Solve the Fraction Subtraction: 1/2 - 2/10 Step by Step

Q: Why can't I just subtract the numerators and denominators separately?

Fractions represent parts of a whole, so you need the same-sized parts (same denominator) to subtract them. It's like trying to subtract 1 apple from 2 oranges - you need to convert to the same unit first!

Q: How do I know which denominator to use as the common denominator?

Use the Least Common Multiple (LCM) of the denominators. For 2 and 10, the LCM is 10 since 10 is already a multiple of 2. This gives you the smallest possible common denominator.

Q: What if my answer comes out as an improper fraction?

That's fine! Improper fractions (where numerator ≥ denominator) are valid answers. You can convert to a mixed number if needed, but $ \frac{3}{10} $ is already proper.

Q: Do I always need to simplify my final answer?

Yes, when possible! Always check if your answer can be reduced to lowest terms by finding common factors. In this case, $ \frac{3}{10} $ cannot be simplified further since 3 and 10 share no common factors.

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

Find what you need to multiply the smaller denominator by to get the larger one. Here: 2 × 5 = 10, so multiply both numerator and denominator of $ \frac{1}{2} $ by 5.

Fraction Subtraction with Common Denominators

Solve the following exercise:

$\frac{1}{2}-\frac{2}{10}=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Multiply by 5 to find the common denominator

00:08 Make sure to multiply both numerator and denominator

00:18 Calculate the products

00:24 Subtract with the common denominator

00:28 Calculate the numerator

00:34 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:

$\frac{1}{2}-\frac{2}{10}=\text{?}$

Step-by-step solution

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

Step 1: Convert $\frac{1}{2}$ to a fraction with denominator $10$ .
Step 2: Subtract $\frac{2}{10}$ from the converted fraction.
Step 3: Simplify the result, if necessary.

Let's go through each step:

Step 1: Convert $\frac{1}{2}$ into a fraction with a denominator of $10$ .
We know that $\frac{1}{2}$ is equivalent to multiplying the numerator and the denominator by $5$ :
$\frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}$

Step 2: Subtract $\frac{2}{10}$ from $\frac{5}{10}$ .
Subtract by keeping the denominator $10$ and subtract the numerators:
$\frac{5}{10} - \frac{2}{10} = \frac{5-2}{10} = \frac{3}{10}$

Step 3: Simplify the result.
The fraction $\frac{3}{10}$ is already in its simplest form.

Therefore, the solution to the problem is $\frac{3}{10}$ .

Final Answer

$\frac{3}{10}$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert fractions to common denominators before subtracting
Technique: Convert $\frac{1}{2}$ to $\frac{5}{10}$ by multiplying by $\frac{5}{5}$
Check: Verify $\frac{5}{10} - \frac{2}{10} = \frac{3}{10}$ and simplify if possible ✓

Common Mistakes

Avoid these frequent errors

Subtracting numerators and denominators separately
Don't subtract $\frac{1}{2} - \frac{2}{10}$ as $\frac{1-2}{2-10} = \frac{-1}{-8}$ ! This breaks fraction rules and gives completely wrong answers. Always find a common denominator first, then subtract only 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 can't I just subtract the numerators and denominators separately?

Fractions represent parts of a whole, so you need the same-sized parts (same denominator) to subtract them. It's like trying to subtract 1 apple from 2 oranges - you need to convert to the same unit first!

How do I know which denominator to use as the common denominator?

Use the Least Common Multiple (LCM) of the denominators. For 2 and 10, the LCM is 10 since 10 is already a multiple of 2. This gives you the smallest possible common denominator.

What if my answer comes out as an improper fraction?

That's fine! Improper fractions (where numerator ≥ denominator) are valid answers. You can convert to a mixed number if needed, but $\frac{3}{10}$ is already proper.

Do I always need to simplify my final answer?

Yes, when possible! Always check if your answer can be reduced to lowest terms by finding common factors. In this case, $\frac{3}{10}$ cannot be simplified further since 3 and 10 share no common factors.

What's the easiest way to convert fractions to common denominators?

Find what you need to multiply the smaller denominator by to get the larger one. Here: 2 × 5 = 10, so multiply both numerator and denominator of $\frac{1}{2}$ by 5.

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