Calculate the Product: (2/3) × (1/2) × (4/5) Step by Step

Fraction Multiplication with Multiple Factors

23×12×45= \frac{2}{3}\times\frac{1}{2}\times\frac{4}{5}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 We'll make sure to multiply numerator by numerator and denominator by denominator
00:09 We'll reduce what we can
00:12 We'll calculate the multiplications
00:16 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

23×12×45= \frac{2}{3}\times\frac{1}{2}\times\frac{4}{5}=

2

Step-by-step solution

To solve this problem, let's multiply the given fractions step-by-step:

  • Step 1: Multiply the numerators of the fractions together: 2×1×4=8 2 \times 1 \times 4 = 8
  • Step 2: Multiply the denominators of the fractions together: 3×2×5=30 3 \times 2 \times 5 = 30
  • Step 3: Form the fraction using the results from Steps 1 and 2: 830 \frac{8}{30}
  • Step 4: Simplify the fraction 830\frac{8}{30}: - Find the greatest common divisor (GCD) of 8 and 30, which is 2. 8÷230÷2=415 \frac{8 \div 2}{30 \div 2} = \frac{4}{15}

The simplified fraction is 415\frac{4}{15}.

Therefore, the correct result of the multiplication is 415 \frac{4}{15} .

3

Final Answer

415 \frac{4}{15}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Multiply all numerators together, then all denominators together
  • Technique: Calculate 2×1×4 = 8 and 3×2×5 = 30 to get 830 \frac{8}{30}
  • Check: Simplify by dividing both 8 and 30 by GCD of 2: 415 \frac{4}{15}

Common Mistakes

Avoid these frequent errors
  • Adding denominators instead of multiplying
    Don't add denominators like 3+2+5 = 10 to get 810 \frac{8}{10} ! This gives completely wrong results because fraction multiplication requires multiplying denominators. Always multiply: 3×2×5 = 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 the fractions in order from left to right?

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No! Multiplication is commutative, so you can multiply fractions in any order. The result will be the same whether you do 23×12×45 \frac{2}{3} \times \frac{1}{2} \times \frac{4}{5} or rearrange them.

Can I simplify before multiplying to make it easier?

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Yes! You can cancel common factors across numerators and denominators. For example, the 2 in the numerator and the 2 in the denominator can cancel out early to simplify your work.

Why do I need to find the GCD to simplify?

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Finding the Greatest Common Divisor (GCD) ensures your fraction is in simplest form. 830 \frac{8}{30} and 415 \frac{4}{15} are equal, but 415 \frac{4}{15} is the preferred simplified answer.

What if one of the fractions is a whole number?

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Treat whole numbers as fractions with denominator 1. For example, if you had 3 × 25 \frac{2}{5} , write it as 31×25=65 \frac{3}{1} \times \frac{2}{5} = \frac{6}{5} .

How do I know when my answer is fully simplified?

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Your fraction is fully simplified when the GCD of the numerator and denominator is 1. This means they share no common factors other than 1.

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