Solve the Fraction Addition: 1/2 + 2/9 Step-by-Step

Q: Why can't I just add 1/2 + 2/9 directly?

You can't add fractions with different denominators because they represent different-sized pieces! It's like trying to add 1 half-pizza slice to 2 ninth-pizza slices - you need equal-sized pieces first.

Q: How do I find the LCD of 2 and 9?

Since 2 and 9 share no common factors (they're relatively prime), multiply them together: 2 × 9 = 18. That's your LCD!

Q: What if the LCD seems too big?

Don't worry! The LCD method always works. For $ \frac{1}{2} + \frac{2}{9} $, using 18 gives us $ \frac{9}{18} + \frac{4}{18} $ which is easy to add.

Q: How can I check my answer is correct?

Convert both fractions to decimals: $ \frac{1}{2} = 0.5 $ and $ \frac{2}{9} ≈ 0.222 $, so the sum should be about 0.722. Check: $ \frac{13}{18} ≈ 0.722 $ ✓

Fraction Addition with Unlike Denominators

Solve the following exercise:

$\frac{1}{2}+\frac{2}{9}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solution

00:03 Multiply each fraction by the second denominator to find the common denominator

00:07 Make sure to multiply both numerator and denominator

00:14 Calculate the products

00:19 Add with the common denominator

00:24 Calculate the numerator

00:27 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:

$\frac{1}{2}+\frac{2}{9}=$

Step-by-step solution

Let's try to find the lowest common denominator between 2 and 9

To find the lowest common denominator, we need to find a number that is divisible by both 2 and 9

In this case, the common denominator is 18

Now we'll multiply each fraction by the appropriate number to reach the denominator 18

We'll multiply the first fraction by 9

We'll multiply the second fraction by 2

$\frac{1\times9}{2\times9}+\frac{2\times2}{9\times2}=\frac{9}{18}+\frac{4}{18}$

Now we'll combine and get:

$\frac{9+4}{18}=\frac{13}{18}$

Final Answer

$\frac{13}{18}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find the least common denominator (LCD) before adding fractions
Technique: Multiply $\frac{1}{2}$ by 9 and $\frac{2}{9}$ by 2 to get LCD of 18
Check: Verify that $\frac{9}{18} + \frac{4}{18} = \frac{13}{18}$ in lowest terms ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators directly
Don't add 1+2=3 and 2+9=11 to get $\frac{3}{11}$ ! This ignores that fractions represent parts of different-sized wholes. Always find the LCD first to make denominators equal, then add only the numerators.

Practice Quiz

Test your knowledge with interactive questions

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

$$ 5:6= $$

FAQ

Everything you need to know about this question

Why can't I just add 1/2 + 2/9 directly?

You can't add fractions with different denominators because they represent different-sized pieces! It's like trying to add 1 half-pizza slice to 2 ninth-pizza slices - you need equal-sized pieces first.

How do I find the LCD of 2 and 9?

Since 2 and 9 share no common factors (they're relatively prime), multiply them together: 2 × 9 = 18. That's your LCD!

Do I need to simplify 13/18?

Check if 13 and 18 have common factors. Since 13 is prime and doesn't divide 18, $\frac{13}{18}$ is already in lowest terms!

What if the LCD seems too big?

Don't worry! The LCD method always works. For $\frac{1}{2} + \frac{2}{9}$ , using 18 gives us $\frac{9}{18} + \frac{4}{18}$ which is easy to add.

How can I check my answer is correct?

Convert both fractions to decimals: $\frac{1}{2} = 0.5$ and $\frac{2}{9} ≈ 0.222$ , so the sum should be about 0.722. Check: $\frac{13}{18} ≈ 0.722$ ✓

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