Solve Fraction Addition: 1/4 + 5/8 Step-by-Step

Q: Why can't I just add 1 + 5 and 4 + 8?

Because fractions represent parts of a whole! Adding $ \frac{1}{4} $ (one-fourth) plus $ \frac{5}{8} $ (five-eighths) means you need the same-sized pieces first.

Q: How do I find the LCD between 4 and 8?

List the multiples of each: 4: 4, 8, 12... and 8: 8, 16, 24... The smallest number that appears in both lists is 8.

Q: What if the LCD is bigger than both denominators?

That's normal! For example, with $ \frac{1}{3} + \frac{1}{4} $, the LCD is 12. You'd convert both fractions: $ \frac{4}{12} + \frac{3}{12} = \frac{7}{12} $.

Q: Do I always need to simplify my answer?

Yes! Always check if your final fraction can be reduced. In this case, $ \frac{7}{8} $ is already in lowest terms since 7 and 8 share no common factors.

Fraction Addition with Different Denominators

Solve the following equation:

$\frac{1}{4}+\frac{5}{8}=$

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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 First, multiply the fraction by 2, so we have a common denominator.

00:13 Remember, multiply both the numerator and the denominator by 2.

00:18 Now, calculate the results of these multiplications.

00:26 Next, add the fractions with the common denominator.

00:30 And there you have it! That's the final solution to our question.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following equation:

$\frac{1}{4}+\frac{5}{8}=$

Step-by-step solution

We must first identify the lowest common denominator between 4 and 8.

In order to determine the lowest common denominator, we need to find a number that is divisible by both 4 and 8.

In this case, the common denominator is 8.

We will then proceed to multiply each fraction by the appropriate number to reach the denominator 8.

We'll multiply the first fraction by 2

We'll multiply the second fraction by 1

$\frac{1\times2}{4\times2}+\frac{5\times1}{8\times1}=\frac{2}{8}+\frac{5}{8}$

Finally we'll combine and obtain the following:

$\frac{2+5}{8}=\frac{7}{8}$

Final Answer

$\frac{7}{8}$

Key Points to Remember

Essential concepts to master this topic

LCD Rule: Find lowest common denominator before adding fractions
Technique: Convert $\frac{1}{4}$ to $\frac{2}{8}$ by multiplying by 2
Check: Verify $\frac{2}{8} + \frac{5}{8} = \frac{7}{8}$ by adding numerators only ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators separately
Don't add $\frac{1}{4} + \frac{5}{8} = \frac{6}{12}$ ! This gives a completely wrong answer because you can't add fractions with different denominators directly. Always find the LCD first and convert both fractions before adding.

Practice Quiz

Test your knowledge with interactive questions

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

$$ 5:6= $$

FAQ

Everything you need to know about this question

Why can't I just add 1 + 5 and 4 + 8?

Because fractions represent parts of a whole! Adding $\frac{1}{4}$ (one-fourth) plus $\frac{5}{8}$ (five-eighths) means you need the same-sized pieces first.

How do I find the LCD between 4 and 8?

List the multiples of each: 4: 4, 8, 12... and 8: 8, 16, 24... The smallest number that appears in both lists is 8.

What if the LCD is bigger than both denominators?

That's normal! For example, with $\frac{1}{3} + \frac{1}{4}$ , the LCD is 12. You'd convert both fractions: $\frac{4}{12} + \frac{3}{12} = \frac{7}{12}$ .

Do I always need to simplify my answer?

Yes! Always check if your final fraction can be reduced. In this case, $\frac{7}{8}$ is already in lowest terms since 7 and 8 share no common factors.

What if one denominator divides evenly into the other?

Great! That makes it easier. Since 8 ÷ 4 = 2, we know 8 is already the LCD. Just convert $\frac{1}{4}$ to eighths and add!

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