Solve: Adding Unit Fractions 1/18 + 1/6 Step-by-Step

Q: Why can't I just add the denominators 18 + 6 = 24?

Adding denominators is never correct when adding fractions! Think of it this way: $ \frac{1}{18} $ means 1 piece out of 18 parts, and $ \frac{1}{6} $ means 1 piece out of 6 parts. You need a common denominator to add them properly.

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

Yes, always simplify! $ \frac{4}{18} $ and $ \frac{2}{9} $ are equal, but $ \frac{2}{9} $ is in simplest form. Divide both numerator and denominator by their greatest common divisor.

Q: What if the denominators are already the same?

Lucky you! When denominators are the same, just add the numerators and keep the denominator: $ \frac{2}{9} + \frac{3}{9} = \frac{5}{9} $.

Q: Can I convert both fractions to decimals instead?

You could, but fraction form is usually more accurate and preferred in math class. Decimals like 0.0556 + 0.1667 can lead to rounding errors and messy calculations.

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

Convert your answer back to decimals or use a calculator: $ \frac{1}{18} = 0.0556 $, $ \frac{1}{6} = 0.1667 $, and $ \frac{2}{9} = 0.2222 $. Check: 0.0556 + 0.1667 ≈ 0.2223 ✓

Fraction Addition with Common Denominators

$\frac{1}{18}+\frac{1}{6}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's solve this problem.

00:07 First, we need to find the least common denominator.

00:10 So, multiply by three. This gives us a common denominator of eighteen.

00:23 Now, calculate the multiplications.

00:28 Add them together under this common denominator.

00:34 Next, let's calculate the numerator.

00:41 Reduce the fraction as much as possible.

00:44 Remember, divide both the numerator and denominator.

00:48 And that's how we find the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\frac{1}{18}+\frac{1}{6}=$

Step-by-step solution

To solve this problem, we need to add the fractions $\frac{1}{18}$ and $\frac{1}{6}$ :

Step 1: Find the least common denominator
The denominators are 18 and 6. The least common multiple of 18 and 6 is 18.

Step 2: Convert each fraction to have the least common denominator
The fraction $\frac{1}{18}$ already has the denominator 18, so it remains $\frac{1}{18}$ .
To convert $\frac{1}{6}$ to a fraction with denominator 18, multiply both the numerator and denominator by 3: $\frac{1 \times 3}{6 \times 3} = \frac{3}{18}$ .

Step 3: Add the converted fractions
Now that both fractions have the same denominator, add them:
$\frac{1}{18} + \frac{3}{18} = \frac{1 + 3}{18} = \frac{4}{18}$ .

Step 4: Simplify the resulting fraction
$\frac{4}{18}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
$\frac{4 \div 2}{18 \div 2} = \frac{2}{9}$ .

Therefore, the sum of $\frac{1}{18}$ and $\frac{1}{6}$ is $\frac{2}{9}$ .

Final Answer

$\frac{2}{9}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find the least common denominator before adding fractions
Technique: Convert $\frac{1}{6}$ to $\frac{3}{18}$ using LCD 18
Check: Simplify final answer: $\frac{4}{18} = \frac{2}{9}$ ✓

Common Mistakes

Avoid these frequent errors

Adding denominators together instead of finding LCD
Don't add $\frac{1}{18} + \frac{1}{6} = \frac{2}{24}$ ! Adding denominators gives completely wrong results. Always find the LCD first, then convert both fractions to equivalent fractions with that denominator.

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 the denominators 18 + 6 = 24?

Adding denominators is never correct when adding fractions! Think of it this way: $\frac{1}{18}$ means 1 piece out of 18 parts, and $\frac{1}{6}$ means 1 piece out of 6 parts. You need a common denominator to add them properly.

How do I find the least common denominator of 18 and 6?

List the multiples of each number: 6: 6, 12, 18, 24... and 18: 18, 36, 54... The smallest number that appears in both lists is 18, so LCD = 18.

Do I always need to simplify my final answer?

Yes, always simplify! $\frac{4}{18}$ and $\frac{2}{9}$ are equal, but $\frac{2}{9}$ is in simplest form. Divide both numerator and denominator by their greatest common divisor.

What if the denominators are already the same?

Lucky you! When denominators are the same, just add the numerators and keep the denominator: $\frac{2}{9} + \frac{3}{9} = \frac{5}{9}$ .

Can I convert both fractions to decimals instead?

You could, but fraction form is usually more accurate and preferred in math class. Decimals like 0.0556 + 0.1667 can lead to rounding errors and messy calculations.

How do I check if my answer is correct?

Convert your answer back to decimals or use a calculator: $\frac{1}{18} = 0.0556$ , $\frac{1}{6} = 0.1667$ , and $\frac{2}{9} = 0.2222$ . Check: 0.0556 + 0.1667 ≈ 0.2223 ✓

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