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 two steps. Can you say how the pattern works? (Hint: 12345 = 11111 + 1111 + 111 + 11 + 1).

Question – 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 two steps. Can you say how the pattern works?
(Hint: 12345 = 11111 + 1111 + 111 + 11 + 1).

Solution 5.    

The pattern works as follows:

⇒1 × 8 + 1 = 9

⇒12 × 8 + 2 = (11 + 1) × 8 + 2

= 11 × 8 + 1 × 8 + 2              [By distributive property i.e., (a+ b)c = ac + cb]

= 88 + 8 +2

= 98

⇒123 × 8 + 3 = (111 + 11 +1) × 8 + 3

[By distributive property i.e., (a+ b+ c)×d = a× d + b ×d + c ×d]

= 111×8 + 11×8 + 1×8 +3

= 888 + 88 + 8 + 3

= 987

⇒1234 × 8 + 4 = (1111 + 111 + 11 + 1) × 8 + 4

[By distributive property i.e., (a+ b+ c+ e)×d = a× d + b ×d + c ×d + e ×d]

= 1111×8 + 111×8 + 11×8 + 1×8 + 4

= 8888 + 888 + 88 + 8 + 4

= 9876

⇒12345 × 8 + 5 = (11111 + 1111 + 111 + 11 + 1) × 8 + 5

[By distributive property i.e., (a+ b+ c+ e + f)×d = a× d + b ×d + c ×d + e ×d + f× d]

= 11111×8 + 1111×8 + 111×8 + 11×8 + 1×8 +5

= 88888 + 8888 + 888 + 88 + 8 + 5

= 98765

And thus, this pattern continues.

After carefully examining the pattern,

We can say that the next two steps are as follows:

123456 × 8 + 6  = 987654

1234567 × 8 + 7 = 9876543

Related Questions – 

• Which of the following will not represent zero (a) 1 + 0  (b) 0 × 0  (c)  0/2  (d) (10-10)/2
• If the product of two whole numbers is zero can we say that one or both of them will be zero ? Justify through examples.
• If the product of two whole numbers is 1, can we say that one or both of them will be 1? Justify through examples.
• Find using distributive property: (a) 728 × 101 (b) 5437 × 1001 (c) 824 × 25 (d) 4275 × 125 (e) 504 × 35