Multiply the Fraction Sequence: 1/4 × 4/3 × 3/2

Fraction Multiplication with Sequential Cancellation

14×43×32= \frac{1}{4}\times\frac{4}{3}\times\frac{3}{2}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:10 Alright, let's solve this problem together!
00:14 First, multiply the numerators and then multiply the denominators. Take your time.
00:20 Next, look for any numbers you can reduce or simplify. You're doing great!
00:25 And there you have it! That's how we solve this question.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

14×43×32= \frac{1}{4}\times\frac{4}{3}\times\frac{3}{2}=

2

Step-by-step solution

To solve this problem, we'll multiply the given fractions step-by-step:

Step 1: Multiply the numerators and the denominators.
Numerators: 1×4×3=121 \times 4 \times 3 = 12.
Denominators: 4×3×2=244 \times 3 \times 2 = 24.

Step 2: Write the new fraction from the results of multiplying the numerators and denominators.
1224\frac{12}{24}.

Step 3: Simplify the fraction by finding common factors in the numerator and denominator.
The greatest common divisor of 12 and 24 is 12. Divide both the numerator and the denominator by 12:
1224=12÷1224÷12=12\frac{12}{24} = \frac{12 \div 12}{24 \div 12} = \frac{1}{2}.

Therefore, the product of the fractions 14\frac{1}{4}, 43\frac{4}{3}, and 32\frac{3}{2} is 12\frac{1}{2}.

3

Final Answer

12 \frac{1}{2}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Multiply all numerators together, then all denominators together
  • Technique: Notice 4 cancels from 14×43 \frac{1}{4} \times \frac{4}{3} and 3 cancels from 43×32 \frac{4}{3} \times \frac{3}{2}
  • Check: Verify 1224=12 \frac{12}{24} = \frac{1}{2} by dividing both by 12 ✓

Common Mistakes

Avoid these frequent errors
  • Adding denominators instead of multiplying
    Don't add denominators like 4 + 3 + 2 = 9 to get 129 \frac{12}{9} ! This mixes addition and multiplication rules. Always multiply denominators: 4 × 3 × 2 = 24.

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?

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Yes! This is actually the smart way! Notice that 4 appears in both numerator and denominator, and 3 appears twice too. Cancel these first to make the math easier.

Why does 14×43×32 \frac{1}{4} \times \frac{4}{3} \times \frac{3}{2} equal 12 \frac{1}{2} and not something bigger?

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When you multiply fractions, you're taking parts of parts. Even though 4/3 and 3/2 are greater than 1, the 1/4 at the beginning makes the final result smaller than 1.

What's the fastest way to solve this problem?

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Look for cancellation opportunities first! The 4 in 43 \frac{4}{3} cancels with the 4 in the denominator of 14 \frac{1}{4} , and the 3s cancel too. This leaves you with 1×1×11×1×2=12 \frac{1 \times 1 \times 1}{1 \times 1 \times 2} = \frac{1}{2} !

How do I know when my fraction is fully simplified?

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A fraction is simplified when the numerator and denominator have no common factors other than 1. Since 1 and 2 share no common factors, 12 \frac{1}{2} is fully simplified.

Do I always need to simplify my final answer?

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Yes, always! Leaving 1224 \frac{12}{24} as your final answer is like stopping halfway. Simplified fractions like 12 \frac{1}{2} are cleaner and easier to understand.

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