Solve: 1/2 + 3/4 + 6/8 Addition of Mixed Denominators

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

That method doesn't work because fractions represent parts of different wholes. $ \frac{1}{2} $ means 1 out of 2 equal parts, while $ \frac{3}{4} $ means 3 out of 4 equal parts. You need the same-sized parts to add them!

Q: Do I need to simplify 6/8 first?

Not necessary! Since we're converting everything to denominator 8 anyway, you can leave $ \frac{6}{8} $ as is. It saves time and reduces chances of error.

Q: What if the LCD is really big?

Don't worry! Use the systematic approach: find the LCD, convert each fraction, add numerators, then simplify. Even with big numbers, this method always works reliably.

Q: How can I check if my LCD is correct?

Your LCD should be divisible by all original denominators. Check: 8 ÷ 2 = 4 ✓, 8 ÷ 4 = 2 ✓, 8 ÷ 8 = 1 ✓. All give whole numbers, so 8 is correct!

Fraction Addition with Common Denominators

$\frac{1}{2}+\frac{3}{4}+\frac{6}{8}=$

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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 Therefore we'll multiply the 4, 2 respectively to find the common denominator

00:09 Remember to multiply both numerator and denominator

00:23 Let's calculate the multiplications

00:30 Add under the common denominator

00:37 Calculate the numerator

00:44 Convert fraction to whole number

00:47 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

$\frac{1}{2}+\frac{3}{4}+\frac{6}{8}=$

Step-by-step solution

To solve this problem, we will add the fractions $\frac{1}{2}$ , $\frac{3}{4}$ , and $\frac{6}{8}$ by first converting each to have a common denominator:

Step 1: Find the Least Common Denominator (LCD). The denominators are $2$ , $4$ , and $8$ . The LCM of these numbers is $8$ .

Step 2: Rewrite each fraction with the denominator of $8$ .

$\frac{1}{2} = \frac{1 \times 4}{2 \times 4} = \frac{4}{8}$
$\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}$
$\frac{6}{8}$ is already expressed with a denominator of $8$ .

Step 3: Add the fractions:

$\frac{4}{8} + \frac{6}{8} + \frac{6}{8} = \frac{4 + 6 + 6}{8} = \frac{16}{8}$

Step 4: Simplify the fraction:

$\frac{16}{8} = 2$

Therefore, the sum of the fractions $\frac{1}{2} + \frac{3}{4} + \frac{6}{8} = 2$ .

Final Answer

$2$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert all fractions to common denominator before adding
Technique: LCD of 2, 4, 8 is 8: $\frac{1}{2} = \frac{4}{8}$
Check: $\frac{4}{8} + \frac{6}{8} + \frac{6}{8} = \frac{16}{8} = 2$ ✓

Common Mistakes

Avoid these frequent errors

Adding denominators and numerators separately
Don't add $\frac{1}{2} + \frac{3}{4} + \frac{6}{8}$ as $\frac{1+3+6}{2+4+8} = \frac{10}{14}$ ! This completely ignores the rules of fraction addition and gives wrong results. Always find the LCD first, convert each fraction, 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 the numerators and denominators?

That method doesn't work because fractions represent parts of different wholes. $\frac{1}{2}$ means 1 out of 2 equal parts, while $\frac{3}{4}$ means 3 out of 4 equal parts. You need the same-sized parts to add them!

How do I find the LCD of 2, 4, and 8?

List multiples of each number: 2 (2, 4, 6, 8...), 4 (4, 8, 12...), 8 (8, 16...). The smallest number that appears in all lists is 8, so LCD = 8.

What if my answer is greater than 1?

That's totally normal! When adding fractions, your sum can be any positive number. In this problem, we get 2, which means we have 2 whole units. Always simplify your final answer!

Do I need to simplify 6/8 first?

Not necessary! Since we're converting everything to denominator 8 anyway, you can leave $\frac{6}{8}$ as is. It saves time and reduces chances of error.

What if the LCD is really big?

Don't worry! Use the systematic approach: find the LCD, convert each fraction, add numerators, then simplify. Even with big numbers, this method always works reliably.

How can I check if my LCD is correct?

Your LCD should be divisible by all original denominators. Check: 8 ÷ 2 = 4 ✓, 8 ÷ 4 = 2 ✓, 8 ÷ 8 = 1 ✓. All give whole numbers, so 8 is correct!

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