Solve the Fraction Equation: 3/2 - ? = 1/2

Q: Why do I need to rearrange the equation instead of just guessing?

Rearranging gives you the exact answer every time! Guessing might work sometimes, but algebraic methods guarantee you'll get the right answer and understand why it's correct.

Q: What if the fractions had different denominators?

You'd need to find a common denominator first! Convert all fractions to the same denominator, then perform the subtraction just like we did here.

Q: How do I check if my answer is correct?

Substitute your answer back into the original equation. If $ \frac{3}{2} - 1 = \frac{1}{2} $, then your answer is right!

Q: What's the difference between this and regular fraction subtraction?

This is solving an equation rather than just subtracting. You're finding an unknown value that makes the equation true, not just computing a subtraction.

Fraction Subtraction with Missing Variables

Complete the missing fraction
$\frac{3}{2}-_{——}=\frac{1}{2}$

What is the missing fraction?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the unknown

00:03 If the denominator of the result equals the given denominator, then the unknown denominator is identical

00:11 Now let's calculate the unknown numerator using the numerators

00:16 This is the matching numerator

00:19 Any number divided by itself always equals 1

00:22 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

Complete the missing fraction
$\frac{3}{2}-_{——}=\frac{1}{2}$

What is the missing fraction?

Step-by-step solution

To solve the problem, we start with the equation:

$\frac{3}{2} - x = \frac{1}{2}$

We need to determine the value of $x$ . To do this, let's isolate $x$ on one side of the equation:

Step 1: Rearrange the equation to solve for $x$ :

$x = \frac{3}{2} - \frac{1}{2}$

Step 2: Perform the subtraction. Since the denominators are the same, you can directly subtract the numerators:

$x = \frac{3 - 1}{2}$

Step 3: Simplify the expression:

$x = \frac{2}{2}$

$x = 1$

Thus, the missing fraction is $1$ .

Final Answer

$1$

Key Points to Remember

Essential concepts to master this topic

Rule: Same denominators allow direct numerator subtraction
Technique: Rearrange to isolate unknown: $x = \frac{3}{2} - \frac{1}{2}$
Check: Verify by substitution: $\frac{3}{2} - 1 = \frac{1}{2}$ ✓

Common Mistakes

Avoid these frequent errors

Not rearranging to isolate the missing fraction
Don't try to guess the answer by trial and error = wasted time and wrong results! This leads to confusion and incorrect values. Always rearrange the equation algebraically to isolate the unknown variable first.

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 do I need to rearrange the equation instead of just guessing?

Rearranging gives you the exact answer every time! Guessing might work sometimes, but algebraic methods guarantee you'll get the right answer and understand why it's correct.

What if the fractions had different denominators?

You'd need to find a common denominator first! Convert all fractions to the same denominator, then perform the subtraction just like we did here.

Can the missing value be a whole number like 1?

Absolutely! Remember that whole numbers are just fractions with denominator 1. So $1 = \frac{1}{1} = \frac{2}{2}$ - they're all the same value.

How do I check if my answer is correct?

Substitute your answer back into the original equation. If $\frac{3}{2} - 1 = \frac{1}{2}$ , then your answer is right!

What's the difference between this and regular fraction subtraction?

This is solving an equation rather than just subtracting. You're finding an unknown value that makes the equation true, not just computing a subtraction.

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