AP Board 6th Class Maths Solutions Chapter 2 Whole Numbers Ex 2.3

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.

AP Board 6th Class Maths Solutions Chapter 2 Whole Numbers Ex 2.3

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