Solve: (5/4) × (1/2) × (3/6) Fraction Multiplication Problem

Fraction Multiplication with Simplification Steps

54×12×36= \frac{5}{4}\times\frac{1}{2}\times\frac{3}{6}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:10 Let's solve this problem together.
00:13 First, multiply the top numbers together. Then, multiply the bottom numbers together.
00:23 Next, perform the multiplications step by step.
00:32 Now, simplify the fraction as much as possible.
00:36 Remember, divide the top and bottom by the same number.
00:45 And that's how we find the solution. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

54×12×36= \frac{5}{4}\times\frac{1}{2}\times\frac{3}{6}=

2

Step-by-step solution

The problem requires multiplying the fractions 54 \frac{5}{4} , 12 \frac{1}{2} , and 36 \frac{3}{6} .

Step 1: Multiply the numerators.

We have: 5×1×3=15 5 \times 1 \times 3 = 15 .

Step 2: Multiply the denominators.

We have: 4×2×6=48 4 \times 2 \times 6 = 48 .

Step 3: Form the fraction from results of the two steps above.

The product of these fractions is 1548 \frac{15}{48} .

Step 4: Simplify the fraction.

To simplify 1548 \frac{15}{48} , we need to find the greatest common divisor (GCD) of 15 and 48. The GCD is 3.

Divide both the numerator and the denominator by their GCD:

15÷348÷3=516 \frac{15 \div 3}{48 \div 3} = \frac{5}{16} .

Thus, the simplified product of the fractions is 516 \frac{5}{16} .

We can compare it against the given answer choices to confirm:

  • Choice 1: 316 \frac{3}{16} - incorrect.
  • Choice 2: 516 \frac{5}{16} - correct.
  • Choice 3: 1548 \frac{15}{48} - correct but not simplified.
  • Choice 4: 1516 \frac{15}{16} - incorrect.

The correct answer choice is Choice 2, 516 \frac{5}{16} .

3

Final Answer

516 \frac{5}{16}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Multiply numerators together, then multiply denominators together separately
  • Technique: Calculate 5×1×3=15 5 \times 1 \times 3 = 15 and 4×2×6=48 4 \times 2 \times 6 = 48
  • Check: Simplify by dividing both parts by GCD: 1548=516 \frac{15}{48} = \frac{5}{16}

Common Mistakes

Avoid these frequent errors
  • Forgetting to simplify the final fraction
    Don't leave your answer as 1548 \frac{15}{48} = incomplete solution! This fraction isn't in simplest form and may not match the answer choices. Always find the GCD and divide both numerator and denominator to get the fully simplified fraction.

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 simplify fractions before multiplying them?

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Yes! You can simplify 36 \frac{3}{6} to 12 \frac{1}{2} first. This gives you 54×12×12 \frac{5}{4} \times \frac{1}{2} \times \frac{1}{2} , which is often easier to work with.

How do I find the GCD of 15 and 48?

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List the factors: 15 = 3 × 5, and 48 = 3 × 16. The greatest common factor they share is 3. You can also use the division method to find it systematically.

What if I get a different answer choice that equals mine?

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Both 1548 \frac{15}{48} and 516 \frac{5}{16} are mathematically equal, but always choose the simplified form unless the problem specifically asks for an unsimplified answer.

Why do I multiply straight across instead of finding common denominators?

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Unlike adding or subtracting fractions, multiplication doesn't require common denominators. You simply multiply numerator × numerator and denominator × denominator!

Can I cancel out numbers while multiplying?

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Yes! You can cross-cancel before multiplying. For example, the 3 in the numerator can cancel with the 6 in the denominator, making the calculation 54×12×12 \frac{5}{4} \times \frac{1}{2} \times \frac{1}{2} easier.

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