Multiply Three Fractions: 2/3 × 3/4 × 4/5 Step-by-Step

Fraction Multiplication with Three Factors

23×34×45= \frac{2}{3}\times\frac{3}{4}\times\frac{4}{5}=

❤️ 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
00:07 Let's solve this problem together.
00:10 First, multiply the numerators together, then the denominators.
00:15 Now, let's reduce the fraction by simplifying where possible.
00:25 And that's the solution to our question! Well done!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

23×34×45= \frac{2}{3}\times\frac{3}{4}\times\frac{4}{5}=

2

Step-by-step solution

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

  • Step 1: Multiply the numerators of the fractions together.
  • Step 2: Multiply the denominators of the fractions together.
  • Step 3: Simplify the resulting fraction, if possible.

Now, let's work through each step:
Step 1: Multiply the numerators: 2×3×4=24 2 \times 3 \times 4 = 24 .
Step 2: Multiply the denominators: 3×4×5=60 3 \times 4 \times 5 = 60 .
Step 3: The resulting fraction is 2460 \frac{24}{60} . Simplify by finding the greatest common divisor of 24 and 60, which is 12.

Divide both the numerator and the denominator by 12:
Numerator: 2412=2 \frac{24}{12} = 2
Denominator: 6012=5 \frac{60}{12} = 5
Thus, the simplified fraction is 25 \frac{2}{5} .

Therefore, the solution to the problem is 25 \frac{2}{5} .

3

Final Answer

25 \frac{2}{5}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Multiply all numerators together, then all denominators together
  • Technique: Look for cancellation: 23×34×45 \frac{2}{3} \times \frac{3}{4} \times \frac{4}{5} shows 3÷3 and 4÷4
  • Check: Verify 25 \frac{2}{5} by converting to decimal: 2÷5 = 0.4 ✓

Common Mistakes

Avoid these frequent errors
  • Adding denominators instead of multiplying them
    Don't add denominators like 3 + 4 + 5 = 12 in the denominator! This breaks the fundamental rule of fraction multiplication and gives completely wrong answers. Always multiply denominators: 3 × 4 × 5 = 60.

Practice Quiz

Test your knowledge with interactive questions

\( \frac{1}{3}+\frac{1}{4}= \)

FAQ

Everything you need to know about this question

Can I cancel numbers before multiplying everything out?

+

Yes! This is actually faster. Notice the 3 in 23 \frac{2}{3} cancels with the 3 in 34 \frac{3}{4} , and the 4 in 34 \frac{3}{4} cancels with the 4 in 45 \frac{4}{5} . This leaves 25 \frac{2}{5} directly!

What if I get a big number like 24/60?

+

That's normal! Just simplify by finding the greatest common factor. For 24 and 60, the GCF is 12, so 2460=24÷1260÷12=25 \frac{24}{60} = \frac{24÷12}{60÷12} = \frac{2}{5} .

Do I multiply from left to right or can I do it any order?

+

With multiplication, order doesn't matter! You can multiply 23×34 \frac{2}{3} \times \frac{3}{4} first, then multiply by 45 \frac{4}{5} , or do all three at once.

How do I know when to simplify?

+

Always simplify your final answer! Look for common factors between the numerator and denominator. If both numbers can be divided by the same value, simplify to get the lowest terms.

What's the fastest way to solve this type of problem?

+

Look for cancellation opportunities first! In 23×34×45 \frac{2}{3} \times \frac{3}{4} \times \frac{4}{5} , you can cancel the 3's and 4's immediately, leaving just 25 \frac{2}{5} without any big multiplication!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Operations with Fractions 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