Multiply Fractions: Solving 4/3 × 1/2 × 6/5 Step by Step

Multiplying Fractions with Three Terms

43×12×65= \frac{4}{3}\times\frac{1}{2}\times\frac{6}{5}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:07 Alright, let's solve a math problem together.
00:10 First, multiply the top numbers with each other... and the bottom numbers with each other.
00:16 Now, calculate these multiplications carefully.
00:28 Great! Next, simplify the fraction as much as possible.
00:32 To do this, divide both the top and bottom numbers by their greatest common factor.
00:39 And that's the final solution to our problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

43×12×65= \frac{4}{3}\times\frac{1}{2}\times\frac{6}{5}=

2

Step-by-step solution

To solve the multiplication of the fractions 43\frac{4}{3}, 12\frac{1}{2}, and 65\frac{6}{5}, we'll follow these steps:

  • Step 1: Multiply the numerators: 4×1×6=244 \times 1 \times 6 = 24.
  • Step 2: Multiply the denominators: 3×2×5=303 \times 2 \times 5 = 30.
  • Step 3: Form the new fraction: 2430\frac{24}{30}.
  • Step 4: Simplify the fraction 2430\frac{24}{30}:
    Find the greatest common divisor (GCD) of 24 and 30, which is 6.
    Divide both the numerator and the denominator by their GCD:
    24÷630÷6=45\frac{24 \div 6}{30 \div 6} = \frac{4}{5}.

Therefore, the product of 43×12×65=45\frac{4}{3} \times \frac{1}{2} \times \frac{6}{5} = \frac{4}{5}.

The correct choice from the given options is : 45\frac{4}{5}.

3

Final Answer

45 \frac{4}{5}

Key Points to Remember

Essential concepts to master this topic
  • Method: Multiply all numerators together, then all denominators together
  • Calculation: (4×1×6)/(3×2×5) = 24/30 before simplifying
  • Check: Simplify 24/30 by dividing both by GCD of 6 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to simplify the final fraction
    Don't leave your answer as 24/30 = incorrect form! This isn't in lowest terms and loses points on tests. Always find the GCD and divide both numerator and denominator to get 4/5.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Do I have to multiply all three fractions at once?

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Yes! When multiplying fractions, you can multiply all numerators together and all denominators together in one step. It's actually easier than doing it two at a time.

How do I find the GCD of 24 and 30?

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List the factors: 24 = 1,2,3,4,6,8,12,24 and 30 = 1,2,3,5,6,10,15,30. The greatest common factor they share is 6.

Can I simplify before multiplying?

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Yes, this is actually a great shortcut! You can cancel common factors across numerators and denominators before multiplying to make the numbers smaller.

What if I get a whole number as my answer?

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That's possible! If your numerator is divisible by your denominator after simplifying, you'll get a whole number. Always check by doing the division.

Why is my answer different from the multiple choice options?

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You probably forgot to simplify your fraction. Make sure to reduce 2430 \frac{24}{30} to 45 \frac{4}{5} by dividing both parts by 6.

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