Evaluate Using the Given Value rs+14s when r=6 and s=1/4

$r s + 14 s$ when $r = 6$ and $s = \frac{1}{4}$

Step 1

Replace the variable $r$ with $6$ in the expression.

$(6) \cdot s + 14 s$

Step 2

Replace the variable $s$ with $\frac{1}{4}$ in the expression.

$(6) \cdot (\frac{1}{4}) + 14 (\frac{1}{4})$

Step 3

Simplify each term.

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$2 (3) \cdot \frac{1}{4} + 14 (\frac{1}{4})$

Factor $2$ out of $4$ .

$2 \cdot 3 \cdot \frac{1}{2 \cdot 2} + 14 (\frac{1}{4})$

Cancel the common factor.

$2 \cdot 3 \cdot \frac{1}{2 \cdot 2} + 14 (\frac{1}{4})$

Rewrite the expression.

$3 \cdot \frac{1}{2} + 14 (\frac{1}{4})$

Combine $3$ and $\frac{1}{2}$ .

$\frac{3}{2} + 14 (\frac{1}{4})$

Cancel the common factor of $2$ .

Factor $2$ out of $14$ .

$\frac{3}{2} + 2 (7) \frac{1}{4}$

Factor $2$ out of $4$ .

$\frac{3}{2} + 2 \cdot 7 \frac{1}{2 \cdot 2}$

Cancel the common factor.

$\frac{3}{2} + 2 \cdot 7 \frac{1}{2 \cdot 2}$

Rewrite the expression.

$\frac{3}{2} + 7 (\frac{1}{2})$

Combine $7$ and $\frac{1}{2}$ .

$\frac{3}{2} + \frac{7}{2}$

Step 4

Combine fractions.

Combine the numerators over the common denominator.

$\frac{3 + 7}{2}$

Simplify the expression.

Add $3$ and $7$ .

$\frac{10}{2}$

Divide $10$ by $2$ .

$5$