Simplify x² + 3½x²: Combining Like Terms with Mixed Numbers

Like terms have the exact same variable part. Both $x^2$ and $3\frac{1}{2}x^2$ have $x^2$, so they can be combined!

Convert $3\frac{1}{2}$ to a decimal (3.5) or improper fraction ($\frac{7}{2}$) for easier addition. Both methods give the same answer!

When no number appears in front of a variable, the invisible coefficient is 1. So $x^2$ really means $1x^2$!

Yes! $4.5x^2$ and $4\frac{1}{2}x^2$ are exactly the same. Choose whichever form your teacher prefers or the problem asks for.

The same rule applies! For $x^2 - 3\frac{1}{2}x^2$, you'd calculate $1 - 3.5 = -2.5 = -2\frac{1}{2}$. Just be careful with your positive and negative signs!

Add the original coefficients: $1 + 3\frac{1}{2} = 4\frac{1}{2}$. If your final coefficient matches this sum, you're right! ✓