Solve the Fraction Addition: 2/4 + 3/8 Step-by-Step

Fraction Addition with Common Denominators

Solve the following exercise:

24+38=? \frac{2}{4}+\frac{3}{8}=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:06 Let's solve this problem together.
00:09 First, we need to find the least common denominator.
00:13 So, let's multiply by 2 to make it 8.
00:17 Remember, we multiply both the numerator and the denominator.
00:22 Now, let's calculate these multiplications.
00:26 Then, add them under the common denominator.
00:31 Finally, let's calculate the numerator.
00:35 And that's how we solve this question!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following exercise:

24+38=? \frac{2}{4}+\frac{3}{8}=\text{?}

2

Step-by-step solution

To solve the problem of adding 24 \frac{2}{4} and 38 \frac{3}{8} , we need to follow these steps:

  • Step 1: Convert 24 \frac{2}{4} to an equivalent fraction with a denominator of 8.
  • Step 2: Add the two fractions with the common denominator.
  • Step 3: Verify the solution and match it against the provided answer choices.

Let's perform each step:

Step 1: Convert 24 \frac{2}{4} to a fraction with a denominator of 8.
To do this, we multiply both the numerator and the denominator of 24 \frac{2}{4} by 2, since 4×2=8 4 \times 2 = 8 .
This gives us 2×24×2=48 \frac{2 \times 2}{4 \times 2} = \frac{4}{8} .

Step 2: Add 48 \frac{4}{8} and 38 \frac{3}{8} .
Since both fractions now have the same denominator, we can add the numerators directly:
48+38=4+38=78 \frac{4}{8} + \frac{3}{8} = \frac{4+3}{8} = \frac{7}{8} .

Step 3: Verify the solution.
The calculated sum of the fractions is 78 \frac{7}{8} . This matches choice 1 in the given answer choices.

The solution to the problem is 78 \frac{7}{8} .

3

Final Answer

78 \frac{7}{8}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Find common denominators before adding numerators together
  • Technique: Convert 24 \frac{2}{4} to 48 \frac{4}{8} by multiplying by 2
  • Check: Verify 48+38=78 \frac{4}{8} + \frac{3}{8} = \frac{7}{8} by ensuring denominators match ✓

Common Mistakes

Avoid these frequent errors
  • Adding numerators and denominators separately
    Don't add 24+38 \frac{2}{4} + \frac{3}{8} as 2+34+8=512 \frac{2+3}{4+8} = \frac{5}{12} ! This treats fractions like separate numbers instead of parts of wholes. Always find a common denominator first, then add only the numerators.

Practice Quiz

Test your knowledge with interactive questions

\( \)\( \frac{4}{5}+\frac{1}{5}= \)

FAQ

Everything you need to know about this question

Why can't I just add the numerators and denominators directly?

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Fractions represent parts of a whole. You can only add parts when they're from the same-sized whole! Different denominators mean different-sized pieces, so you must make them the same size first.

How do I find the common denominator between 4 and 8?

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Since 8 is a multiple of 4 (4 × 2 = 8), use 8 as your common denominator. For other cases, find the least common multiple (LCM) of both denominators.

What if my answer doesn't match any of the choices?

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Double-check your work! Make sure you converted to the right common denominator and added only the numerators. If you still don't match, try simplifying your answer.

Do I need to simplify my final answer?

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Not always, but it's good practice! Check if the numerator and denominator share any common factors. In this case, 78 \frac{7}{8} is already in simplest form.

Can I use a different common denominator besides 8?

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Yes! You could use any common multiple of 4 and 8, like 16 or 24. However, using the smallest common denominator (8) makes the math easier and reduces errors.

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