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

Fraction Addition with Different Denominators

Solve the following exercise:

12+29= \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 Solve
00:03 Multiply each fraction by the second denominator to find the common denominator
00:07 Make sure to multiply both numerator and denominator
00:15 Calculate the multiplications
00:21 Add with the common denominator
00:25 Calculate the numerator
00:30 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following exercise:

12+29= \frac{1}{2}+\frac{2}{9}=

2

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

1×92×9+2×29×2=918+418 \frac{1\times9}{2\times9}+\frac{2\times2}{9\times2}=\frac{9}{18}+\frac{4}{18}

Now we'll combine and get:

9+418=1318 \frac{9+4}{18}=\frac{13}{18}

3

Final Answer

1318 \frac{13}{18}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Find LCD before adding fractions with different denominators
  • Technique: Convert 12 \frac{1}{2} to 918 \frac{9}{18} and 29 \frac{2}{9} to 418 \frac{4}{18}
  • Check: Verify 918+418=1318 \frac{9}{18} + \frac{4}{18} = \frac{13}{18} cannot be simplified further ✓

Common Mistakes

Avoid these frequent errors
  • Adding numerators and denominators separately
    Don't add 1+2=3 and 2+9=11 to get 311 \frac{3}{11} ! This completely ignores different denominators and gives a meaningless result. Always find the LCD first, then convert both fractions before adding.

Practice Quiz

Test your knowledge with interactive questions

\( \frac{2}{4}+\frac{1}{4}= \)\( \)

FAQ

Everything you need to know about this question

How do I find the LCD of 2 and 9?

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Since 2 and 9 share no common factors (2 is even, 9 is odd), their LCD is simply their product: 2×9=18 2 \times 9 = 18 . This works for any two numbers that are relatively prime.

Why can't I just add the tops and bottoms?

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Fractions represent parts of a whole. 12 \frac{1}{2} means 1 out of 2 equal parts, while 29 \frac{2}{9} means 2 out of 9 equal parts. You can't combine different-sized pieces without making them the same size first!

Do I always multiply denominators to get the LCD?

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Not always! Only when the denominators share no common factors. For example, LCD of 4 and 6 is 12 (not 24), because both are divisible by 2.

How do I know what to multiply each fraction by?

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Divide the LCD by each denominator: 18÷2=9 18 ÷ 2 = 9 and 18÷9=2 18 ÷ 9 = 2 . These are your multipliers for the numerator and denominator of each fraction.

Can I simplify the final answer?

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Always try! Check if the numerator and denominator have common factors. For 1318 \frac{13}{18} , since 13 is prime and doesn't divide 18, this fraction is already in simplest form.

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