1. Calculate using suitable rearrangements:
(i) 31 + 32 + 33 + 34 + 35 + 65 + 66 + 67 + 68 + 69
(ii) 1 + 2 + 3 + 4 + 996 + 997 + 998 + 999
2. What is the difference between the largest number of 5 digits and the smallest 6 digits?
3. The digits of 6 and 9 of the number 36490 are interchanged. Find the difference between the original number and the new number.
4. Determine the products by suitable rearrangement:
(i) 8 x 125 x 40 x 25
(ii) 250 x 60 x 50 x 8
(iii) 37256 x 25 x 9 x 40
5. Determine the product of:
6. (i) The greatest number of 4-digits and the smallest number of 3-digits
(ii) Smallest number of 2-digits and the greatest number of 5-digits.
7. A dealer purchased 120 LCD television sets. If the cost of each set is Rs. 20000, determine the cost of all sets together.
8. Find the value of each of the following using properties:
(i) 493 x 9 + 493 x 2
(ii) 1568 x 184 – 1568 x 84
Answers
Answer:
(i) 31 + 32 + 33 + 34 + 35 + 65 + 66 + 67 + 68 + 69
=500
(ii) 1 + 2 + 3 + 4 + 996 + 997 + 998 + 999=4000
2) If we take only natural numbers then, Largest number of 5digits is 99999, and smallest 6 digits number is 100000..
100000-99999=1
3)
THE ORIGINAL NUMBER IS 36490
AFTER INTERCHANGING 6 AND 9 WE GET A NUMBER
THE NUMBER IS 39460
ACCORDING TO THE QUESTION,
WE HAVE TO FIND OUT THE DIFFERENCE BETWEEN THEIR ORIGINAL AND NEW NUMBER TO GET THE DIFFERENCE.
ORIGINAL VALUE - NEW VALUE
36490 - 39460
-2970
i) 8 x 125 x 40 x 25 =1000000
ii) 250 x 60 x 50 x 8 =6000000
iii) 37256 x 25 x 9 x 40=335304000
6)i)The smallest 4-digit positive integer is 1000 and the largest 3-digit positive integer is 999, so the difference between them is 1. If negative numbers are allowed, then the smallest 4-digit integer is -9999 and the largest 3-digit integer is 999; -9999 = 999 = -10998.
ii) Smallest number of 5 digits = 10000. (If one is added to 9999, we get 9999 + 1 = 10000). Thus, if 1 is added to 9 (greatest 1-digit number), we get 10 (smallest 2-digit number). If 1 is added to 99 (greatest 2-digit number), we get 100 (smallest 3-digit number).
7) the cost of 120 LCD TVs = 120 × 20,000 = 2400000. that means 120 LCD TV set cost = 24,00000.
8)i) 493 x 9 + 493 x 2 =5423
ii) 1568 x 184 =288512
1568 x 84 =131712
288512-131712= 156800