Solve the Nested Division Expression: 38:(6:(2:6))

Q: Why do I start with the innermost parentheses 2:6?

The order of operations requires you to work from the inside out! Think of parentheses like boxes - you must open the smallest box first before you can work with the bigger ones.

Q: How do I convert division to multiplication with fractions?

Division is the same as multiplying by the reciprocal! So $ a:b = a \times \frac{1}{b} $ and $ a:(\frac{c}{d}) = a \times \frac{d}{c} $. Just flip the fraction after the colon.

Q: What does 2:6 equal as a fraction?

$ 2:6 = \frac{2}{6} = \frac{1}{3} $ after simplifying. Always reduce fractions to their simplest form to make calculations easier!

Q: Can I use a calculator for this problem?

Yes, but be very careful with parentheses! Enter it exactly as written: 38÷(6÷(2÷6)). Missing even one parenthesis will give you the wrong answer.

Q: How do I check if 2⅑ is correct?

Work backwards! Convert $ 2\frac{1}{9} $ to $ \frac{19}{9} $, then verify: $ \frac{19}{9} \times 18 = \frac{19 \times 18}{9} = \frac{19 \times 2}{1} = 38 $ ✓

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 We always solve parentheses first, even within parentheses this rule applies

00:06 We'll start with the innermost parentheses

00:09 We'll write division when there's

00:12 Division is also multiplication by the reciprocal

00:23 We'll raise the multiplication to the numerator

00:28 Division is also multiplication by the reciprocal

00:34 We'll raise the multiplication to the numerator

00:41 Let's factor 38 into factors of 19 and 2

00:50 Let's factor 6 into factors of 3 and 2

00:58 Let's reduce what we can

01:04 Let's factor 19 into 18 plus 1

01:09 Let's break down the fraction into a whole number and remainder

01:15 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

$38:(6:(2:6))=\text{?}$

2

Step-by-step solution

First, let's write the multiplication exercise in the inner parentheses as a fraction:

$38:(6:\frac{2}{6})=$

Now let's flip the fraction to create a multiplication exercise:

$38:(6\times\frac{6}{2})=$

Let's add the 6 to the fraction's numerator to create a multiplication exercise:

$38:\frac{6\times6}{2}=$

Let's flip the fraction to create a multiplication exercise:

$38\times\frac{2}{6\times6}=$

Let's add the 38 to the fraction's numerator to create a multiplication exercise:

$\frac{38\times2}{6\times6}=$

Let's break down the 38 and the two 6's in the denominator into smaller multiplication exercises:

$\frac{19\times2\times2}{2\times3\times2\times3}=$

Let's reduce the 2 in both numerator and denominator:

$\frac{19}{3\times3}=\frac{19}{9}$

Let's separate the fraction into an addition exercise between fractions:

$\frac{18+1}{9}=\frac{18}{9}+\frac{1}{9}=2+\frac{1}{9}=2\frac{1}{9}$

3

Final Answer

$2\frac{1}{9}$

Key Points to Remember

Essential concepts to master this topic

Rule: Work from innermost parentheses outward, left to right
Technique: Convert division to multiplication: $6:(2:6) = 6 \times \frac{6}{2} = 18$
Check: Substitute back step by step: $38:18 = \frac{38}{18} = 2\frac{1}{9}$ ✓

Common Mistakes

Avoid these frequent errors

Working left to right without considering parentheses
Don't calculate 38:6 first = 6.33! This ignores the nested structure and gives completely wrong results. Always solve the innermost parentheses first, then work outward to respect the proper order of operations.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why do I start with the innermost parentheses 2:6?

+

The order of operations requires you to work from the inside out! Think of parentheses like boxes - you must open the smallest box first before you can work with the bigger ones.

How do I convert division to multiplication with fractions?

+

Division is the same as multiplying by the reciprocal! So $a:b = a \times \frac{1}{b}$ and $a:(\frac{c}{d}) = a \times \frac{d}{c}$ . Just flip the fraction after the colon.

What does 2:6 equal as a fraction?

+

$2:6 = \frac{2}{6} = \frac{1}{3}$ after simplifying. Always reduce fractions to their simplest form to make calculations easier!

Why is the final answer a mixed number?

+

When the numerator is larger than the denominator, convert to a mixed number! $\frac{19}{9} = \frac{18+1}{9} = \frac{18}{9} + \frac{1}{9} = 2 + \frac{1}{9} = 2\frac{1}{9}$

Can I use a calculator for this problem?

+

Yes, but be very careful with parentheses! Enter it exactly as written: 38÷(6÷(2÷6)). Missing even one parenthesis will give you the wrong answer.

How do I check if 2⅑ is correct?

+

Work backwards! Convert $2\frac{1}{9}$ to $\frac{19}{9}$ , then verify: $\frac{19}{9} \times 18 = \frac{19 \times 18}{9} = \frac{19 \times 2}{1} = 38$ ✓

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Solve the Nested Division Expression: 38:(6:(2:6))

Order of Operations with Nested Division

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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 start with the innermost parentheses 2:6?

How do I convert division to multiplication with fractions?

What does 2:6 equal as a fraction?

Why is the final answer a mixed number?

Can I use a calculator for this problem?

How do I check if 2⅑ is correct?

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