AP State Syllabus AP Board 6th Class Maths Solutions Chapter 2 Whole Numbers Ex 2.3 Textbook Questions and Answers.

## AP State Syllabus 6th Class Maths Solutions 2nd Lesson 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:

12 × 8 + 2 = 98

123 × 8 + 3 = 987

1234 × 8 + 4 = 9876

12345 × 8 + 5 = 98765

123456 × 8 + 6 = 987654

1234567 × 8 + 7 = 9876543

12345678 × 8 + 8 = 98765432

123456789 × 8 + 9 = 987654321

The digits on the L.H.S. are in increasing order and the digits on the result (right side) are in decreasing order.

Question 2.

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)

Distributive property of multiplication over subtraction.

= 13680347 × 10 – 13680347 × 1

= 136803470 – 13680347

= 123123123

ii) 35702369 × 9 = 35702369 × (10 – 1)

Distributive property of multiplication over subtraction.

= 35702369 × 10 – 35702369 × 1

= 357023690 – 35702369

= 321321321

iii) 25692359 × 9 = 25692359 × (10 – 1)

Distributive property of multiplication over subtraction.

= 25692359 × 10 – 25692359 × 1

= 256923590 – 25692359

= 231231231