Question

Evaluate:
$7\frac{1}{4}-[\frac{5}{6}\div[\frac{1}{3}-(\frac{1}{2}\times(\frac{3}{4}-\frac{1}{4}))]]$

• A. -3 1/4
• B. 3 1/4
• C. -2 3/4
• D. 2 3/4

Answer 1

Answer:

C. -2 3/4

Evaluate step by step:

$7\frac{1}{4}-\left[\frac{5}{6}\div\left[\frac{1}{3}-\left(\frac{1}{2}\times\left(\frac{3}{4}-\frac{1}{4}\right)\right)\right]\right]$

Simplify inside parentheses

$\frac{3}{4} - \frac{1}{4} = \frac{2}{4} = \frac{1}{2}$

Multiply

$\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$

Subtract

$\frac{1}{3} - \frac{1}{4} = \frac{4 - 3}{12} = \frac{1}{12}$

Division

$\frac{5}{6} \div \frac{1}{12} = \frac{5}{6} \times 12 = 10$

Convert mixed number

$7\frac{1}{4} = \frac{29}{4}$

Final subtraction

$\frac{29}{4} - 10 = \frac{29}{4} - \frac{40}{4} = -\frac{11}{4}$

Final Answer:

$-\frac{11}{4}$

We already got:

$-\frac{11}{4}$

Now convert to a mixed fraction:

$11 \div 4 = 2 \text{ remainder } 3$

So,

$-\frac{11}{4} = -2\frac{3}{4}$