Simplify x² - 4¼x²: Combining Like Terms with Fractions

Q: Why can I combine these terms but not x² and x³?

You can only combine like terms - terms with identical variables and exponents. Since both terms have $ x^2 $, they're like terms. But $ x^2 $ and $ x^3 $ are different powers, so they can't be combined.

Q: How do I handle the mixed number 4¼?

Convert $ 4\frac{1}{4} $ to an improper fraction: $ \frac{17}{4} $, or use decimals: 4.25. Either way, remember it's negative in this problem: $ -4\frac{1}{4} $.

Q: What does the coefficient of x² mean when there's no number written?

When you see just $ x^2 $, the coefficient is +1 (understood). It's like writing $ 1x^2 $. So $ (+x^2) $ means $ (+1x^2) $.

Q: Why is my answer negative?

Because you're adding $ +1 $ and $ -4\frac{1}{4} $. Since $ 4\frac{1}{4} > 1 $, the negative term "wins" and pulls the result into the negative direction: $ 1 - 4\frac{1}{4} = -3\frac{1}{4} $.

Q: Can I leave my answer as a decimal instead of a mixed number?

Yes! $ -3\frac{1}{4}x^2 $ and $ -3.25x^2 $ are equivalent. However, if the problem uses fractions, it's usually best to keep your answer in fraction form too.

Combining Like Terms with Mixed Numbers

$(+x^2)+(-4\frac{1}{4}x^2)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Simply

00:03 Open parentheses

00:11 Subtract between expressions

00:17 It seems the expression is negative, so we'll take the opposite solution

00:21 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

$(+x^2)+(-4\frac{1}{4}x^2)=$

Step-by-step solution

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

Step 1: Identify the coefficients for each term.
Step 2: Combine the coefficients using arithmetic rules for signed numbers.
Step 3: Write the result in terms of $x^2$ .

Now, let's work through each step:
Step 1: The expression has the terms $+x^2$ and $-4 \frac{1}{4} x^2$ . Here, the coefficients are $+1$ for the first term and $-4 \frac{1}{4}$ for the second term, which is equivalent to $-4.25$ .

Step 2: We combine the coefficients $+1$ and $-4.25$ as follows:
$1 - 4.25 = -3.25$ .

Step 3: Attach the coefficient back to $x^2$ , which results in:
$-3.25x^2$ or $-3\frac{1}{4}x^2$ .

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

Final Answer

$-3\frac{1}{4}x^2$

Key Points to Remember

Essential concepts to master this topic

Like Terms: Terms with identical variables and exponents can be combined
Technique: Add coefficients: 1 + (-4¼) = -3¼
Check: Verify both terms have x² and coefficients add correctly ✓

Common Mistakes

Avoid these frequent errors

Adding absolute values instead of using signed arithmetic
Don't add |1| + |4¼| = 5¼ and then guess the sign! This ignores the negative sign and gives +5¼x² or -5¼x² instead of the correct answer. Always use signed arithmetic: (+1) + (-4¼) = -3¼.

Practice Quiz

Test your knowledge with interactive questions

a is negative number.

b is negative number.

What is the sum of a+b?

FAQ

Everything you need to know about this question

Why can I combine these terms but not x² and x³?

You can only combine like terms - terms with identical variables and exponents. Since both terms have $x^2$ , they're like terms. But $x^2$ and $x^3$ are different powers, so they can't be combined.

How do I handle the mixed number 4¼?

Convert $4\frac{1}{4}$ to an improper fraction: $\frac{17}{4}$ , or use decimals: 4.25. Either way, remember it's negative in this problem: $-4\frac{1}{4}$ .

What does the coefficient of x² mean when there's no number written?

When you see just $x^2$ , the coefficient is +1 (understood). It's like writing $1x^2$ . So $(+x^2)$ means $(+1x^2)$ .

Why is my answer negative?

Because you're adding $+1$ and $-4\frac{1}{4}$ . Since $4\frac{1}{4} > 1$ , the negative term "wins" and pulls the result into the negative direction: $1 - 4\frac{1}{4} = -3\frac{1}{4}$ .

Can I leave my answer as a decimal instead of a mixed number?

Yes! $-3\frac{1}{4}x^2$ and $-3.25x^2$ are equivalent. However, if the problem uses fractions, it's usually best to keep your answer in fraction form too.

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