Solve the Fraction Addition: 2/9 + 3/18 Step-by-Step

Q: Why can't I just add 2+3 and 9+18 to get 5/27?

Because fractions represent parts of wholes! $ \frac{2}{9} $ means 2 parts out of 9, while $ \frac{3}{18} $ means 3 parts out of 18. These are different-sized pieces, so you must make them the same size first.

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

Look for the Least Common Multiple (LCM) of the denominators. Since 18 is a multiple of 9 (18 = 9 × 2), use 18 as your common denominator. This keeps numbers smaller and easier to work with.

Q: How do I check if my answer is in simplest form?

Find the Greatest Common Factor (GCF) of the numerator and denominator. Since 7 and 18 share no common factors other than 1, $ \frac{7}{18} $ is already simplified!

Fraction Addition with Different Denominators

$\frac{2}{9}+\frac{3}{18}=$

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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 2, in order to get the common denominator 18

00:09 Remember to multiply both numerator and denominator

00:14 Let's calculate the multiplications

00:22 Add under the common denominator

00:28 Calculate the numerator

00:32 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

$\frac{2}{9}+\frac{3}{18}=$

Step-by-step solution

To solve this problem, we will first convert $\frac{2}{9}$ to have a denominator of 18, then proceed to add the fractions.

Step 1: Convert $\frac{2}{9}$ to have a denominator of 18.
To convert $\frac{2}{9}$ to a fraction with a denominator of 18, recognize that 18 is twice 9. Therefore, multiply both the numerator and the denominator by 2:
$\frac{2}{9} = \frac{2 \times 2}{9 \times 2} = \frac{4}{18}$ .

Step 2: Add the fractions $\frac{4}{18}$ and $\frac{3}{18}$ .
Since the fractions now have the same denominator, simply add the numerators:
$\frac{4}{18} + \frac{3}{18} = \frac{4 + 3}{18} = \frac{7}{18}$ .

There is no need to simplify further as $\frac{7}{18}$ is already in its simplest form.

The correct answer choice is $\frac{7}{18}$ , which matches choice 1.

Therefore, the sum of $\frac{2}{9}$ and $\frac{3}{18}$ is $\frac{7}{18}$ .

Final Answer

$\frac{7}{18}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find common denominator before adding numerators together
Technique: Convert $\frac{2}{9}$ to $\frac{4}{18}$ by multiplying by $\frac{2}{2}$
Check: Verify $\frac{4}{18} + \frac{3}{18} = \frac{7}{18}$ is in simplest form ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators separately
Don't add $\frac{2}{9} + \frac{3}{18}$ as $\frac{2+3}{9+18} = \frac{5}{27}$ ! This ignores that fractions represent parts of different-sized wholes. Always find a common denominator 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 2+3 and 9+18 to get 5/27?

Because fractions represent parts of wholes! $\frac{2}{9}$ means 2 parts out of 9, while $\frac{3}{18}$ means 3 parts out of 18. These are different-sized pieces, so you must make them the same size first.

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

Look for the Least Common Multiple (LCM) of the denominators. Since 18 is a multiple of 9 (18 = 9 × 2), use 18 as your common denominator. This keeps numbers smaller and easier to work with.

What if both fractions need to be converted?

That's fine! Sometimes you'll need to convert both fractions. For example, adding $\frac{1}{4} + \frac{1}{6}$ requires converting both to denominators of 12: $\frac{3}{12} + \frac{2}{12}$ .

How do I check if my answer is in simplest form?

Find the Greatest Common Factor (GCF) of the numerator and denominator. Since 7 and 18 share no common factors other than 1, $\frac{7}{18}$ is already simplified!

Is there a shortcut for this type of problem?

When one denominator divides evenly into the other (like 9 into 18), use the larger one as your common denominator. This saves time because you only need to convert one fraction!

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