When is the sum of two multiples of 3, a multiple of 6 and when is it not? Explain the different Class 8

When is the sum of two multiples of 3, a multiple of 6 and when is it not? Explain the different Class 8

Question 1.

When is the sum of two multiples of 3, a multiple of 6 and when is it not? Explain the different possible cases, and generalise the pattern. Class 8

Solution:

Sums of 3 × 3 and 3 × 5, 3 × 5 and 3 × 9, 3 × 7 and 3 × 11, etc. are multiples of 6.

Also, sums of 3 × 2 and 3 × 6, 3 × 4 and 3 × 6, 3 × 4 and 3 × 10, etc. are multiple of 6.

But sums of 3 × 3 and 3 × 6, 3 × 6 and 3 × 9, 3 × 4 and 3 × 5, etc. are not multiple of 6.

That is sums of two odd multiples of 3 as well as sums of two even multiples of 3 are multiples of 6, but sums of an odd multiple of 3 and an even multiple of 3 are not multiples of 6.

Question 2.

Sreelatha says, “I have a number that is divisible by 9. If I reverse its digits, it will still be divisible by 9”. Class 8

(i) Examine if her conjecture is true for any multiple of 9.

(ii) Are any other digit shuffles possible such that the number formed is still a multiple of 9?

Solution:

(i) Yes, her conjecture is true for any multiple of 9.

(ii) Yes, reshuffling any digits, the number formed will still be a multiple of 9, because sum of the digits of the number will still remains a multiple of 9.