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

Fraction Multiplication with Basic Operations

35×12= \frac{3}{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
00:06 Let's calculate the multiplications
00:09 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

35×12= \frac{3}{5}\times\frac{1}{2}=

2

Step-by-step solution

To solve this problem, we need to multiply the fractions 35 \frac{3}{5} and 12 \frac{1}{2} .

  • Step 1: Multiply the numerators of the fractions. The numerators are 33 and 11, so 3×1=33 \times 1 = 3.
  • Step 2: Multiply the denominators of the fractions. The denominators are 55 and 22, so 5×2=105 \times 2 = 10.
  • Step 3: Combine the results from steps 1 and 2 to form the new fraction. The fraction becomes 310\frac{3}{10}.
  • Step 4: Simplify the fraction, if possible. In this case, 310\frac{3}{10} is already in its simplest form.

Therefore, the solution to 35×12\frac{3}{5} \times \frac{1}{2} is 310\frac{3}{10}.

3

Final Answer

310 \frac{3}{10}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Multiply numerators together, then multiply denominators together
  • Technique: Calculate 3 × 1 = 3 and 5 × 2 = 10
  • Check: Verify 3/10 cannot be simplified further since GCD(3,10) = 1 ✓

Common Mistakes

Avoid these frequent errors
  • Adding or subtracting fractions instead of multiplying
    Don't add numerators and denominators like 3+1=4 and 5+2=7 to get 4/7! This treats multiplication like addition and gives completely wrong results. Always multiply numerators together and denominators together when multiplying fractions.

Practice Quiz

Test your knowledge with interactive questions

\( \frac{1}{3}+\frac{1}{4}= \)

FAQ

Everything you need to know about this question

Why don't I need a common denominator when multiplying fractions?

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Unlike addition and subtraction, multiplication of fractions is straightforward - you just multiply straight across! Common denominators are only needed when adding or subtracting fractions.

Do I always multiply numerator by numerator and denominator by denominator?

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Yes! This is the fundamental rule for multiplying fractions. ab×cd=a×cb×d \frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d} always works.

How do I know if my answer needs to be simplified?

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Check if the numerator and denominator share any common factors. In this case, 3 and 10 share no common factors except 1, so 310 \frac{3}{10} is already simplified!

Can I simplify before multiplying instead of after?

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Absolutely! You can cross-cancel common factors before multiplying. For example, if you had 45×28 \frac{4}{5} \times \frac{2}{8} , you could cancel the 4 and 8 first to make calculations easier.

What if one of the fractions is actually a whole number?

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Treat the whole number as a fraction 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} .

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