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

Solve the following:

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

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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