Solve Fraction Multiplication: Calculate 2/4 × 1/2

Q: Why do I multiply straight across instead of finding common denominators?

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.

Q: Can I simplify before multiplying?

Absolutely! This makes calculations easier. You can cancel common factors diagonally before multiplying. For $ \frac{2}{4} \times \frac{1}{2} $, notice that 2 appears in both numerator and denominator.

Q: How do I know if my simplified answer is correct?

Convert your fractions to decimals and multiply: $ \frac{2}{4} = 0.5 $ and $ \frac{1}{2} = 0.5 $, so $ 0.5 \times 0.5 = 0.25 = \frac{1}{4} $ ✓

Fraction Multiplication with Simplification

$\frac{2}{4}\times\frac{1}{2}=$

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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 Simplify what we can

00:09 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\frac{2}{4}\times\frac{1}{2}=$

Step-by-step solution

To solve this multiplication of fractions problem, we will follow these steps:

Step 1: Multiply the numerators of the fractions.
Step 2: Multiply the denominators of the fractions.
Step 3: Simplify the resulting fraction, if possible.

Now, let's carry out these steps:
Step 1: Multiply the numerators: $2 \times 1 = 2$ .
Step 2: Multiply the denominators: $4 \times 2 = 8$ .
Step 3: The resulting fraction is $\frac{2}{8}$ . We simplify by dividing the numerator and the denominator by their greatest common divisor, which is 2. So, $\frac{2}{8} = \frac{2 \div 2}{8 \div 2} = \frac{1}{4}$ .

Therefore, the solution to the problem is $\frac{1}{4}$ .

Final Answer

$\frac{1}{4}$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply numerators together, then multiply denominators together
Technique: Calculate $2 \times 1 = 2$ and $4 \times 2 = 8$ to get $\frac{2}{8}$
Check: Always simplify by dividing by GCD: $\frac{2}{8} = \frac{1}{4}$ ✓

Common Mistakes

Avoid these frequent errors

Adding or subtracting fractions instead of multiplying
Don't add numerators and denominators like $\frac{2}{4} + \frac{1}{2} = \frac{3}{6}$ ! This gives completely wrong results because multiplication follows different rules. Always multiply straight across: numerator × numerator and denominator × denominator.

Practice Quiz

Test your knowledge with interactive questions

$\frac{2}{3}\times\frac{5}{7}=$

FAQ

Everything you need to know about this question

Why do I multiply straight across instead of finding common denominators?

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 always have to simplify my answer?

Yes! Always check if your answer can be simplified. Find the Greatest Common Divisor (GCD) of the numerator and denominator, then divide both by it. For example, $\frac{2}{8}$ becomes $\frac{1}{4}$ when divided by 2.

Can I simplify before multiplying?

Absolutely! This makes calculations easier. You can cancel common factors diagonally before multiplying. For $\frac{2}{4} \times \frac{1}{2}$ , notice that 2 appears in both numerator and denominator.

What if one of the fractions is a whole number?

Treat the whole number as a fraction with denominator 1. For example, $3 \times \frac{1}{2}$ becomes $\frac{3}{1} \times \frac{1}{2} = \frac{3}{2}$ .

How do I know if my simplified answer is correct?

Convert your fractions to decimals and multiply: $\frac{2}{4} = 0.5$ and $\frac{1}{2} = 0.5$ , so $0.5 \times 0.5 = 0.25 = \frac{1}{4}$ ✓

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