Question

Compute the following difference

$(11.6\times 10.4)-(11.3\times 10.7)$

• A. $-0.54$
• B. $-0.27$
• C. $-0.81$
• D. $-0.33$

Answer 1

The correct option is B

$-0.27$

The given expression is

$(11.6\times 10.4)-(11.3\times 10.7$)

$=(11+0.6)(11-0.6)-(11+0.3)(11-0.3)$

$=[{11}^2-(0.6{)}^2]-[{11}^2-{0.3}^2]$

$={11}^2-{0.6}^2-{11}^2+{0.3}^2$

$={0.3}^2-{0.6}^2$

$=(0.3+0.6)(0.3-0.6)$ $[a^2-b^2=(a+b\left)\right(a-b\left)\right]$

$=0.9\times -0.3$

$=-0.27$