Solve: 3½a + 12¼b - (1¼a - 2½b) Mixed Number Expression

The negative sign acts like -1 multiplying everything inside the parentheses. So $-(1\frac{1}{4}a - 2\frac{1}{2}b)$ becomes $-1\frac{1}{4}a + 2\frac{1}{2}b$ because negative times negative equals positive!

Convert to improper fractions first: $3\frac{1}{2} = \frac{7}{2}$ and $1\frac{1}{4} = \frac{5}{4}$. Then find common denominator: $\frac{14}{4} - \frac{5}{4} = \frac{9}{4} = 2\frac{1}{4}$

The variable b stays with both terms! You're adding the coefficients: $12\frac{1}{4} + 2\frac{1}{2} = 14\frac{3}{4}$, so the result is $14\frac{3}{4}b$, not just the number.

Yes, but be extra careful with the arithmetic! Converting to improper fractions first usually prevents mistakes, especially when finding common denominators for addition and subtraction.

Only combine like terms - terms with the same variable and same power. In this problem, combine all the a terms together and all the b terms together, but never mix them!