Solve the Fraction Addition: 1/2 + 2/4 + 3/6

Q: Why do I need to simplify the fractions first?

Simplifying makes the problem much easier! When you reduce $ \frac{2}{4} $ to $ \frac{1}{2} $ and $ \frac{3}{6} $ to $ \frac{1}{2} $, all fractions have the same denominator, so you can add directly.

Q: What if the fractions don't all simplify to the same denominator?

No problem! First simplify each fraction, then find the least common denominator (LCD) of all the simplified fractions. Convert each fraction to have that common denominator before adding.

Q: How do I know if a fraction can be simplified?

Look for common factors in the numerator and denominator. For example, in $ \frac{2}{4} $, both 2 and 4 are divisible by 2, so you can divide both by 2 to get $ \frac{1}{2} $.

Q: Can I leave my answer as an improper fraction?

Yes! $ \frac{3}{2} $ is perfectly correct as an improper fraction. You could also write it as $ 1\frac{1}{2} $ (mixed number) or 1.5 (decimal), but the improper fraction is the most exact form.

Q: What if I get confused with all the different denominators?

Take it step by step! First, write down each fraction. Then simplify each one individually. Finally, add the simplified fractions. Don't try to do everything at once - breaking it into steps prevents mistakes.

Fraction Addition with Simplified Terms

$\frac{1}{2}+\frac{2}{4}+\frac{3}{6}=$

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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 Therefore we'll multiply by 6, 3, and 2 respectively to find the common denominator

00:09 Remember to multiply both numerator and denominator

00:28 Let's calculate the multiplications

00:39 Let's add under the common denominator

00:49 Let's calculate the numerator

00:55 Let's reduce the fraction as much as possible

00:58 Remember to divide both numerator and denominator

01:10 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

$\frac{1}{2}+\frac{2}{4}+\frac{3}{6}=$

Step-by-step solution

To solve this problem, we will simplify and add the fractions $\frac{1}{2} + \frac{2}{4} + \frac{3}{6}$ step-by-step:

Step 1: Simplify fractions where possible.
$\frac{2}{4}$ simplifies to $\frac{1}{2}$ because the numerator and denominator can both be divided by 2.
Similarly, $\frac{3}{6}$ simplifies to $\frac{1}{2}$ because both the numerator and denominator are divisible by 3.
Step 2: Add the simplified fractions.
The equation becomes $\frac{1}{2} + \frac{1}{2} + \frac{1}{2}$ .
Step 3: Since all fractions now have the same denominator, they can be added directly:
Add the numerators: $1 + 1 + 1 = 3$ and keep the denominator the same: 2.
This gives us $\frac{3}{2}$ .

Therefore, the solution to the problem is $\frac{3}{2}$ .

Final Answer

$\frac{3}{2}$

Key Points to Remember

Essential concepts to master this topic

Simplification: Reduce each fraction to lowest terms before adding
Technique: Convert $\frac{2}{4}$ to $\frac{1}{2}$ and $\frac{3}{6}$ to $\frac{1}{2}$
Check: Verify $\frac{1}{2} + \frac{1}{2} + \frac{1}{2} = \frac{3}{2}$ matches original calculation ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators separately
Don't add $\frac{1}{2} + \frac{2}{4} + \frac{3}{6}$ as $\frac{6}{12}$ ! This ignores different denominators and gives the wrong answer. Always simplify fractions first, then add using common denominators.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why do I need to simplify the fractions first?

Simplifying makes the problem much easier! When you reduce $\frac{2}{4}$ to $\frac{1}{2}$ and $\frac{3}{6}$ to $\frac{1}{2}$ , all fractions have the same denominator, so you can add directly.

What if the fractions don't all simplify to the same denominator?

No problem! First simplify each fraction, then find the least common denominator (LCD) of all the simplified fractions. Convert each fraction to have that common denominator before adding.

How do I know if a fraction can be simplified?

Look for common factors in the numerator and denominator. For example, in $\frac{2}{4}$ , both 2 and 4 are divisible by 2, so you can divide both by 2 to get $\frac{1}{2}$ .

Can I leave my answer as an improper fraction?

Yes! $\frac{3}{2}$ is perfectly correct as an improper fraction. You could also write it as $1\frac{1}{2}$ (mixed number) or 1.5 (decimal), but the improper fraction is the most exact form.

What if I get confused with all the different denominators?

Take it step by step! First, write down each fraction. Then simplify each one individually. Finally, add the simplified fractions. Don't try to do everything at once - breaking it into steps prevents mistakes.

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