (b) 9,876 + 124 + 1,000 = 1,000 + ________ + 9,876
(c) 8,769 + 3,000 + 231 = 231 + 3,000 + ________
2. Add the following by suitable rearrangements.
(a) 437 + 680 + 363 + 220 (b) 1 + 2 + 3 + 4 + 5 + 95 + 96 + 97 + 98 + 99
(c) 14,419 + 888 + 112 + 581 (d) 21 + 22 + 23 + 24 + 25 + 75 + 76 + 77 + 78 + 79

3. Find the products by applying suitable properties.
(a) 238 × 103 (b) 154 × 99 (c) 387 × 11 (d) 1,003 × 138
4. Find the products using suitable rearrangements.
(a) 250 × 35 × 40 (b) 125 × 60 × 8 (c) 25 × 451 × 4 (d) 625 × 20 × 50 × 8
5. Find the values of the following:

(a) 497 × 37 + 497 × 13 (b) 4,279 × 92 + 8 × 4,279
(c) 8,126 × 169 – 8,126 × 69 (d) 1,684 × 782 + 1,684 × 218
6. Divide 6,750 by 13 and verify the result by division algorithm.
7. Divide 26,755 by 16 and verify the result by division algorithm.
8. Evaluate the following:
(a) (625 ÷ 25) ÷ 5 (b) 0 ÷ 21 (c) 22 ÷ 0 (d) (15,625 ÷ 125) ÷ 25
9. In the number 6,43,590 the digits 3 and 9 were interchanged by mistake. Find the difference
of the original number and the number formed by mistake.

10. Find the difference between the smallest five-digit number and the largest three-digit
number.

11. How many digits are there in a successor of a three-digit number?
12. A theatre is to be constructed in which each row must have 40 seats. If the required seating
capacity of the theatre is 960, find the number of rows in the theatre.
13. Find the number which on dividing by 25 gives 30 as the quotient and 15 as the remainder.

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