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)