Solve the Fraction Division Problem: (1 7/8 ÷ 4/5) ÷ (3 x 8) = ?

Q: Why do I convert the mixed number first?

Mixed numbers like $ 1\frac{7}{8} $ are much harder to work with in division problems. Converting to improper fractions like $ \frac{15}{8} $ makes the math cleaner and prevents errors.

Q: What does the colon (:) mean in this problem?

The colon means division, just like ÷. So $ \frac{15}{8}:\frac{4}{5} $ is the same as $ \frac{15}{8} \div \frac{4}{5} $. Remember to multiply by the reciprocal!

Q: How do I know when to simplify fractions?

Always simplify your final answer! Look for common factors in the numerator and denominator. Here, both 75 and 768 are divisible by 3, giving us $ \frac{25}{256} $.

Q: Why is my answer so small when I started with bigger numbers?

You're dividing by large numbers (first by a fraction less than 1, then by 24), which naturally makes results smaller. This is completely normal in complex division problems!

Q: Can I use a calculator for this?

While calculators help, show your work step-by-step for full credit. Convert mixed numbers first, then follow order of operations carefully to avoid input errors.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Convert from number and fraction to fraction

00:10 Division is also multiplication by the reciprocal

00:25 Make sure to multiply numerator by numerator and denominator by denominator

00:39 Division moves to the denominator

00:42 Break down 15 into factors 5 and 3

00:51 Reduce what's possible

00:54 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$(1\frac{7}{8}:\frac{4}{5}):(3\cdot8)=\text{?}$

2

Step-by-step solution

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

Step 1: Convert mixed number to improper fraction.
Step 2: Perform division of fractions and evaluate further operations.
Step 3: Simplify the final expression.

Let's work through each step:
Step 1: Convert $1\frac{7}{8}$ to an improper fraction:
$1\frac{7}{8} = \frac{15}{8}$ , since $1 \times 8 + 7 = 15$ .

Step 2: Divide $\frac{15}{8}$ by $\frac{4}{5}$ :
Instead of dividing, multiply by the reciprocal of $\frac{4}{5}$ . Thus, $\frac{15}{8} : \frac{4}{5} = \frac{15}{8} \times \frac{5}{4} = \frac{75}{32}$ .

Step 3: Divide the result by $3 \cdot 8$ , which equals $24$ :
We have $\frac{75}{32} : 24 = \frac{75}{32} \times \frac{1}{24} = \frac{75}{768}$ .

Simplifying $\frac{75}{768}$ , we find the greatest common divisor of the numerator and the denominator is 3:
$\frac{75 \div 3}{768 \div 3} = \frac{25}{256}$ .

Therefore, the answer to the problem is $\frac{25}{256}$ .

3

Final Answer

$\frac{25}{256}$

Key Points to Remember

Essential concepts to master this topic

Order of Operations: Solve parentheses first, then division from left to right
Mixed to Improper: Convert $1\frac{7}{8} = \frac{15}{8}$ using (1×8)+7=15
Check Division: Verify $\frac{25}{256} \times 24 = \frac{75}{32}$ matches first step ✓

Common Mistakes

Avoid these frequent errors

Solving operations in wrong order
Don't solve 3×8 first and then work backwards = completely different problem! This changes the entire expression structure and leads to massive calculation errors. Always solve what's in parentheses first, then division operations from left to right.

Practice Quiz

Test your knowledge with interactive questions

$70:(14\times5)=$

FAQ

Everything you need to know about this question

Why do I convert the mixed number first?

+

Mixed numbers like $1\frac{7}{8}$ are much harder to work with in division problems. Converting to improper fractions like $\frac{15}{8}$ makes the math cleaner and prevents errors.

What does the colon (:) mean in this problem?

+

The colon means division, just like ÷. So $\frac{15}{8}:\frac{4}{5}$ is the same as $\frac{15}{8} \div \frac{4}{5}$ . Remember to multiply by the reciprocal!

How do I know when to simplify fractions?

+

Always simplify your final answer! Look for common factors in the numerator and denominator. Here, both 75 and 768 are divisible by 3, giving us $\frac{25}{256}$ .

Why is my answer so small when I started with bigger numbers?

+

You're dividing by large numbers (first by a fraction less than 1, then by 24), which naturally makes results smaller. This is completely normal in complex division problems!

Can I use a calculator for this?

+

While calculators help, show your work step-by-step for full credit. Convert mixed numbers first, then follow order of operations carefully to avoid input errors.

What if I get a different denominator?

+

Double-check your arithmetic! The most common errors happen when multiplying fractions or finding reciprocals. Make sure you multiply numerators together and denominators together correctly.

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Solve the Fraction Division Problem: (1 7/8 ÷ 4/5) ÷ (3 x 8) = ?

Complex Fraction Division with Mixed Numbers

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