Calculate the Product: 1/3 × 4/7 Step-by-Step

Fraction Multiplication with Simplification Check

13×47= \frac{1}{3}\times\frac{4}{7}=

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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
00:07 Calculate the multiplications
00:10 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

13×47= \frac{1}{3}\times\frac{4}{7}=

2

Step-by-step solution

To solve this problem, we need to multiply two fractions, 13 \frac{1}{3} and 47 \frac{4}{7} , by following these steps:

  • Step 1: Multiply the numerators:
    1×4=4 1 \times 4 = 4 .
  • Step 2: Multiply the denominators:
    3×7=21 3 \times 7 = 21 .
  • Step 3: Combine the results to form a new fraction:
    Thus, 13×47=421 \frac{1}{3} \times \frac{4}{7} = \frac{4}{21} .

This fraction, 421 \frac{4}{21} , is in its simplest form since there are no common factors between 4 and 21 other than 1.

Therefore, the solution to the problem is 421 \frac{4}{21} .

3

Final Answer

421 \frac{4}{21}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Multiply numerators together, then multiply denominators together
  • Technique: 1×4=4 1 \times 4 = 4 over 3×7=21 3 \times 7 = 21 gives 421 \frac{4}{21}
  • Check: Verify no common factors exist between 4 and 21 for simplest form ✓

Common Mistakes

Avoid these frequent errors
  • Adding denominators instead of multiplying them
    Don't add the denominators like 3 + 7 = 10 to get 410 \frac{4}{10} ! This treats multiplication like addition and gives wrong answers. Always multiply both numerators together AND multiply both denominators together.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why don't I need a common denominator when multiplying fractions?

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Unlike addition or subtraction, multiplication of fractions doesn't require common denominators! You simply multiply straight across: numerator × numerator and denominator × denominator.

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

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Check if the numerator and denominator share any common factors other than 1. For 421 \frac{4}{21} , since 4 = 2×2 and 21 = 3×7, they share no common factors, so it's already simplified!

What if I get a fraction bigger than 1?

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That's perfectly normal! If your numerator is larger than your denominator, you have an improper fraction. You can leave it as is or convert it to a mixed number if needed.

Can I cancel numbers before multiplying?

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Yes! If you see common factors in the numerator of one fraction and denominator of another, you can cancel them first. This makes the multiplication easier and gives you the simplified answer directly.

What's the difference between multiplying and adding fractions?

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  • Adding: Need common denominators, then add numerators
  • Multiplying: Multiply numerators together AND denominators together - no common denominator needed!

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