Multiply Three Fractions: 3/4 × 1/2 × 1/6 Step-by-Step

Fraction Multiplication with Three Factors

34×12×16= \frac{3}{4}\times\frac{1}{2}\times\frac{1}{6}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:06 Let's solve the problem together.
00:09 First, multiply the numerators with each other. Then, multiply the denominators with each other.
00:16 Now, let's do the math step-by-step for these multiplications.
00:26 And there you have it! That's the solution to our problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

34×12×16= \frac{3}{4}\times\frac{1}{2}\times\frac{1}{6}=

2

Step-by-step solution

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

  • Step 1: Multiply the numerators of the given fractions.

  • Step 2: Multiply the denominators of the given fractions.

  • Step 3: Combine the results into a single fraction.

  • Step 4: Simplify the fraction if needed.

Now, let's work through each step:
Step 1: Multiply the numerators: 3×1×1=3 3 \times 1 \times 1 = 3 .
Step 2: Multiply the denominators: 4×2×6=48 4 \times 2 \times 6 = 48 .
Step 3: The resulting fraction is 348 \frac{3}{48} .

Therefore, the solution to the problem is 348 \frac{3}{48} .

3

Final Answer

348 \frac{3}{48}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Multiply all numerators together, then all denominators together
  • Technique: Calculate step-by-step: 3×1×1 = 3 and 4×2×6 = 48
  • Check: Verify 348 \frac{3}{48} cannot be simplified further since GCD(3,48) = 3 ✓

Common Mistakes

Avoid these frequent errors
  • Adding denominators instead of multiplying them
    Don't add denominators like 4 + 2 + 6 = 12 to get 312 \frac{3}{12} ! This gives a completely wrong answer because fraction multiplication requires multiplying denominators. Always multiply: 4 × 2 × 6 = 48.

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 multiply the fractions in order or all at once?

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You can do either! All at once is often easier: multiply all numerators (3×1×1=3) and all denominators (4×2×6=48). The result is the same either way.

Should I simplify 348 \frac{3}{48} to its lowest terms?

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Yes! 348 \frac{3}{48} can be simplified by dividing both 3 and 48 by their greatest common factor, which is 3. This gives 116 \frac{1}{16} .

Why isn't the answer one of the other choices like 316 \frac{3}{16} ?

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Common error! 316 \frac{3}{16} comes from incorrectly calculating the denominator as 4×2×2 instead of 4×2×6. Always double-check your multiplication of denominators.

Can I cancel numbers before multiplying?

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Yes! You can cancel common factors across numerators and denominators first. For example, cancel the 2 in the denominator with factors in numerators to make calculations easier.

What if one of the fractions was a mixed number?

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You'd need to convert mixed numbers to improper fractions first, then multiply using the same method. Always work with improper fractions when multiplying.

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