Multiply the Fractions: Calculate 2/7 × 3/5 Step-by-Step

Fraction Multiplication with Basic Numerators

27×35= \frac{2}{7}\times\frac{3}{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
00:07 Calculate the multiplications
00:11 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

27×35= \frac{2}{7}\times\frac{3}{5}=

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, if necessary.

Now, let's work through each step:
Step 1: Multiply the numerators: 2×3=6 2 \times 3 = 6 .
Step 2: Multiply the denominators: 7×5=35 7 \times 5 = 35 .
Thus, the product of the fractions is 635 \frac{6}{35} .

Therefore, the solution to the problem is 635 \frac{6}{35} .

3

Final Answer

635 \frac{6}{35}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Multiply numerators together, then multiply denominators together
  • Technique: Calculate 2×3=6 and 7×5=35 to get 635 \frac{6}{35}
  • Check: Verify fraction is in lowest terms by checking for common factors ✓

Common Mistakes

Avoid these frequent errors
  • Adding denominators instead of multiplying
    Don't add denominators like 7+5=12 to get 612 \frac{6}{12} ! This confuses addition and multiplication of fractions, giving completely wrong results. Always multiply both numerators together AND 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 do I multiply straight across instead of finding a common denominator?

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Unlike adding fractions, multiplying fractions doesn't need common denominators! You simply multiply numerator × numerator and denominator × denominator straight across.

Do I always need to simplify the answer?

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It's good practice to check if your answer can be simplified. For 635 \frac{6}{35} , since 6 and 35 share no common factors, it's already in lowest terms.

What if one of the fractions is a whole number?

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Remember that any whole number can be written as a fraction with denominator 1. For example, 3 = 31 \frac{3}{1} , so you can multiply normally!

How can I check if my multiplication is correct?

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Double-check your arithmetic: 2×3=6 and 7×5=35. You can also estimate: 27 \frac{2}{7} is about 0.3 and 35 \frac{3}{5} is 0.6, so 0.3×0.6≈0.18, which matches 635 \frac{6}{35} ≈0.17.

Why is my answer smaller than both original fractions?

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When you multiply two proper fractions (where numerator < denominator), the result is always smaller than either fraction. Think of it as taking a fraction of a fraction!

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