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

Fraction Multiplication with Cross-Numerator Methods

23×57= \frac{2}{3}\times\frac{5}{7}=

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Step-by-step video solution

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00:00 Solve
00:03 Make sure to multiply numerator by numerator and denominator by denominator
00:06 Let's calculate the multiplications
00:09 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

23×57= \frac{2}{3}\times\frac{5}{7}=

2

Step-by-step solution

Let us solve the problem of multiplying the two fractions 23\frac{2}{3} and 57\frac{5}{7}.

  • Step 1: Identify the numerators and denominators. Here, the numerators are 22 and 55, and the denominators are 33 and 77.
  • Step 2: Multiply the numerators: 2×5=102 \times 5 = 10.
  • Step 3: Multiply the denominators: 3×7=213 \times 7 = 21.
  • Step 4: Put the results together in a new fraction: 1021\frac{10}{21}.
  • Step 5: Simplify the fraction if needed. In this case, 1021\frac{10}{21} is already in its simplest form as 1010 and 2121 have no common factors besides 11.

Therefore, the solution to the problem 23×57 \frac{2}{3} \times \frac{5}{7} is 1021\frac{10}{21}.

3

Final Answer

1021 \frac{10}{21}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Multiply numerators together, then multiply denominators together
  • Technique: Calculate 2×5=10 and 3×7=21 to get 1021 \frac{10}{21}
  • Check: Verify 10 and 21 share no common factors for simplest form ✓

Common Mistakes

Avoid these frequent errors
  • Adding instead of multiplying fractions
    Don't add numerators and denominators like 2+53+7=710 \frac{2+5}{3+7} = \frac{7}{10} ! This gives a completely wrong answer. Always multiply straight across: numerator×numerator and denominator×denominator.

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 common denominators?

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Unlike addition and subtraction, multiplication of fractions doesn't need common denominators! You simply multiply the tops together and the bottoms together. It's actually easier than adding fractions.

Do I always need to simplify my answer?

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Yes! Always check if your answer can be simplified by finding the Greatest Common Factor (GCF) of the numerator and denominator. In this case, 1021 \frac{10}{21} is already simplified since 10 and 21 share no common factors.

What if one of the fractions is a whole number?

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Convert the whole number to a fraction first! For example, 3 becomes 31 \frac{3}{1} . Then multiply normally: 23×31=63=2 \frac{2}{3} \times \frac{3}{1} = \frac{6}{3} = 2 .

Can I cancel before multiplying?

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Yes! You can cross-cancel if you spot common factors. For instance, if you had 49×38 \frac{4}{9} \times \frac{3}{8} , you could cancel the 4 and 8, then the 3 and 9 before multiplying.

How do I check if my multiplication is correct?

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Try converting both fractions to decimals and multiply them, then convert your answer to a decimal. They should match! For 23×57 \frac{2}{3} \times \frac{5}{7} : 0.667 × 0.714 ≈ 0.476, and 1021 \frac{10}{21} ≈ 0.476 ✓

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