Solve Complex Fraction: 30/(3/(13:2)) Step-by-Step

Complex Fraction Operations with Division Notation

30/(3/(13:2))=? 30/(3/(13:2))=\text{?}

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:07 Let's write division as a fraction
00:12 Division is also multiplication by the reciprocal
00:26 Let's move the multiplication to the numerator
00:30 Division is also multiplication by the reciprocal
00:39 Let's move the multiplication to the numerator
00:42 Let's factor 30 into 10 and 3
00:50 Let's reduce what we can
00:57 Let's factor 10 into 5 and 2
01:01 Let's reduce what we can
01:04 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

30/(3/(13:2))=? 30/(3/(13:2))=\text{?}

2

Step-by-step solution

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

30/(3:132)= 30/(3:\frac{13}{2})=

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

30/(3×213)= 30/(3\times\frac{2}{13})=

Let's add 13 to the fraction's numerator in a multiplication exercise:

30/(3×213)= 30/(\frac{3\times2}{13})=

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

30×133×2= 30\times\frac{13}{3\times2}=

Let's add 30 to the fraction's numerator in a multiplication exercise:

30×133×2= \frac{30\times13}{3\times2}=

Let's break down the 30 into a smaller multiplication exercise:

10×3×133×2= \frac{10\times3\times13}{3\times2}=

Let's reduce between the 3 in the numerator and denominator:

10×132= \frac{10\times13}{2}=

Let's break down the 10 into a smaller multiplication exercise:

5×2×132= \frac{5\times2\times13}{2}=

Let's reduce between the 2 in the numerator and denominator to get:

5×13=65 5\times13=65

3

Final Answer

65

Key Points to Remember

Essential concepts to master this topic
  • Division Rule: Dividing by a fraction means multiplying by its reciprocal
  • Technique: Convert 30/(3/(13/2)) 30/(3/(13/2)) to 30×136 30 \times \frac{13}{6}
  • Check: Verify 30/(3/(13/2))=30×213×13=65 30/(3/(13/2)) = 30 \times \frac{2}{13} \times \frac{1}{3} = 65

Common Mistakes

Avoid these frequent errors
  • Working from left to right instead of inside parentheses first
    Don't solve 30/3 first and ignore the inner fraction = wrong order of operations! This gives 10/(13/2) instead of the correct path. Always work from the innermost parentheses outward following 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 need to work from inside the parentheses first?

+

The order of operations requires you to solve expressions in parentheses first! In 30/(3/(13:2)) 30/(3/(13:2)) , you must handle the innermost operation 13:2 13:2 before anything else.

What does the colon notation 13:2 mean?

+

The colon : symbol means division, so 13:2=132 13:2 = \frac{13}{2} . It's just another way to write division that you might see in some textbooks or regions.

How do I handle dividing by a fraction like 3/(13/2)?

+

When dividing by a fraction, multiply by its reciprocal! So 3÷132=3×213=613 3 \div \frac{13}{2} = 3 \times \frac{2}{13} = \frac{6}{13} .

Why does the final answer come out to be a whole number?

+

Complex fractions can simplify to whole numbers when the factors cancel out nicely! In this case, 30×136 \frac{30 \times 13}{6} simplifies perfectly because 30 and 6 share common factors.

Can I use a calculator for this type of problem?

+

Yes, but be careful with parentheses! Enter it as 30÷(3÷(13÷2)) to make sure your calculator follows the correct order of operations.

What if I get confused by all the nested fractions?

+

Take it one step at a time! Start with the innermost expression, write down each step, and work your way outward. Don't try to do multiple operations at once.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Commutative, Distributive and Associative Properties questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations