Multiply the Fractions: Calculate 1/4 × 3/2 Step-by-Step

Fraction Multiplication with Proper Fractions

14×32= \frac{1}{4}\times\frac{3}{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 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

14×32= \frac{1}{4}\times\frac{3}{2}=

2

Step-by-step solution

To solve the problem of multiplying the fractions 14\frac{1}{4} and 32\frac{3}{2}, we will follow these steps:

  • Step 1: Multiply the numerators of the fractions.
  • Step 2: Multiply the denominators of the fractions.
  • Step 3: Write the result as a fraction and simplify if needed.

Now, let's work through each step:

Step 1: Multiply the numerators:
The numerators are 11 and 33. Thus, 1×3=31 \times 3 = 3.

Step 2: Multiply the denominators:
The denominators are 44 and 22. Thus, 4×2=84 \times 2 = 8.

Step 3: Write the result as a fraction and simplify:
The resulting fraction is 38\frac{3}{8}. This fraction is already in simplest form.

Therefore, the solution to the problem is 38\frac{3}{8}.

Among the choices provided, the correct answer is choice 3: 38\frac{3}{8}.

3

Final Answer

38 \frac{3}{8}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Multiply numerators together, then denominators together
  • Technique: Calculate 1×3=3 1 \times 3 = 3 and 4×2=8 4 \times 2 = 8
  • Check: Verify 38 \frac{3}{8} cannot be simplified further (GCD of 3 and 8 is 1) ✓

Common Mistakes

Avoid these frequent errors
  • Adding numerators and denominators instead of multiplying
    Don't calculate 1+34+2=46 \frac{1+3}{4+2} = \frac{4}{6} ! This addition method only applies to adding fractions with common denominators, not multiplication. Always multiply straight across: numerator times numerator, denominator times denominator.

Practice Quiz

Test your knowledge with interactive questions

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

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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With multiplication, you don't need common denominators! Just multiply numerator × numerator and denominator × denominator. Common denominators are only needed for adding or subtracting fractions.

Do I need to simplify the answer?

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Always check if you can simplify! For 38 \frac{3}{8} , since 3 and 8 share no common factors except 1, it's already in simplest form.

What if one of the fractions is a whole number?

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Convert the whole number to a fraction first! For example, 2 becomes 21 \frac{2}{1} , then multiply: 14×21=24=12 \frac{1}{4} \times \frac{2}{1} = \frac{2}{4} = \frac{1}{2}

Can I cancel before multiplying?

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Yes! If you see common factors, you can cross-cancel first. For instance, if you had 23×34 \frac{2}{3} \times \frac{3}{4} , cancel the 3s first to get 24=12 \frac{2}{4} = \frac{1}{2} .

How do I check if my answer is correct?

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Convert both fractions to decimals and multiply: 14=0.25 \frac{1}{4} = 0.25 and 32=1.5 \frac{3}{2} = 1.5 . So 0.25 × 1.5 = 0.375, which equals 38 \frac{3}{8} !

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