Question

If we have a algebraic expression \[(2m)k = 6\] then \[mk = \]
A). 3
B). 4
C). 5
D). 6

Answer 1

Hint: Here we are given the value of \[(2m)k\] and told to find the value of \[mk\] we will use associative property of multiplication to separate 2 and mk and then we we will solve the equation to find the value of mk.

Complete step-by-step answer:
So we know that in associative property of multiplication we can write
\[(a \times b) \times c = a \times (b \times c)\]
So from here we can solve this as \[(2m)k = (2 \times m) \times k\]
Now by associative property we can write \[(2 \times m) \times k = 2 \times (m \times k)\]
Which means that \[2 \times (m \times k) = 6\] .
Now If we take the 2 from LHS to RHS as it is in multiplication in LHS it will be in division inRHS which means
\[\begin{array}{l}
\therefore 2 \times (m \times k) = 6\\
 \Rightarrow (m \times k) = \dfrac{6}{2}\\
 \Rightarrow mk = 3
\end{array}\]
Hence it is clear that option A is the correct option here.

Note: In associative property it must be noted that if a,b,c belongs to a set say S and \[ \circ \] is a binary operation in S then we can write \[(a \circ b) \circ c = a \circ (b \circ c)\] . We have used this property of associates to discriminate 2 from mk.