Which of the following is not true?

MCQ

Which of the following is not true$?$

A
$(7 + 8) + 9 = 7 + (8 + 9)$
B
$(7 \times 8) \times 9 = 7 \times (8 \times 9)$
✓
$7 + 8 \times 9 = (7 + 8) \times (7 + 9)$
D
$7 \times (8 + 9) = (7 \times 8) + (7 \times 9)$

✓

Answer

Correct option: C.

$7 + 8 \times 9 = (7 + 8) \times (7 + 9)$

$a.$ We have, $(7 + 8) + 9 = 7 + (8 + 9)$
$\text{LHS} = (7 + 8) + 9 = 15 + 9 =24$
$\text{RHS} = 7 + (8 + 9) = 7 + 17=24$
$\text{LHS} = \text{RHS}$ So, it is true.
$b.$ We have, $(7 \times 8) \times 9 = 7 \times (8 \times 9)$
$\text{LHS} = (7 \times 8) \times 9= 56 \times 9 = 504$
$\text{RHS} = 7 \times (8 \times 9)= 7 \times 72 = 504$
$\text{LHS} = \text{RHS}$ So, it is true.
$c.$ We have, $7 + 8 \times 9 = (7 + 8) \times (7 + 9)$
$\text{LHS} = 7 + 8 \times 9 = 7 + 72 = 79$
$\text{RHS} = (7 + 8) \times (7 + 9)=15 \times 16 = 240$
$\therefore 79 \neq 240$
$\therefore \text{LHS} \neq \text{RHS}$ So, it is false.
$d.$ We have, $7 \times (8 + 9) = (7 \times 8) + (7 \times 9)$
$\text{LHS} = 7 \times (8 + 9)=7 \times 17 = 119$
$\text{RHS} = (7 \times 8) + (7 \times 9) = 56 + 63=119$
$\therefore \text{LHS} = \text{RHS}$ So, it is true.

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