Solve the Fraction Chain: 3/4 × 1/2 × 1/2 Step-by-Step

Fraction Multiplication with Multiple Terms

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:08 Let's solve this problem together.
00:11 Remember, multiply the numerators together. Then, multiply the denominators.
00:17 Now, calculate these multiplications. Take your time and double-check your work.
00:30 And there you have it. That's how we find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

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

2

Step-by-step solution

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

  • Step 1: Multiply the numerators
  • Step 2: Multiply the denominators
  • Step 3: Simplify the resulting fraction
  • Step 4: Verify the solution with the given choices

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:
4×2×2=16 4 \times 2 \times 2 = 16 .

Step 3: Write the resulting fraction:
316 \frac{3}{16} .

Step 4: Look at the multiple-choice list provided. Our answer, 316 \frac{3}{16} , matches choice 1.

The resulting fraction is already in its simplest form. Therefore, the solution to the problem is 316 \frac{3}{16} .

3

Final Answer

316 \frac{3}{16}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Multiply all numerators together, then all denominators together
  • Technique: Calculate 3×1×1=3 3 \times 1 \times 1 = 3 and 4×2×2=16 4 \times 2 \times 2 = 16
  • Check: Verify 316 \frac{3}{16} cannot be simplified further by checking common factors ✓

Common Mistakes

Avoid these frequent errors
  • Adding denominators instead of multiplying
    Don't add denominators like 4 + 2 + 2 = 8 to get 38 \frac{3}{8} ! This mixes addition and multiplication rules incorrectly. Always multiply denominators: 4 × 2 × 2 = 16.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why do I multiply the fractions instead of adding them?

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The × symbol means multiplication! When you see 34×12×12 \frac{3}{4} \times \frac{1}{2} \times \frac{1}{2} , you're finding what portion of a portion you have, which requires multiplication.

Can I multiply the fractions in a different order?

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Yes! Multiplication is commutative, so you can multiply in any order. You could do 12×12=14 \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} first, then multiply by 34 \frac{3}{4} .

How do I know if my fraction is in simplest form?

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Check if the numerator and denominator share any common factors. Since 3 and 16 only share the factor 1, 316 \frac{3}{16} is already simplified!

What if I get confused with all the multiplication?

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Take it one step at a time! First multiply just two fractions, then multiply that result by the third fraction. Breaking it down makes it much easier.

Why is my answer so much smaller than the original fractions?

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When you multiply fractions, you're finding a part of a part! Each multiplication makes the result smaller, so 316 \frac{3}{16} being smaller than 34 \frac{3}{4} makes perfect sense.

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