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

Fraction Multiplication with Three Terms

25×12×23= \frac{2}{5}\times\frac{1}{2}\times\frac{2}{3}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:07 Let's solve this problem!
00:10 First, multiply the numerators. Then, multiply the denominators.
00:16 Now, let's reduce any fractions if possible.
00:21 Go ahead and calculate these multiplications.
00:27 Great job! This is how we find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

25×12×23= \frac{2}{5}\times\frac{1}{2}\times\frac{2}{3}=

2

Step-by-step solution

To solve this problem, we'll proceed with the following steps:

  • Step 1: Multiply the numerators together.
  • Step 2: Multiply the denominators together.
  • Step 3: Simplify the resulting fraction.

Let's perform these calculations:
Step 1: Multiply the numerators: 2×1×2=4 2 \times 1 \times 2 = 4 .
Step 2: Multiply the denominators: 5×2×3=30 5 \times 2 \times 3 = 30 .
Step 3: Form the resulting fraction: 430 \frac{4}{30} . Now, simplify the fraction

To simplify 430 \frac{4}{30} , find the greatest common divisor (GCD) of 4 and 30, which is 2.
Thus, divide both the numerator and the denominator by 2:

4÷230÷2=215\frac{4 \div 2}{30 \div 2} = \frac{2}{15}.

Therefore, the solution to the problem is 215 \frac{2}{15} .

3

Final Answer

215 \frac{2}{15}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Multiply all numerators together, then all denominators together
  • Technique: Calculate 2 × 1 × 2 = 4 and 5 × 2 × 3 = 30
  • Check: Simplify 430 \frac{4}{30} by dividing by GCD of 2 = 215 \frac{2}{15}

Common Mistakes

Avoid these frequent errors
  • Adding denominators instead of multiplying them
    Don't add denominators like 5 + 2 + 3 = 10 to get 410 \frac{4}{10} ! This ignores how fraction multiplication works and gives completely wrong results. Always multiply denominators: 5 × 2 × 3 = 30.

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 have to multiply fractions in a specific order?

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No! Multiplication is commutative, so you can multiply fractions in any order. The result will always be the same. However, multiplying from left to right helps you stay organized.

Can I simplify before multiplying all three fractions?

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Yes, and it's often easier! You can cancel common factors between any numerator and denominator before multiplying. For example, the 2 in the first numerator cancels with the 2 in the second denominator.

How do I find the GCD to simplify my answer?

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List the factors of both numbers and find the largest one they share. For 430 \frac{4}{30} : factors of 4 are 1, 2, 4 and factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. The greatest common factor is 2.

What if my final fraction can't be simplified?

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That's perfectly fine! Not all fractions can be reduced. If the numerator and denominator share no common factors other than 1, your fraction is already in lowest terms.

Why don't I add the fractions instead of multiplying?

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The × symbol tells you to multiply, not add! When you see 25×12×23 \frac{2}{5} \times \frac{1}{2} \times \frac{2}{3} , you're finding what fraction you get when you take 2/5 of 1/2 of 2/3.

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