Solve the Nested Division: 2/7 ÷ (3/5 ÷ (7÷8))

Q: Why do I start with 7÷8 when it's at the end?

Because of the nested parentheses structure! You must work from the innermost parentheses outward, just like with regular order of operations. Think of it like peeling an onion - start from the center.

Q: How do I remember when to flip fractions?

Remember: Division by a fraction means multiply by its reciprocal. So $ a ÷ \frac{b}{c} = a \times \frac{c}{b} $. Flip the second fraction and change division to multiplication!

Q: Can I convert everything to decimals instead?

While possible, it's not recommended for nested problems like this. Decimals can get messy with repeating patterns, and you might lose precision. Keep fractions for exact answers.

Q: What if I get confused by all the parentheses?

Try rewriting each step clearly. Start with 7÷8 = $ \frac{7}{8} $, then work on $ \frac{3}{5} ÷ \frac{7}{8} $, and finally the outermost division. Take it one layer at a time!

Q: How do I check if $ \frac{5}{12} $ is really correct?

Work backwards! If $ \frac{2}{7} ÷ (something) = \frac{5}{12} $, then $ \frac{5}{12} \times (something) $ should equal $ \frac{2}{7} $. Calculate $ \frac{3}{5} ÷ \frac{7}{8} = \frac{24}{35} $ first, then verify!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:10 Let's solve the problem together.

00:13 Remember, always tackle the parentheses first. Even if they're within other sets of parentheses.

00:20 Begin with the innermost set of parentheses.

00:24 Convert division into a fraction.

00:28 Think of division as multiplying by the reciprocal. This will help us simplify.

00:33 Multiply the numerators together and the denominators together.

00:41 Remember, division becomes multiplication by the reciprocal.

00:49 Again, multiply numerators by numerators and denominators by denominators.

00:55 Now, let's reduce, or simplify, what we can.

01:02 Break down the number eight into factors of two and four.

01:07 And simplify any further if possible.

01:11 And that's how we find the solution to our question! Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$\frac{2}{7}:(\frac{3}{5}:(7:8))=\text{?}$

2

Step-by-step solution

First, we rewrite the multiplication exercise inside parentheses as a fraction:

$\frac{2}{7}:(\frac{3}{5}:\frac{7}{8})=$

Now we invert the fraction to create a multiplication exercise:

$\frac{2}{7}:(\frac{3}{5}\times\frac{8}{7})=\frac{2}{7}:(\frac{3\times8}{5\times7})$

Now we invert the fraction to create a multiplication exercise:

$\frac{2}{7}\times\frac{5\times7}{3\times8}=\frac{2\times5\times7}{7\times3\times8}$

We simplify the 7 in the numerator and denominator:

$\frac{2\times5}{3\times8}=$

We break down the 8 into a shorter multiplication exercise:

$\frac{2\times5}{3\times2\times4}=$

We simplify the 2 in the numerator and denominator:

$\frac{5}{3\times4}=\frac{5}{12}$

3

Final Answer

$\frac{5}{12}$

Key Points to Remember

Essential concepts to master this topic

Order Rule: Work from innermost parentheses outward, simplifying step by step
Division Technique: Convert 7÷8 to $\frac{7}{8}$ , then invert and multiply
Verification: Check by working backwards: $\frac{5}{12} \times \frac{24}{5} = 2$ ✓

Common Mistakes

Avoid these frequent errors

Working from left to right instead of innermost parentheses first
Don't calculate $\frac{2}{7} ÷ \frac{3}{5}$ first = wrong order and incorrect answer! This ignores the nested structure completely. Always start with the deepest parentheses (7÷8) and work outward systematically.

Practice Quiz

Test your knowledge with interactive questions

$$ 100-(30-21)= $$

FAQ

Everything you need to know about this question

Why do I start with 7÷8 when it's at the end?

+

Because of the nested parentheses structure! You must work from the innermost parentheses outward, just like with regular order of operations. Think of it like peeling an onion - start from the center.

How do I remember when to flip fractions?

+

Remember: Division by a fraction means multiply by its reciprocal. So $a ÷ \frac{b}{c} = a \times \frac{c}{b}$ . Flip the second fraction and change division to multiplication!

Can I convert everything to decimals instead?

+

While possible, it's not recommended for nested problems like this. Decimals can get messy with repeating patterns, and you might lose precision. Keep fractions for exact answers.

What if I get confused by all the parentheses?

+

Try rewriting each step clearly. Start with 7÷8 = $\frac{7}{8}$ , then work on $\frac{3}{5} ÷ \frac{7}{8}$ , and finally the outermost division. Take it one layer at a time!

How do I check if $\frac{5}{12}$ is really correct?

+

Work backwards! If $\frac{2}{7} ÷ (something) = \frac{5}{12}$ , then $\frac{5}{12} \times (something)$ should equal $\frac{2}{7}$ . Calculate $\frac{3}{5} ÷ \frac{7}{8} = \frac{24}{35}$ first, then verify!

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Solve the Nested Division: 2/7 ÷ (3/5 ÷ (7÷8))

Nested Division with Multiple Fraction Operations

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do I start with 7÷8 when it's at the end?

How do I remember when to flip fractions?

Can I convert everything to decimals instead?

What if I get confused by all the parentheses?

How do I check if $\frac{5}{12}$ is really correct?

🌟 Unlock Your Math Potential

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❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do I start with 7÷8 when it's at the end?

How do I remember when to flip fractions?

Can I convert everything to decimals instead?

What if I get confused by all the parentheses?

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🌟 Unlock Your Math Potential

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