Solve the Fraction Addition: 2/9 + 1/2

Fraction Addition with Unlike Denominators

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:06 Let's solve this math problem together!
00:09 First, we need to find the least common denominator.
00:12 Multiply each fraction by the other fraction's denominator.
00:18 Make sure to multiply both the numerator and the denominator.
00:23 Got it? Now, let's calculate these multiplications.
00:33 Next, we add the fractions under the common denominator.
00:37 Now, let's calculate the new numerator.
00:43 And that's how we find the solution to this question!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

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

2

Step-by-step solution

To solve the addition of the fractions 29\frac{2}{9} and 12\frac{1}{2}, follow these steps:

  • Step 1: Determine the Common Denominator.
    The least common denominator for 9 and 2 is 1818 because 9×2=189 \times 2 = 18.
  • Step 2: Adjust Each Fraction.
    Convert 29\frac{2}{9} to a fraction over 18. Multiply both the numerator and the denominator by 2:
    29=2×29×2=418\frac{2}{9} = \frac{2 \times 2}{9 \times 2} = \frac{4}{18}.
    Convert 12\frac{1}{2} to a fraction over 18. Multiply both the numerator and the denominator by 9:
    12=1×92×9=918\frac{1}{2} = \frac{1 \times 9}{2 \times 9} = \frac{9}{18}.
  • Step 3: Add the Fractions.
    Add the resulting fractions: 418+918=4+918=1318\frac{4}{18} + \frac{9}{18} = \frac{4 + 9}{18} = \frac{13}{18}.

Thus, the sum of 29\frac{2}{9} and 12\frac{1}{2} is 1318\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 29 \frac{2}{9} to 418 \frac{4}{18} and 12 \frac{1}{2} to 918 \frac{9}{18}
  • Check: Verify LCD is correct: 18 ÷ 9 = 2 and 18 ÷ 2 = 9 ✓

Common Mistakes

Avoid these frequent errors
  • Adding numerators and denominators separately
    Don't add 29+12 \frac{2}{9} + \frac{1}{2} as 311 \frac{3}{11} ! This ignores that fractions need common denominators first. Always find the LCD and convert both fractions before adding numerators.

Practice Quiz

Test your knowledge with interactive questions

Solve the following:

\( \frac{5}{9}:\frac{7}{18}= \)

FAQ

Everything you need to know about this question

How do I find the LCD of 9 and 2?

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Since 9 and 2 share no common factors, their LCD is simply 9×2=18 9 \times 2 = 18 . For larger numbers, list multiples or use prime factorization.

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

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Fractions represent parts of a whole. 29 \frac{2}{9} means 2 ninths, and 12 \frac{1}{2} means 1 half. You can't add different-sized pieces directly - they need to be the same size first!

Do I need to simplify my answer?

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Always check if your answer can be simplified! For 1318 \frac{13}{18} , since 13 is prime and doesn't divide 18, it's already in lowest terms.

What if my LCD seems too big?

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Don't worry! The LCD might seem large, but it ensures accurate addition. For 29+12 \frac{2}{9} + \frac{1}{2} , using LCD = 18 gives the correct answer 1318 \frac{13}{18} .

Can I convert to decimals instead?

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While possible, exact fraction answers are usually preferred in math class. Converting 29 \frac{2}{9} to decimal gives 0.222..., which is harder to work with than the fraction form.

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