Using this shortcut, find out whether the following numbers are divisible by 11. Further, find the remainder Class 8

Using this shortcut, find out whether the following numbers are divisible by 11. Further, find the remainder Class 8

Question 1.

Using this shortcut, find out whether the following numbers are divisible by 11.

Further, find the remainder if the number is not divisible by 11. Class 8

(i) 158

(ii) 841

(iii) 481

(iv) 5529

(v) 90904

(vi) 857076

Solution:

(i) 158 = 100 + 50 + 8 Remainder by shortcut = 1 - 5 + 8 = 4.

So, 158 is not divisible by 11.

Remainder is 4.

(ii) 841 = 800 + 40 + 1 Remainder by shortcut = 8 - 4 + 1 = 5.

So, 841 is not divisible by 1.

Remainder is 5.

(iii) 481 = 400 + 80 + 1

Remainder by shortcut = 4 - 8 + 1 = -3.

So, 481 is not divisible by 11.

Remainder is -3 + 11 = 8.

(iv) 5529 = 5000 + 500 + 20 + 9

Remainder by shortcut = - 5 + 5 — 2 + 9 = 7.

So, 5529 is not divisible by 11.

Remainder is 7.

(v) 90904 = 90000 + 0 × 1000 + 900 + 0 × 10 + 4

Remainder by shortcut = 9 - 0 + 9 - 0 + 4 = 22.

22 is a multiple of 11.

So, 90904 is divisible by 11.

(vi) 857076 = 800000 + 50000 + 7000 + 0 × 100 + 70 + 6

Remainder by shortcut = -8 + 5 - 7 + 0 - 7 + 6 = -11.

-11 is divisible by 11.

So, 857076 is divisible by 11.