Solve the Fraction Addition: 1/3 + 3/6 Step-by-Step

Fraction Addition with Unlike Denominators

Solve the following equation:

13+36= \frac{1}{3}+\frac{3}{6}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Let's solve the problem together!
00:08 First, multiply the fraction by two. This helps us find a common denominator.
00:14 Remember, multiply both the top number and the bottom number by two.
00:20 Now, let's do the multiplication. Take your time!
00:24 Add them together with the common denominator. Almost there!
00:28 And that's how we find the solution. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following equation:

13+36= \frac{1}{3}+\frac{3}{6}=

2

Step-by-step solution

We must first identify the lowest common denominator between 3 and 6.

In order to determine the lowest common denominator, we need to find a number that is divisible by both 3 and 6.

In this case, the common denominator is 6.

We'll then proceed to multiply each fraction by the appropriate number to reach the denominator 6.

We'll multiply the first fraction by 2

We'll multiply the second fraction by 1

1×23×2+3×16×1=26+36 \frac{1\times2}{3\times2}+\frac{3\times1}{6\times1}=\frac{2}{6}+\frac{3}{6}

Finally we'll combine and obtain the following:

2+36=56 \frac{2+3}{6}=\frac{5}{6}

3

Final Answer

56 \frac{5}{6}

Key Points to Remember

Essential concepts to master this topic
  • LCD Rule: Find the lowest common denominator for different denominators
  • Technique: Convert 13 \frac{1}{3} to 26 \frac{2}{6} by multiplying by 22 \frac{2}{2}
  • Check: Verify 26+36=56 \frac{2}{6} + \frac{3}{6} = \frac{5}{6} by adding numerators ✓

Common Mistakes

Avoid these frequent errors
  • Adding numerators and denominators separately
    Don't add 1+3=4 and 3+6=9 to get 49 \frac{4}{9} ! This creates a completely wrong fraction because you're not working with equivalent fractions. Always find the LCD first and convert both fractions before adding only the numerators.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why can't I just add 1/3 + 3/6 directly?

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You can only add fractions when they have the same denominator! Think of it like adding apples and oranges - you need to convert them to the same "unit" first. Here, convert both to sixths: 26+36 \frac{2}{6} + \frac{3}{6} .

How do I find the LCD of 3 and 6?

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List the multiples of each number: 3 (3, 6, 9, 12...) and 6 (6, 12, 18...). The smallest common multiple is 6, so that's your LCD!

Do I need to simplify 3/6 first?

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You could simplify 36=12 \frac{3}{6} = \frac{1}{2} first, but it's not necessary. The LCD method works with any equivalent fractions, so you can work with 36 \frac{3}{6} directly.

What if my LCD is wrong?

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If you use a number that's not divisible by both denominators, you'll get stuck trying to convert the fractions. Always check that your LCD divides evenly into both original denominators.

Can I convert both fractions to a different common denominator?

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Yes! You could use 12 instead of 6, giving you 412+612=1012 \frac{4}{12} + \frac{6}{12} = \frac{10}{12} . But using the LCD (6) keeps numbers smaller and makes calculations easier.

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