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

You have a pair of denominators, what is their least common multiple?

$\boxed 2~~~\boxed5$

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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