Question

Solve using properties of integers:

$\frac{(3+2)+5+2\times (3+5)}{2\times 3+2\times 5+3+(2+5)}=?$

• A. 1
• B. 2
• C. 5
• D. 10

Answer 1

Answer: (A)

Here,
The distributive property of integers under multiplication states that $a\times (b+c)=a\times b+a\times c$
Now, we can write
$2\times (3+5)=2\times 3+2\times 5$
The associativity property of integers under addition states that $a+(b+c)=(a+b)+c$
Now, we can write
$3+(2+5)=(3+2)+5$
Writing the denominator by applying both Distributive property and Associative property,
$2\times 3+2\times 5+3+(2+5)=2\times (3+5)+(3+2)+5$
Since, numerator and denominator becomes equal.
$\Rightarrow$ $\frac{(3+2)+5+2\times (3+5)}{2\times 3+2\times 5+3+(2+5)}$

$=\frac{(3+2)+5+2\times (3+5)}{2\times (3+5)++3+(2+5)}$

$=1$

Hence, Option $B$ is correct.