Solve: 1/2 - 3/8 + 2/4 Fraction Operations Problem

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

Because fractions represent parts of a whole. Adding $ \frac{1}{2} + \frac{3}{8} $ is like adding half a pizza to three-eighths of a pizza - you need the same size pieces first!

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

List multiples: 2: 2, 4, 6, 8..., 4: 4, 8, 12..., 8: 8, 16.... The smallest number that appears in all lists is 8.

Q: What if I simplify 2/4 to 1/2 first?

That's fine! You'd have $ \frac{1}{2} - \frac{3}{8} + \frac{1}{2} $. The LCD is still 8, and you get the same answer: $ \frac{5}{8} $.

Q: Do I need to simplify my final answer?

Always check if you can simplify! For $ \frac{5}{8} $, since 5 and 8 share no common factors, it's already in lowest terms.

Q: What's the difference between LCD and LCM?

They're the same thing! LCD (Least Common Denominator) and LCM (Least Common Multiple) both find the smallest number divisible by all given numbers.

Fraction Operations with Mixed Denominators

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's solve this together.

00:10 First, multiply each fraction by four and two to find a common denominator.

00:16 Be sure to multiply both the top or numerator, and the bottom or denominator, of each fraction.

00:28 Now, let's calculate these multiplications.

00:44 Then, add together the fractions with the common denominator.

00:53 Let's calculate the sum of the numerators.

00:58 And that's how we find the answer. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

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

Step-by-step solution

Let's try to find the least common multiple (LCM) between 2, 8, and 4

To find the least common multiple, we need to find a number that is divisible by 2, 8, and 4

In this case, the least common multiple is 8

Now we'll multiply each fraction by the appropriate number to reach the denominator 8

We'll multiply the first fraction by 4

We'll multiply the second fraction by 1

We'll multiply the third fraction by 2

$\frac{1\times4}{2\times4}-\frac{3\times1}{8\times1}+\frac{2\times2}{4\times2}=\frac{4}{8}-\frac{3}{8}+\frac{4}{8}$

Now we'll subtract and then add:

$\frac{4-3+4}{8}=\frac{1+4}{8}=\frac{5}{8}$

Final Answer

$\frac{5}{8}$

Key Points to Remember

Essential concepts to master this topic

Common Denominator: Find LCD to add/subtract fractions with different denominators
Conversion: Transform $\frac{1}{2}$ to $\frac{4}{8}$ and $\frac{2}{4}$ to $\frac{4}{8}$
Check: Verify $\frac{4}{8} - \frac{3}{8} + \frac{4}{8} = \frac{5}{8}$ by adding numerators ✓

Common Mistakes

Avoid these frequent errors

Adding denominators together
Don't add 2 + 8 + 4 = 14 as the new denominator! This creates $\frac{6}{14}$ which is completely wrong. The denominators show different-sized pieces that can't be combined directly. Always find the LCD first to make all fractions have the same denominator.

Practice Quiz

Test your knowledge with interactive questions

You have a pair of denominators, what is their least common multiple?

$\boxed 2~~~\boxed5$

FAQ

Everything you need to know about this question

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

Because fractions represent parts of a whole. Adding $\frac{1}{2} + \frac{3}{8}$ is like adding half a pizza to three-eighths of a pizza - you need the same size pieces first!

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

List multiples: 2: 2, 4, 6, 8..., 4: 4, 8, 12..., 8: 8, 16.... The smallest number that appears in all lists is 8.

What if I simplify 2/4 to 1/2 first?

That's fine! You'd have $\frac{1}{2} - \frac{3}{8} + \frac{1}{2}$ . The LCD is still 8, and you get the same answer: $\frac{5}{8}$ .

Do I need to simplify my final answer?

Always check if you can simplify! For $\frac{5}{8}$ , since 5 and 8 share no common factors, it's already in lowest terms.

What's the difference between LCD and LCM?

They're the same thing! LCD (Least Common Denominator) and LCM (Least Common Multiple) both find the smallest number divisible by all given numbers.

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