For statement given below, determine whether it is always true, s… - Vidyadip

Question

For statement given below, determine whether it is always true, sometimes true, or never true. Explain your answer. Mention examples and non-examples as appropriate. Justify your claim using algebra.
The sum of a multiple of 6 and a multiple of 3 is a multiple of 9.

✓

Answer

Let multiple of 6 be 6 a, multiple of 3 be 3b.
Sum : $6 a +3 b=3(2 a + b )$.
For it to divisible by $9,2 a+b$ must be divisible by 3 .
Example :
$6(6 \times 1)+3(3 \times 1)=9 \rightarrow$ divisible by 9
$6+6=12 \rightarrow$ not divisible by 9
Conclusion : Sometimes true.

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