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
00:00 Solve
00:03 We want to find the least common denominator
00:06 Multiply each fraction by the other denominator to find the common denominator
00:12 Remember to multiply both numerator and denominator
00:27 Calculate the multiplications
00:31 Add under the common denominator
00:37 Calculate the numerator
00:42 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

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

Complete the following exercise:

\( \frac{3}{4}:\frac{5}{6}=\text{?} \)

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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