Solve: 1/4a + 1/3x + 2/4a + 1/8 + 3/8 - Fraction Expression Simplification

Q: Why can't I combine the x term with the a terms?

Variables must match exactly! You can only combine terms with the same variable. Think of a as apples and x as oranges - you can't add apples and oranges together!

Q: How do I know which fractions to add together?

Look for fractions with no variables (constant terms) or fractions with identical variables. In this problem: $ \frac{1}{4}a + \frac{2}{4}a $ and $ \frac{1}{8} + \frac{3}{8} $ can be combined.

Q: Do I need to convert 2/4 to 1/2 before adding?

Not necessary! Since both fractions already have the same denominator (4), you can add directly: $ \frac{1}{4} + \frac{2}{4} = \frac{3}{4} $. Converting to simplest form comes at the very end.

Q: What's the final step after combining like terms?

Always arrange your answer neatly! Put variable terms first, then constant terms: $ \frac{3}{4}a + \frac{1}{3}x + \frac{1}{2} $. Check that all fractions are in lowest terms.

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

Substitute easy values like a = 4 and x = 3 into both the original and simplified expressions. If you get the same result from both, your simplification is correct!

Fraction Simplification with Mixed Variables

$\frac{1}{4}a+\frac{1}{3}x+\frac{2}{4}a+\frac{1}{8}+\frac{3}{8}=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Simplify the expression

00:03 Mark the appropriate variables

00:06 Use the commutative law and arrange the appropriate variables together

00:23 Group terms, add with common denominator

00:56 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

$\frac{1}{4}a+\frac{1}{3}x+\frac{2}{4}a+\frac{1}{8}+\frac{3}{8}=\text{?}$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Combine like terms.
Step 2: Simplify the expression.

Now, let's work through each step:
Step 1: Start by identifying and combining like terms in the expression $\frac{1}{4}a + \frac{1}{3}x + \frac{2}{4}a + \frac{1}{8} + \frac{3}{8}$ . Recognize that $\frac{1}{4}a$ and $\frac{2}{4}a$ are like terms since they both involve the variable $a$ .

Combine these terms:

$\frac{1}{4}a + \frac{2}{4}a = \frac{3}{4}a$

Step 2: Look at the constant terms $\frac{1}{8} + \frac{3}{8}$ . Since these fractions have a common denominator, add them directly:

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

Combine all the terms together to form the simplified expression:

$\frac{3}{4}a + \frac{1}{3}x + \frac{1}{2}$

Therefore, the solution to the problem is $\frac{3}{4}a + \frac{1}{3}x + \frac{1}{2}$ .

Final Answer

$\frac{3}{4}a+\frac{1}{3}x+\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Like Terms: Combine only terms with identical variable parts
Technique: Add fractions with same denominators: $\frac{1}{8} + \frac{3}{8} = \frac{4}{8}$
Check: Count terms in original vs simplified: 5 terms become 3 ✓

Common Mistakes

Avoid these frequent errors

Combining unlike terms incorrectly
Don't add $\frac{1}{3}x$ and $\frac{1}{4}a$ = wrong combination! These have different variables so they cannot be combined. Always group only terms with identical variable parts first.

Practice Quiz

Test your knowledge with interactive questions

$3x+4x+7+2=\text{?}$

FAQ

Everything you need to know about this question

Why can't I combine the x term with the a terms?

Variables must match exactly! You can only combine terms with the same variable. Think of a as apples and x as oranges - you can't add apples and oranges together!

How do I know which fractions to add together?

Look for fractions with no variables (constant terms) or fractions with identical variables. In this problem: $\frac{1}{4}a + \frac{2}{4}a$ and $\frac{1}{8} + \frac{3}{8}$ can be combined.

Do I need to convert 2/4 to 1/2 before adding?

Not necessary! Since both fractions already have the same denominator (4), you can add directly: $\frac{1}{4} + \frac{2}{4} = \frac{3}{4}$ . Converting to simplest form comes at the very end.

What's the final step after combining like terms?

Always arrange your answer neatly! Put variable terms first, then constant terms: $\frac{3}{4}a + \frac{1}{3}x + \frac{1}{2}$ . Check that all fractions are in lowest terms.

How can I check if my simplification is correct?

Substitute easy values like a = 4 and x = 3 into both the original and simplified expressions. If you get the same result from both, your simplification is correct!

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