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

Q: Why do I flip the second fraction when dividing?

Division by a fraction is the same as multiplication by its reciprocal. So $ \frac{1}{4} \div \frac{8}{9} $ becomes $ \frac{1}{4} \times \frac{9}{8} $. This makes the calculation much easier!

Q: How do I know what common denominator to use?

Find the least common multiple (LCM) of all denominators. In this problem, we need LCM of 32, 16, and 2, which is 32. This lets us add and subtract all fractions easily.

Q: What does the colon symbol (:) mean in math?

The colon (:) is another way to write division, just like the ÷ symbol. So $ \frac{1}{4}:\frac{8}{9} $ means the same as $ \frac{1}{4} \div \frac{8}{9} $.

Q: Why do I need parentheses in this problem?

Parentheses show which operations to do first! Without them, you'd subtract $ \frac{1}{2} - \frac{1}{4} $ first instead of handling the complex fraction operations inside the parentheses.

Q: Can I convert everything to decimals instead?

You could, but fractions give you the exact answer! Decimals might round off and give you an approximate result. Plus, the answer choices are all fractions, so stick with fractions.

Q: How do I check if my final answer is correct?

Work backwards! Start with $ \frac{5}{32} $ and verify that $ \frac{1}{2} - \frac{11}{32} = \frac{16}{32} - \frac{11}{32} = \frac{5}{32} $ ✓

Complex Fraction Operations with Mixed Division

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

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

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

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

Step-by-step solution

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 $\frac{5}{32}$ .

Final Answer

$\frac{5}{32}$

Key Points to Remember

Essential concepts to master this topic

Division Rule: Change division to multiplication by the reciprocal
Technique: $\frac{1}{4} \div \frac{8}{9} = \frac{1}{4} \times \frac{9}{8} = \frac{9}{32}$
Check: Convert all fractions to common denominator 32 and verify ✓

Common Mistakes

Avoid these frequent errors

Adding fractions with different denominators directly
Don't add $\frac{9}{32} + \frac{1}{16} = \frac{10}{48}$ ! This ignores different denominators and gives wrong results. Always find a common denominator first: convert $\frac{1}{16}$ to $\frac{2}{32}$ before adding.

Practice Quiz

Test your knowledge with interactive questions

$$ 100-(5+55)= $$

FAQ

Everything you need to know about this question

Why do I flip the second fraction when dividing?

Division by a fraction is the same as multiplication by its reciprocal. So $\frac{1}{4} \div \frac{8}{9}$ becomes $\frac{1}{4} \times \frac{9}{8}$ . This makes the calculation much easier!

How do I know what common denominator to use?

Find the least common multiple (LCM) of all denominators. In this problem, we need LCM of 32, 16, and 2, which is 32. This lets us add and subtract all fractions easily.

What does the colon symbol (:) mean in math?

The colon (:) is another way to write division, just like the ÷ symbol. So $\frac{1}{4}:\frac{8}{9}$ means the same as $\frac{1}{4} \div \frac{8}{9}$ .

Why do I need parentheses in this problem?

Parentheses show which operations to do first! Without them, you'd subtract $\frac{1}{2} - \frac{1}{4}$ first instead of handling the complex fraction operations inside the parentheses.

Can I convert everything to decimals instead?

You could, but fractions give you the exact answer! Decimals might round off and give you an approximate result. Plus, the answer choices are all fractions, so stick with fractions.

How do I check if my final answer is correct?

Work backwards! Start with $\frac{5}{32}$ and verify that $\frac{1}{2} - \frac{11}{32} = \frac{16}{32} - \frac{11}{32} = \frac{5}{32}$ ✓

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