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

$3\frac{1}{2}a+12\frac{1}{4}b-(1\frac{1}{4}a-2\frac{1}{2}b)=\text{?}$

We begin by addressing the parenthesis:

Remember that:

When we multiply a positive number by a negative number, the result will be negative.

When we multiply a negative number by a negative number, the result will be positive.

We obtain the following equation:

$3\frac{1}{2}a+12\frac{1}{4}b-1\frac{1}{4}a+2\frac{1}{2}b=$

Next we join the a coefficients:

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

We then join the b coefficients:

$12\frac{1}{4}b+2\frac{1}{2}b=14\frac{3}{4}b$

Lastly we obtain:

$2\frac{1}{4}a+14\frac{3}{4}b=$