Solve the Fraction Subtraction: 3/2 - 1/2 Step-by-Step

Q: Why don't I subtract the denominators too?

The denominator tells you what size pieces you're working with. Since both fractions use halves (denominator 2), you keep working with halves - only the number of halves changes!

Q: Do I always need to simplify my answer?

Yes! Always check if your fraction can be simplified. $ \frac{2}{2} $ equals 1, which is much cleaner than leaving it as an improper fraction.

Q: What if the denominators were different?

Then you'd need to find a common denominator first! Convert both fractions to equivalent fractions with the same denominator, then subtract the numerators.

Q: How can I check if 1 is really the right answer?

Think about it practically: $ \frac{3}{2} $ is 1½ and $ \frac{1}{2} $ is ½. So 1½ - ½ = 1. It works!

Q: Is there a shortcut when denominators are the same?

Yes! When denominators match, just subtract the top numbers and keep the bottom number. It's like subtracting regular numbers, but with a fraction bar.

Fraction Subtraction with Common Denominators

Solve the following exercise:

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 First, let's mark the number of squares we have according to the given data

00:07 Let's write the numerical representation of each square

00:17 Now let's subtract (remove) the number of squares according to the corresponding fraction

00:21 The remaining number of squares is the numerator of the answer

00:24 The denominator of the answer equals the number of parts we divided the whole into:

00:27 Any number divided by itself always equals 1

00:30 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:

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

Step-by-step solution

To solve the problem $\frac{3}{2} - \frac{1}{2}$ , we will follow these steps:

Step 1: Identify that both fractions have the same denominator, which allows us to directly subtract their numerators.
Step 2: Perform the subtraction of the numerators while maintaining the common denominator.

Let's apply the steps:
Step 1: The expression is $\frac{3}{2} - \frac{1}{2}$ . Both fractions have a common denominator of 2.

Step 2: Subtract the numerators:
$\frac{3 - 1}{2} = \frac{2}{2}$ .

The expression simplifies to 1 as $\frac{2}{2} = 1$ .

Therefore, the correct answer to the problem is 1.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Subtract numerators when denominators are the same
Technique: Keep denominator 2, subtract: 3 - 1 = 2
Check: Simplify final answer: $\frac{2}{2} = 1$ ✓

Common Mistakes

Avoid these frequent errors

Subtracting both numerators and denominators
Don't subtract denominators like 3/2 - 1/2 = 2/0 = undefined! This creates division by zero or wrong fractions. Always keep the common denominator and only subtract the numerators.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

$\frac{8}{5}-\frac{4}{5}=\text{?}$

FAQ

Everything you need to know about this question

Why don't I subtract the denominators too?

The denominator tells you what size pieces you're working with. Since both fractions use halves (denominator 2), you keep working with halves - only the number of halves changes!

Do I always need to simplify my answer?

Yes! Always check if your fraction can be simplified. $\frac{2}{2}$ equals 1, which is much cleaner than leaving it as an improper fraction.

What if the denominators were different?

Then you'd need to find a common denominator first! Convert both fractions to equivalent fractions with the same denominator, then subtract the numerators.

How can I check if 1 is really the right answer?

Think about it practically: $\frac{3}{2}$ is 1½ and $\frac{1}{2}$ is ½. So 1½ - ½ = 1. It works!

Is there a shortcut when denominators are the same?

Yes! When denominators match, just subtract the top numbers and keep the bottom number. It's like subtracting regular numbers, but with a fraction bar.

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