Question

Question 18
Which of the following is not true?
(A) $(7+8)+9=7+(8+9)$
(B) $(7\times 8)\times 9=7\times (8\times 9)$
(C) $7+8\times 9=(7+8)\times (7+9)$
(D) $7\times (8+9)=(7\times 8)+(7\times 9)$

Answer 1

Let us solve each option and find out which one is not true.

(a) We have, $(7+8)+9=7+(8+9)$
LHS $=(7+8)+9$
$=15+9=24$
RHS $=7+(8+9)$
$=7+17=24$
$\therefore$ LHS = RHS
So, it is true.

(b) We have, $(7\times 8)\times 9=7\times (8\times 9)$
LHS $=(7\times 8)\times 9=56\times 9=504$
RHS $=7\times (8\times 9)=7\times 72=504$
$\therefore$ LHS = RHS
So, it is true.

(c) We have,$7+8\times 9=(7+8)\times (7+9)$
LHS $=7+8\times 9=7+72=79$
RHS $=(7+8)\times (7+9)=15\times 16=240$
$\because 79\ne 240$
$\because$ LHS $\ne$ RHS
So, it is false.

(d) We have, $7\times (8+9)=(7\times 8)+(7\times 9)$
LHS $=7\times (8+9)=7\times 17=119$
RHS $=(7\times 8)+(7\times 9)=56+63=119$
$\therefore$ LHS = RHS
So, it is true.

Hence, the answer is Option (C).