Solve the Fraction Subtraction: 1/2 - 1/4 Step-by-Step

Q: Why can't I just subtract 1/2 - 1/4 directly?

You need equal-sized pieces to subtract! Think of it like pizza slices - you can't subtract a quarter slice from a half slice until you cut them into the same size pieces (fourths).

Q: How do I find the common denominator?

Look for the smallest number that both denominators divide into evenly. For 2 and 4, the LCD is 4 because 4 ÷ 2 = 2 and 4 ÷ 4 = 1.

Q: What if I get zero as my answer?

Zero is possible! But in this problem, $ \frac{1}{2} - \frac{1}{4} $ equals $ \frac{1}{4} $, not zero. Double-check your common denominator conversion.

Q: Do I need to simplify my final answer?

Always check if you can simplify! In this case, $ \frac{1}{4} $ is already in lowest terms since 1 and 4 share no common factors other than 1.

Q: What's the easiest way to convert fractions?

Use the multiplication method: multiply both top and bottom by the same number. For $ \frac{1}{2} $, multiply by 2/2 to get $ \frac{2}{4} $.

Fraction Subtraction with Common Denominators

Solve the following exercise:

$\frac{1}{2}-\frac{1}{4}=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Multiply the fraction by 2 to get to the common denominator

00:07 Make sure to multiply both numerator and denominator

00:14 Calculate the multiplications

00:18 Subtract with the common denominator

00:24 Calculate the numerator

00:27 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

Solve the following exercise:

$\frac{1}{2}-\frac{1}{4}=\text{?}$

Step-by-step solution

To solve the subtraction $\frac{1}{2} - \frac{1}{4}$ , follow these steps:

Step 1: Identify a common denominator. Here, the least common denominator of 2 and 4 is 4.
Step 2: Convert $\frac{1}{2}$ to a fraction with denominator 4. This involves multiplying both the numerator and denominator by 2: $\frac{1}{2} = \frac{2}{4}$ .
Step 3: $\frac{1}{4}$ already has the denominator of 4, so we don't need any adjustment there.
Step 4: Subtract the numerators: $2 - 1 = 1$ .
Step 5: Write the result over the common denominator: $\frac{1}{4}$ .

Therefore, the solution to $\frac{1}{2} - \frac{1}{4}$ is $\frac{1}{4}$ .

Final Answer

$\frac{1}{4}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find common denominator before subtracting fraction numerators
Technique: Convert $\frac{1}{2}$ to $\frac{2}{4}$ by multiplying by 2
Check: Verify $\frac{2}{4} - \frac{1}{4} = \frac{1}{4}$ ✓

Common Mistakes

Avoid these frequent errors

Subtracting denominators along with numerators
Don't subtract both numerators AND denominators like 1-1=0 and 2-4=-2 = wrong answer! This gives nonsensical results because denominators show the size of parts, not quantities to subtract. Always keep the common denominator and only subtract numerators.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

$\frac{3}{2}-\frac{1}{2}=\text{?}$

FAQ

Everything you need to know about this question

Why can't I just subtract 1/2 - 1/4 directly?

You need equal-sized pieces to subtract! Think of it like pizza slices - you can't subtract a quarter slice from a half slice until you cut them into the same size pieces (fourths).

How do I find the common denominator?

Look for the smallest number that both denominators divide into evenly. For 2 and 4, the LCD is 4 because 4 ÷ 2 = 2 and 4 ÷ 4 = 1.

What if I get zero as my answer?

Zero is possible! But in this problem, $\frac{1}{2} - \frac{1}{4}$ equals $\frac{1}{4}$ , not zero. Double-check your common denominator conversion.

Do I need to simplify my final answer?

Always check if you can simplify! In this case, $\frac{1}{4}$ is already in lowest terms since 1 and 4 share no common factors other than 1.

What's the easiest way to convert fractions?

Use the multiplication method: multiply both top and bottom by the same number. For $\frac{1}{2}$ , multiply by 2/2 to get $\frac{2}{4}$ .

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