Students can practice TS 6th Class Maths Solutions Chapter 2 Whole Numbers Ex 2.3 to get the best methods of solving problems.
TS 6th Class Maths Solutions Chapter 2 Whole Numbers Exercise 2.3
Question 1.
Study the pattern:
1 × 8 + 1 = 9
12 × 8 + 2 = 98
123 × 8 + 3 = 987
1234 × 8 + 4 = 9876
12345 × 8 + 5 = 98765
Write the next four steps. Can you find out how the pattern works?
Answer:
123456 × 8 + 6 = 987654 .
1234567 × 8 + 7 = 9876543
12345678 × 8 + 8 = 98765432
123456789 × 8 + 9 = 987654321
Working pattern is as follows:
1) Write the smallest of the natural numbers, multiply it by 8 and add 1 to product obtained. You get a single digit number (i.e.) 9. i.e., 1 × 8 + 1 = 9
2) Write the number formed by the first two natural numbers in the same order, multiply it by 8 and add 2 to the product obtained. You get a two digit number with 9 tens place and the next digit (succeeding digit) decreases by 1.
i.e., 12 × 8 + 2 = 98
3) Write the number formed by the first three natural numbers in the same order, multiply it by 8 and add 3 to the product obtained. You get a three digit number with 9 in hundreds place and the next two digits gradually decrease by 1,
i.e., 123 × 8 + 3 = 987 and so on.
Question 2.
Study the pattern:
91 × 11 × 1 = 1001
91 × 11 × 2 = 2002
91 × 11 × 3 = 3003
Write next seven steps. Check, whether the result is correct.
Try the pattern for 143 × 7 × 1, 143 × 7 × 2 ………..
Answer:
91 × 11 × 4 = 4004
91 × 11 × 5 = 5005
91 × 11 × 6 = 6006
91 × 11 × 7 = 7007
91 × 11 × 8 = 8008
91 × 11 × 9 = 9009
91 × 11 × 10= 10010
Verification :
91 × 11 × 4 = 91 × 44
= 91 × (40 + 4)
= (91 × 40) + (91 × 4)
= 3640 + 364
= 4004
143 × 7 × 1 = 1001
143 × 7 × 2 = 2002
143 × 7 × 3 = 3003
143 × 7 × 4 = 4004
143 × 7 × 5 = 5005
Question 3.
How would we multiply the numbers 13680347, 35702369 and 25692359 with 9 mentally? What is the pattern that emerges.
Answer:
(i) 13680347 × 9 = 13680347 × (10 – 1)
= 13680347 × 10 – 13680347 × 1
= 136803470 – 13680347
= 123123123
(ii) 35702369 × 9 = 35702369 × (10 – 1)
= 35702369 × 10 – 35702369 × 1
= 357023690 – 35702369
= 321321321
(iii) 25692359 × 9
= 25692359 × (10 – 1)
= 25692359 × 10 – 25692359 × 1
= 256923590 – 25692359
= 231231231
Working pattern : If any number is to be multiplied by 9, first multiply the given number by 10 (write ‘0’ at the end of the number) and subtract the given number from the product obtained. (∴ 9 = 10-1)