Solve the Fraction Multiplication: 2/5 × 1/2

Fraction Multiplication with Simplification Required

25×12= \frac{2}{5}\times\frac{1}{2}=

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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
00:08 Calculate the multiplications
00:14 Reduce the fraction as much as possible
00:17 Make sure to divide both numerator and denominator
00:23 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

25×12= \frac{2}{5}\times\frac{1}{2}=

2

Step-by-step solution

To solve this problem, let's multiply the fractions 25 \frac{2}{5} and 12 \frac{1}{2} .

Step 1: Multiply the numerators:
2×1=2 2 \times 1 = 2

Step 2: Multiply the denominators:
5×2=10 5 \times 2 = 10

Step 3: Construct the fraction using the products from steps 1 and 2:
210 \frac{2}{10}

Step 4: Simplify the fraction. We can divide both the numerator and the denominator by their greatest common divisor, which is 2:
2÷210÷2=15 \frac{2 \div 2}{10 \div 2} = \frac{1}{5}

Thus, the product of 25 \frac{2}{5} and 12 \frac{1}{2} is 15 \frac{1}{5} .

Therefore, the solution to the problem is 15 \frac{1}{5} .

3

Final Answer

15 \frac{1}{5}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Multiply numerators together and denominators together separately
  • Technique: 25×12=2×15×2=210 \frac{2}{5} \times \frac{1}{2} = \frac{2 \times 1}{5 \times 2} = \frac{2}{10}
  • Check: Always simplify final answer by dividing by GCD: 210=15 \frac{2}{10} = \frac{1}{5}

Common Mistakes

Avoid these frequent errors
  • Adding fractions instead of multiplying
    Don't add numerators and denominators like 25+12=37 \frac{2}{5} + \frac{1}{2} = \frac{3}{7} = wrong answer! This completely ignores the multiplication sign. Always multiply straight across: numerator × numerator and denominator × denominator.

Practice Quiz

Test your knowledge with interactive questions

Solve the following:

\( \frac{5}{9}:\frac{7}{18}= \)

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 addition and subtraction, multiplication of fractions doesn't need common denominators! Just multiply the top numbers together and the bottom numbers together. It's actually simpler than adding fractions.

Do I always need to simplify my answer?

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Yes! Always check if your final fraction can be simplified. Find the Greatest Common Divisor (GCD) of the numerator and denominator, then divide both by it. 210 \frac{2}{10} simplifies to 15 \frac{1}{5} because GCD(2,10) = 2.

Can I simplify before multiplying instead of after?

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Absolutely! This actually makes calculations easier. Look for numbers that can cancel: 25×12 \frac{2}{5} \times \frac{1}{2} - the 2's cancel, giving 15×11=15 \frac{1}{5} \times \frac{1}{1} = \frac{1}{5} directly.

What if one of the fractions is a whole number?

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Treat whole numbers as fractions with denominator 1. For example: 3×12=31×12=32 3 \times \frac{1}{2} = \frac{3}{1} \times \frac{1}{2} = \frac{3}{2}

How do I know if I multiplied correctly?

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Convert your answer to a decimal and check if it makes sense. 25=0.4 \frac{2}{5} = 0.4 and 12=0.5 \frac{1}{2} = 0.5 , so 0.4×0.5=0.2=15 0.4 \times 0.5 = 0.2 = \frac{1}{5}

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