Solve the Fraction Addition: 1/2 + 2/4 Step by Step

Q: Why can't I just add 1+2 and 2+4 to get 3/6?

Because fractions represent parts of a whole! $ \frac{1}{2} $ means 1 out of 2 equal parts, while $ \frac{2}{4} $ means 2 out of 4 equal parts. You need the same-sized parts to add them correctly.

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

Look for the Least Common Multiple (LCM) of the denominators. For 2 and 4, the LCM is 4 since 4 is already a multiple of 2. This makes conversion easier!

Q: Can I convert both fractions instead of just one?

Absolutely! You could convert both to eighths: $ \frac{4}{8} + \frac{4}{8} = \frac{8}{8} = 1 $. Using the smallest common denominator just makes the arithmetic easier.

Fraction Addition with Common Denominators

$\frac{1}{2}+\frac{2}{4}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 We want to find the least common denominator

00:06 So we'll multiply by 2, to get the common denominator 4

00:11 Remember to multiply both numerator and denominator

00:21 Let's calculate the multiplications

00:28 Add under the common denominator

00:35 Calculate the numerator

00:38 Any number divided by itself always equals 1

00:41 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

$\frac{1}{2}+\frac{2}{4}=$

Step-by-step solution

To solve the problem $\frac{1}{2} + \frac{2}{4}$ , we'll follow these steps:

Step 1: Convert $\frac{1}{2}$ to have a denominator of 4. Multiply the numerator and the denominator by 2 to get $\frac{2}{4}$ .
Step 2: With both fractions now having a common denominator, add them: $\frac{2}{4} + \frac{2}{4}$ .
Step 3: Combine the numerators and place the sum over the common denominator: $\frac{2+2}{4} = \frac{4}{4}$ .
Step 4: Simplify the fraction $\frac{4}{4}$ to $1$ .

Therefore, the solution to the problem is $1$ .

Final Answer

$1$

Key Points to Remember

Essential concepts to master this topic

Rule: Find common denominator before adding fractions together
Technique: Convert $\frac{1}{2}$ to $\frac{2}{4}$ by multiplying by 2
Check: $\frac{2}{4} + \frac{2}{4} = \frac{4}{4} = 1$ ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators separately
Don't add straight across like $\frac{1}{2} + \frac{2}{4} = \frac{3}{6}$ = wrong answer! This ignores the need for common denominators and creates meaningless fractions. Always convert to common denominators first, then add only the numerators.

Practice Quiz

Test your knowledge with interactive questions

$$ $\frac{4}{5}+\frac{1}{5}=$

FAQ

Everything you need to know about this question

Why can't I just add 1+2 and 2+4 to get 3/6?

Because fractions represent parts of a whole! $\frac{1}{2}$ means 1 out of 2 equal parts, while $\frac{2}{4}$ means 2 out of 4 equal parts. You need the same-sized parts to add them correctly.

How do I know which common denominator to use?

Look for the Least Common Multiple (LCM) of the denominators. For 2 and 4, the LCM is 4 since 4 is already a multiple of 2. This makes conversion easier!

What if the answer doesn't simplify to a whole number?

That's totally normal! Many fraction additions result in proper fractions. Just make sure to reduce to lowest terms by dividing both numerator and denominator by their greatest common factor.

Can I convert both fractions instead of just one?

Absolutely! You could convert both to eighths: $\frac{4}{8} + \frac{4}{8} = \frac{8}{8} = 1$ . Using the smallest common denominator just makes the arithmetic easier.

How do I check if my final answer is correct?

Convert your answer back to the original denominators or use a visual method. $1 = \frac{2}{2} = \frac{4}{4}$ , and $\frac{2}{2}$ does equal $\frac{1}{2} + \frac{2}{4}$ ✓

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