Solve 15/(4/(2:8)): Complex Division with Nested Fractions

Q: Why do I need to solve 2:8 first?

The colon notation 2:8 means $ 2 \div 8 = \frac{2}{8} = \frac{1}{4} $. This is inside the deepest parentheses, so by order of operations, you must solve it first!

Q: What does the colon symbol mean in math?

The colon : means division, just like ÷. So $ 2:8 $ is the same as $ 2 \div 8 $ or $ \frac{2}{8} $.

Q: How do I divide by a fraction?

To divide by a fraction, multiply by its reciprocal. So $ 15 \div \frac{4}{1/4} $ becomes $ 15 \times \frac{1/4}{4} $.

Q: Can I use a calculator for this problem?

Yes, but be careful with parentheses! Enter it exactly as written: 15÷(4÷(2÷8)). Make sure all parentheses are properly placed.

Q: How can I check if 15/16 is correct?

Work backwards! If $ \frac{15}{16} $ is correct, then $ \frac{15}{16} \times 16 = 15 $. Since $ 4 \div \frac{1}{4} = 16 $, this checks out!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:05 Let's write division as a fraction

00:11 Division is also multiplication by the reciprocal

00:25 Let's move the multiplication to the numerator

00:32 Division is also multiplication by the reciprocal

00:38 Let's move the multiplication to the denominator

00:46 Let's factor 4 into 2 and 2

00:52 Let's reduce what we can

00:58 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

$15/(4/(2:8))=\text{?}$

2

Step-by-step solution

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

$15/(4:\frac{2}{8})=$

Now we invert the fraction to create a multiplication exercise:

$15/(4\times\frac{8}{2})=$

We add the 4 to the numerator of the fraction in the multiplication exercise:

$15/(\frac{4\times8}{2})=$

Now we invert the fraction to create a multiplication exercise:

$15\times\frac{2}{4\times8}=$

We add the 15 to the numerator of the fraction in the multiplication exercise:

$\frac{15\times2}{4\times8}=$

We separate the 4 into a smaller multiplication exercise:

$\frac{15\times2}{2\times2\times8}=$

We simplify the 2 in the numerator and denominator:

$\frac{15}{2\times8}=\frac{15}{16}$

3

Final Answer

$\frac{15}{16}$

Key Points to Remember

Essential concepts to master this topic

Order: Work from innermost parentheses outward systematically
Division Technique: Convert $a \div b$ to $a \times \frac{1}{b}$
Check: Verify $\frac{15}{16} \times \frac{32}{15} = \frac{32}{16} = 2$ ✓

Common Mistakes

Avoid these frequent errors

Solving operations in wrong order
Don't work left to right ignoring parentheses = wrong answer like 30! This ignores order of operations completely. Always solve innermost operations first, then work outward step by step.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why do I need to solve 2:8 first?

+

The colon notation 2:8 means $2 \div 8 = \frac{2}{8} = \frac{1}{4}$ . This is inside the deepest parentheses, so by order of operations, you must solve it first!

What does the colon symbol mean in math?

+

The colon : means division, just like ÷. So $2:8$ is the same as $2 \div 8$ or $\frac{2}{8}$ .

How do I divide by a fraction?

+

To divide by a fraction, multiply by its reciprocal. So $15 \div \frac{4}{1/4}$ becomes $15 \times \frac{1/4}{4}$ .

Why does 4/(1/4) equal 16?

+

When you divide by a fraction, you multiply by its reciprocal: $4 \div \frac{1}{4} = 4 \times \frac{4}{1} = 4 \times 4 = 16$ .

Can I use a calculator for this problem?

+

Yes, but be careful with parentheses! Enter it exactly as written: 15÷(4÷(2÷8)). Make sure all parentheses are properly placed.

How can I check if 15/16 is correct?

+

Work backwards! If $\frac{15}{16}$ is correct, then $\frac{15}{16} \times 16 = 15$ . Since $4 \div \frac{1}{4} = 16$ , this checks out!

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Solve 15/(4/(2:8)): Complex Division with Nested Fractions

Complex Division with Multiple Operations

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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 need to solve 2:8 first?

What does the colon symbol mean in math?

How do I divide by a fraction?

Why does 4/(1/4) equal 16?

Can I use a calculator for this problem?

How can I check if 15/16 is correct?

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