Multiply Three Fractions: 1/3 × 2/4 × 7/5 Step-by-Step

Fraction Multiplication with Three Fractions

13×24×75= \frac{1}{3}\times\frac{2}{4}\times\frac{7}{5}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Make sure to multiply numerator by numerator and denominator by denominator
00:10 Calculate the multiplications
00:24 Reduce the fraction as much as possible
00:27 Make sure to divide both numerator and denominator
00:32 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

13×24×75= \frac{1}{3}\times\frac{2}{4}\times\frac{7}{5}=

2

Step-by-step solution

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

  • Step 1: Multiply the numerators of all fractions.
  • Step 2: Multiply the denominators of all fractions.
  • Step 3: Simplify the resulting fraction.

Now, let's work through each step:
Step 1: Multiply the numerators: 1×2×7=141 \times 2 \times 7 = 14.
Step 2: Multiply the denominators: 3×4×5=603 \times 4 \times 5 = 60.
Step 3: The resulting fraction is 1460\frac{14}{60}. Now, we simplify this fraction.

To simplify 1460\frac{14}{60}, find the greatest common divisor (GCD) of 14 and 60, which is 2. Divide both the numerator and the denominator by their GCD:
1460=14÷260÷2=730\frac{14}{60} = \frac{14 \div 2}{60 \div 2} = \frac{7}{30}.

Therefore, the solution to the problem is 730 \frac{7}{30} , which corresponds to choice 3.

3

Final Answer

730 \frac{7}{30}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Multiply all numerators together, then all denominators together
  • Technique: Calculate 1×2×7 = 14 and 3×4×5 = 60
  • Check: Simplify by dividing both by GCD: 14÷2 = 7, 60÷2 = 30 ✓

Common Mistakes

Avoid these frequent errors
  • Adding denominators instead of multiplying them
    Don't add denominators like 3+4+5 = 12 to get 1412 \frac{14}{12} ! This gives a completely wrong answer because fraction multiplication requires multiplying denominators. Always multiply all denominators: 3×4×5 = 60.

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 need to find a common denominator first?

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No! Unlike addition or subtraction, multiplication of fractions never requires finding a common denominator. Just multiply straight across: numerators together, denominators together.

Why do we get 1460 \frac{14}{60} first instead of the final answer?

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We always get the unsimplified result first by multiplying: 1×2×7 = 14 and 3×4×5 = 60. Then we simplify by dividing both by their GCD (2) to get 730 \frac{7}{30} .

How do I find the GCD of 14 and 60?

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List the factors: 14 has factors 1, 2, 7, 14 and 60 has factors 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. The greatest common factor they share is 2.

Can I simplify before multiplying?

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Yes! You can cancel common factors diagonally. For example, the 2 in 24 \frac{2}{4} cancels with the 4, giving you 13×12×75 \frac{1}{3} \times \frac{1}{2} \times \frac{7}{5} to make calculations easier.

What if my final answer doesn't match any of the choices?

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Double-check your work! Make sure you simplified correctly by finding the right GCD. If you got 1460 \frac{14}{60} , you're not done - you must simplify to 730 \frac{7}{30} .

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