Solve the Fraction Addition: 1/3 + 2/4 Step by Step

Fraction Addition with Different Denominators

Solve the following exercise:

13+24=? \frac{1}{3}+\frac{2}{4}=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 We'll multiply each fraction by the second denominator to find a common denominator
00:13 Remember to multiply both numerator and denominator
00:25 Let's calculate the multiplications
00:33 Add under common denominator
00:38 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

Solve the following exercise:

13+24=? \frac{1}{3}+\frac{2}{4}=\text{?}

2

Step-by-step solution

To solve this problem, let's follow these steps:

  • Step 1: Simplify the fractions if possible.
  • Step 2: Identify the common denominator.
  • Step 3: Convert each fraction to have this common denominator.
  • Step 4: Add the fractions.
  • Step 5: Simplify the result, if necessary.

Step 1: Simplify 24 \frac{2}{4} . It simplifies to 12 \frac{1}{2} .

Step 2: The denominators are now 3 and 2. Find the least common multiple of 3 and 2, which is 6.

Step 3: Convert each fraction to have the common denominator of 6:
13=1×23×2=26\frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6}
12=1×32×3=36\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}

Step 4: Add the fractions:
26+36=2+36=56\frac{2}{6} + \frac{3}{6} = \frac{2 + 3}{6} = \frac{5}{6}

Step 5: The fraction 56\frac{5}{6} is already in its simplest form.

Therefore, the solution to the problem is 56\frac{5}{6}.

3

Final Answer

1012 \frac{10}{12}

Key Points to Remember

Essential concepts to master this topic
  • Common Denominator Rule: Find LCD before adding fractions with different denominators
  • Conversion Technique: 13=412 \frac{1}{3} = \frac{4}{12} and 24=612 \frac{2}{4} = \frac{6}{12} using LCD 12
  • Verification Check: 412+612=1012=56 \frac{4}{12} + \frac{6}{12} = \frac{10}{12} = \frac{5}{6} in simplest form ✓

Common Mistakes

Avoid these frequent errors
  • Adding numerators and denominators separately
    Don't add 13+24 \frac{1}{3} + \frac{2}{4} as 37 \frac{3}{7} by doing 1+2=3 and 3+4=7! This ignores that fractions represent parts of different-sized wholes. Always find a common denominator first, then add only the 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

Why can't I just add the top numbers and bottom numbers?

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Because 13 \frac{1}{3} and 24 \frac{2}{4} represent pieces of different-sized wholes! It's like trying to add 1 slice of a 3-piece pizza to 2 slices of a 4-piece pizza - you need equal-sized pieces first.

How do I find the least common denominator (LCD)?

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List the multiples of each denominator until you find the smallest number that appears in both lists. For 3 and 4: multiples of 3 are 3, 6, 9, 12... and multiples of 4 are 4, 8, 12... So LCD = 12.

Do I always need to simplify my final answer?

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Yes, always simplify! In this problem, 1012 \frac{10}{12} simplifies to 56 \frac{5}{6} by dividing both numerator and denominator by their GCD of 2.

What if one fraction is already simplified and the other isn't?

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Always simplify first, then find the LCD! In this problem, 24=12 \frac{2}{4} = \frac{1}{2} , so you're really adding 13+12 \frac{1}{3} + \frac{1}{2} with LCD = 6.

Why does the explanation show a different LCD than the answer choices?

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The explanation correctly uses LCD = 6, giving 56 \frac{5}{6} . The answer choices use denominator 12, where 56=1012 \frac{5}{6} = \frac{10}{12} . Both approaches work - just remember to match the format requested!

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