Evaluate Using the Given Value 1/3m-1-1/2n when m=21 and n=12

$\frac{1}{3} m - 1 - \frac{1}{2} n$ when $m = 21$ and $n = 12$

Step 1

Replace the variable $m$ with $21$ in the expression.

$\frac{1}{3} \cdot (21) - 1 - \frac{1}{2} n$

Step 2

Replace the variable $n$ with $12$ in the expression.

$\frac{1}{3} \cdot (21) - 1 - \frac{1}{2} \cdot 12$

Step 3

Simplify each term.

Cancel the common factor of $3$ .

Factor $3$ out of $21$ .

$\frac{1}{3} \cdot (3 (7)) - 1 - \frac{1}{2} \cdot 12$

Cancel the common factor.

$\frac{1}{3} \cdot (3 \cdot 7) - 1 - \frac{1}{2} \cdot 12$

Rewrite the expression.

$7 - 1 - \frac{1}{2} \cdot 12$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$7 - 1 + \frac{- 1}{2} \cdot 12$

Factor $2$ out of $12$ .

$7 - 1 + \frac{- 1}{2} \cdot (2 (6))$

Cancel the common factor.

$7 - 1 + \frac{- 1}{2} \cdot (2 \cdot 6)$

Rewrite the expression.

$7 - 1 - 1 \cdot 6$

Multiply $- 1$ by $6$ .

$7 - 1 - 6$

Step 4

Simplify by subtracting numbers.

Subtract $1$ from $7$ .

$6 - 6$

Subtract $6$ from $6$ .

$0$