Adding Fractions: Solve 1/4 + 7/8 Step by Step

Q: Why can't I just add 1+7 and 4+8 directly?

Because fractions represent parts of a whole, and you can only add parts that are the same size! $ \frac{1}{4} $ means 1 piece out of 4, while $ \frac{7}{8} $ means 7 pieces out of 8. These are different-sized pieces, so you need to make them the same size first.

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

List the multiples: 4: (4, 8, 12, 16...) and 8: (8, 16, 24...). The smallest number that appears in both lists is 8, so LCD = 8.

Q: What if my answer is an improper fraction like 9/8?

That's perfectly correct! $ \frac{9}{8} $ is a valid answer. You can also write it as a mixed number: $ 1\frac{1}{8} $, but the improper fraction form is fine too.

Q: How can I check if my answer is right?

Convert both fractions to decimals: $ \frac{1}{4} = 0.25 $ and $ \frac{7}{8} = 0.875 $. Add them: 0.25 + 0.875 = 1.125. Then check: $ \frac{9}{8} = 1.125 $ ✓

Fraction Addition with Different Denominators

$\frac{1}{4}+\frac{7}{8}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solution

00:03 We want to find the least common denominator

00:06 Multiply by 2 to find the common denominator

00:09 Remember to multiply both numerator and denominator

00:17 Calculate the products

00:22 Add under the common denominator

00:28 Calculate the numerator

00:31 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\frac{1}{4}+\frac{7}{8}=$

Step-by-step solution

To find the sum $\frac{1}{4} + \frac{7}{8}$ , follow these steps:

Step 1: Identify the least common denominator (LCD) of the fractions. The denominators 4 and 8 have an LCD of 8.
Step 2: Convert $\frac{1}{4}$ to an equivalent fraction with a denominator of 8. Multiply both the numerator and the denominator by 2: $\frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8}$ .
Step 3: The second fraction, $\frac{7}{8}$ , already has the correct denominator. Therefore, it remains $\frac{7}{8}$ .
Step 4: Add the numerators of the two fractions: $\frac{2}{8} + \frac{7}{8} = \frac{2+7}{8} = \frac{9}{8}$ .

Therefore, the sum of $\frac{1}{4}$ and $\frac{7}{8}$ is $\frac{9}{8}$ .

Final Answer

$\frac{9}{8}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find the least common denominator (LCD) before adding fractions
Technique: Convert $\frac{1}{4}$ to $\frac{2}{8}$ by multiplying by 2/2
Check: Verify $\frac{2}{8} + \frac{7}{8} = \frac{9}{8}$ equals 1.125 ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators separately
Don't add 1+7=8 and 4+8=12 to get $\frac{8}{12}$ ! This creates a completely wrong fraction because you're not following proper fraction addition rules. Always find the LCD first, convert fractions to equivalent forms, then add only the numerators.

Practice Quiz

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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 1+7 and 4+8 directly?

Because fractions represent parts of a whole, and you can only add parts that are the same size! $\frac{1}{4}$ means 1 piece out of 4, while $\frac{7}{8}$ means 7 pieces out of 8. These are different-sized pieces, so you need to make them the same size first.

How do I find the LCD of 4 and 8?

List the multiples: 4: (4, 8, 12, 16...) and 8: (8, 16, 24...). The smallest number that appears in both lists is 8, so LCD = 8.

What if my answer is an improper fraction like 9/8?

That's perfectly correct! $\frac{9}{8}$ is a valid answer. You can also write it as a mixed number: $1\frac{1}{8}$ , but the improper fraction form is fine too.

Do I always need to find the LCD?

Yes, when denominators are different! If one denominator divides evenly into the other (like 4 and 8), the larger one is your LCD. This makes converting fractions much easier.

How can I check if my answer is right?

Convert both fractions to decimals: $\frac{1}{4} = 0.25$ and $\frac{7}{8} = 0.875$ . Add them: 0.25 + 0.875 = 1.125. Then check: $\frac{9}{8} = 1.125$ ✓

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Adding Fractions: Solve 1/4 + 7/8 Step by Step

Fraction Addition with Different Denominators

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why can't I just add 1+7 and 4+8 directly?

How do I find the LCD of 4 and 8?

What if my answer is an improper fraction like 9/8?

Do I always need to find the LCD?

How can I check if my answer is right?

🌟 Unlock Your Math Potential

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