Solve: 1/2 - (1/4 ÷ 8/9 + 3/4 ÷ 12) Complex Fraction Operations

Question

$\frac{1}{2}-(\frac{1}{4}:\frac{8}{9}+\frac{3}{4}:(4\cdot3))=\text{?}$

00:00 Solve

00:05 Division is also multiplication by the reciprocal

00:15 Move the division to the denominator

00:20 Multiply numerator by numerator and denominator by denominator

00:23 Simplify what we can

00:31 Negative times positive is always negative

00:43 Find a common denominator, multiply by each denominator

00:56 Combine into one fraction

01:03 And this is the solution to the question

To solve this problem, we'll follow these equations:

Step 1: Simplify $\frac{1}{4} \div \frac{8}{9} = \frac{1}{4} \times \frac{9}{8} = \frac{9}{32}$ .
Step 2: Simplify $\frac{3}{4} \div (4 \cdot 3) = \frac{3}{4} \div 12 = \frac{3}{4} \times \frac{1}{12} = \frac{3}{48} = \frac{1}{16}$ .
Step 3: Add the results from Steps 1 and 2: $\frac{9}{32} + \frac{1}{16}$ . Convert $\frac{1}{16}$ to $\frac{2}{32}$ to have common denominators:
$\frac{9}{32} + \frac{2}{32} = \frac{11}{32}$ .
Step 4: Subtract $\frac{11}{32}$ from $\frac{1}{2}$ . Convert $\frac{1}{2}$ to $\frac{16}{32}$ :
$\frac{16}{32} - \frac{11}{32} = \frac{5}{32}$ .

Therefore, the solution to the problem is $\frac{5}{32}$ .

$\frac{5}{32}$