Solve the Fraction Addition: 1/2 + 3/8 Step by Step

Fraction Addition with Different Denominators

Solve the following equation:

12+38= \frac{1}{2}+\frac{3}{8}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Let's solve this problem together!
00:08 Multiply the whole fraction by 4, to find a common denominator.
00:13 Remember, to multiply both the top, and the bottom numbers.
00:18 Now, calculate each multiplication carefully.
00:23 Combine your results with the common denominator.
00:26 Great job! That's how we find the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following equation:

12+38= \frac{1}{2}+\frac{3}{8}=

2

Step-by-step solution

Let's first identify the lowest common denominator between 2 and 8.

In order to determine the lowest common denominator, we need to first find a number that is divisible by both 2 and 8.

In this case, the common denominator is 8.

We'll then proceed to multiply each fraction by the appropriate number in order to reach the denominator 8.

We'll multiply the first fraction by 4

We'll multiply the second fraction by 1

1×42×4+3×18×1=48+38 \frac{1\times4}{2\times4}+\frac{3\times1}{8\times1}=\frac{4}{8}+\frac{3}{8}

Finally we'll combine and obtain the following:

4+38=78 \frac{4+3}{8}=\frac{7}{8}

3

Final Answer

78 \frac{7}{8}

Key Points to Remember

Essential concepts to master this topic
  • LCD Rule: Find the least common denominator before adding fractions
  • Technique: Convert 12 \frac{1}{2} to 48 \frac{4}{8} by multiplying by 44 \frac{4}{4}
  • Check: Verify 48+38=78 \frac{4}{8} + \frac{3}{8} = \frac{7}{8} by adding numerators only ✓

Common Mistakes

Avoid these frequent errors
  • Adding denominators together
    Don't add 2 + 8 = 10 to get 410 \frac{4}{10} ! This creates a completely wrong fraction because denominators represent different-sized pieces. Always find the LCD first, then add 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 1/2 + 3/8 directly?

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You can't add fractions with different denominators because they represent different-sized pieces! It's like trying to add apples and oranges. You must convert them to the same denominator first.

How do I know 8 is the LCD of 2 and 8?

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Since 8 is already a multiple of 2 (2 × 4 = 8), the LCD is simply 8. The LCD is the smallest number that both denominators divide into evenly.

What if I chose a different common denominator like 16?

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You could use 16! You'd get 816+616=1416 \frac{8}{16} + \frac{6}{16} = \frac{14}{16} , which simplifies to 78 \frac{7}{8} . However, using the LCD saves work and keeps numbers smaller.

Do I need to simplify 7/8?

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78 \frac{7}{8} is already in simplest form because 7 and 8 share no common factors other than 1. Always check if your final answer can be simplified!

What's the fastest way to find the LCD?

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  • If one denominator divides evenly into the other, use the larger number
  • Otherwise, list multiples of each denominator until you find a match
  • For 2 and 8: multiples of 8 are 8, 16, 24... and 8 ÷ 2 = 4, so LCD = 8

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