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

Fraction Subtraction with Common Denominators

Solve the following exercise:

3212=? \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 Subtract in the common denominator
00:07 Calculate the numerator
00:12 Any number divided by itself always equals 1
00:15 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

Solve the following exercise:

3212=? \frac{3}{2}-\frac{1}{2}=\text{?}

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Recognize that the fractions 32\frac{3}{2} and 12\frac{1}{2} have a common denominator.
  • Step 2: Subtract the numerators, keeping the denominator unchanged.
  • Step 3: Simplify the resulting fraction if needed.

Now, let's work through each step:

Step 1: The fractions involved are 32\frac{3}{2} and 12\frac{1}{2}, both with the denominator of 2.

Step 2: Subtract the numerators: 31=23 - 1 = 2. So, the fraction becomes 22\frac{2}{2}.

Step 3: Simplify 22\frac{2}{2}. Since 22=1\frac{2}{2} = 1, the solution is a whole number.

Therefore, the solution to the problem is 1 1 . This corresponds to choice number 2.

3

Final Answer

1 1

Key Points to Remember

Essential concepts to master this topic
  • Rule: With same denominators, subtract numerators and keep denominator unchanged
  • Technique: 3212=312=22 \frac{3}{2} - \frac{1}{2} = \frac{3-1}{2} = \frac{2}{2}
  • Check: Simplify final fraction: 22=1 \frac{2}{2} = 1

Common Mistakes

Avoid these frequent errors
  • Subtracting denominators along with numerators
    Don't subtract both numerators and denominators like 3122=20 \frac{3-1}{2-2} = \frac{2}{0} ! This creates undefined expressions and wrong answers. Always keep the common denominator unchanged and only subtract the 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 don't I subtract the denominators too?

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The denominator tells you what size pieces you're working with. When subtracting 3212 \frac{3}{2} - \frac{1}{2} , you're taking away 1 half from 3 halves - the piece size stays the same!

What if the denominators were different?

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You'd need to find a common denominator first! Convert both fractions so they have the same bottom number, then subtract the numerators.

How do I know when to simplify my answer?

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Always check if your final fraction can be reduced! If the numerator and denominator share a common factor, divide both by that factor to get the simplest form.

Can the answer be a whole number?

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Absolutely! When the numerator equals the denominator (like 22 \frac{2}{2} ), the fraction equals 1. Any fraction where the top divides evenly into the bottom gives a whole number.

What if I get a negative answer?

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That's possible! If you're subtracting a larger numerator from a smaller one, you'll get a negative fraction. Just follow the same rules and keep the negative sign.

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