AI Tutor
If you have half a tank of gas and add three-fourths of a tank, how much gas do you have? Real-world quantities rarely come in neat whole numbers, and neither do algebraic expressions.
A coefficient is the number multiplying a variable. Just like with integers, you can only combine like termsβ€”terms that share the exact same variable part.
Adding fourths is easy because the pieces are already the same size. But what happens when your fractional coefficients have completely different denominators?

Finding a Common Denominator

To add or subtract fractional coefficients, convert them so they share a least common denominator (LCD)β€”the smallest number that both denominators divide into evenly.
Let's simplify 23x+14x\frac{2}{3}x + \frac{1}{4}x. The denominators are 33 and 44, so their LCD is 1212.
A common mistake is adding both the top and bottom numbers: 23+14β‰ 37\frac{2}{3} + \frac{1}{4} \neq \frac{3}{7}. The denominator simply names the size of each piece, so it stays 1212 while only the numerators add together.
What happens when an expression contains multiple variables, constants, and negative fractions all at once?

Multi-Variable Expressions and Signs

Always group matching variable families together first, and make sure the sign (+(+ or βˆ’)-) stays attached to the coefficient directly following it.
Consider 35mβˆ’12kβˆ’15m+34k\frac{3}{5}m - \frac{1}{2}k - \frac{1}{5}m + \frac{3}{4}k. Group the mm-terms: (35βˆ’15)m=25m(\frac{3}{5} - \frac{1}{5})m = \frac{2}{5}m.