Basic Math Examples

$\frac{5}{9} \cdot (F - 39) = - 15$

Step 1

Multiply both sides of the equation by $\frac{9}{5}$ .

$\frac{9}{5} (\frac{5}{9} \cdot (F - 39)) = \frac{9}{5} \cdot - 15$

Step 2

Simplify both sides of the equation.

Tap for more steps...

Step 2.1

Simplify the left side.

Tap for more steps...

Step 2.1.1

Simplify $\frac{9}{5} (\frac{5}{9} \cdot (F - 39))$ .

Tap for more steps...

Step 2.1.1.1

Apply the distributive property.

$\frac{9}{5} (\frac{5}{9} F + \frac{5}{9} \cdot - 39) = \frac{9}{5} \cdot - 15$

Step 2.1.1.2

Combine $\frac{5}{9}$ and $F$ .

$\frac{9}{5} (\frac{5 F}{9} + \frac{5}{9} \cdot - 39) = \frac{9}{5} \cdot - 15$

Step 2.1.1.3

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.1.1.3.1

Factor $3$ out of $9$ .

$\frac{9}{5} (\frac{5 F}{9} + \frac{5}{3 (3)} \cdot - 39) = \frac{9}{5} \cdot - 15$

Step 2.1.1.3.2

Factor $3$ out of $- 39$ .

$\frac{9}{5} (\frac{5 F}{9} + \frac{5}{3 \cdot 3} \cdot (3 \cdot - 13)) = \frac{9}{5} \cdot - 15$

Step 2.1.1.3.3

Cancel the common factor.

$\frac{9}{5} (\frac{5 F}{9} + \frac{5}{3 \cdot 3} \cdot (3 \cdot - 13)) = \frac{9}{5} \cdot - 15$

Step 2.1.1.3.4

Rewrite the expression.

$\frac{9}{5} (\frac{5 F}{9} + \frac{5}{3} \cdot - 13) = \frac{9}{5} \cdot - 15$

Step 2.1.1.4

Combine $\frac{5}{3}$ and $- 13$ .

$\frac{9}{5} (\frac{5 F}{9} + \frac{5 \cdot - 13}{3}) = \frac{9}{5} \cdot - 15$

Step 2.1.1.5

Simplify the expression.

Tap for more steps...

Step 2.1.1.5.1

Multiply $5$ by $- 13$ .

$\frac{9}{5} (\frac{5 F}{9} + \frac{- 65}{3}) = \frac{9}{5} \cdot - 15$

Step 2.1.1.5.2

Move the negative in front of the fraction.

$\frac{9}{5} (\frac{5 F}{9} - \frac{65}{3}) = \frac{9}{5} \cdot - 15$

Step 2.1.1.6

Apply the distributive property.

$\frac{9}{5} \cdot \frac{5 F}{9} + \frac{9}{5} (- \frac{65}{3}) = \frac{9}{5} \cdot - 15$

Step 2.1.1.7

Cancel the common factor of $9$ .

Tap for more steps...

Step 2.1.1.7.1

Cancel the common factor.

$\frac{9}{5} \cdot \frac{5 F}{9} + \frac{9}{5} (- \frac{65}{3}) = \frac{9}{5} \cdot - 15$

Step 2.1.1.7.2

Rewrite the expression.

$\frac{1}{5} (5 F) + \frac{9}{5} (- \frac{65}{3}) = \frac{9}{5} \cdot - 15$

Step 2.1.1.8

Cancel the common factor of $5$ .

Tap for more steps...

Step 2.1.1.8.1

Factor $5$ out of $5 F$ .

$\frac{1}{5} (5 (F)) + \frac{9}{5} (- \frac{65}{3}) = \frac{9}{5} \cdot - 15$

Step 2.1.1.8.2

Cancel the common factor.

$\frac{1}{5} (5 F) + \frac{9}{5} (- \frac{65}{3}) = \frac{9}{5} \cdot - 15$

Step 2.1.1.8.3

Rewrite the expression.

$F + \frac{9}{5} (- \frac{65}{3}) = \frac{9}{5} \cdot - 15$

Step 2.1.1.9

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.1.1.9.1

Move the leading negative in $- \frac{65}{3}$ into the numerator.

$F + \frac{9}{5} \cdot \frac{- 65}{3} = \frac{9}{5} \cdot - 15$

Step 2.1.1.9.2

Factor $3$ out of $9$ .

$F + \frac{3 (3)}{5} \cdot \frac{- 65}{3} = \frac{9}{5} \cdot - 15$

Step 2.1.1.9.3

Cancel the common factor.

$F + \frac{3 \cdot 3}{5} \cdot \frac{- 65}{3} = \frac{9}{5} \cdot - 15$

Step 2.1.1.9.4

Rewrite the expression.

$F + \frac{3}{5} \cdot - 65 = \frac{9}{5} \cdot - 15$

Step 2.1.1.10

Cancel the common factor of $5$ .

Tap for more steps...

Step 2.1.1.10.1

Factor $5$ out of $- 65$ .

$F + \frac{3}{5} \cdot (5 (- 13)) = \frac{9}{5} \cdot - 15$

Step 2.1.1.10.2

Cancel the common factor.

$F + \frac{3}{5} \cdot (5 \cdot - 13) = \frac{9}{5} \cdot - 15$

Step 2.1.1.10.3

Rewrite the expression.

$F + 3 \cdot - 13 = \frac{9}{5} \cdot - 15$

Step 2.1.1.11

Multiply $3$ by $- 13$ .

$F - 39 = \frac{9}{5} \cdot - 15$

Step 2.2

Simplify the right side.

Tap for more steps...

Step 2.2.1

Simplify $\frac{9}{5} \cdot - 15$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 2.2.1.1.1

Factor $5$ out of $- 15$ .

$F - 39 = \frac{9}{5} \cdot (5 (- 3))$

Step 2.2.1.1.2

Cancel the common factor.

$F - 39 = \frac{9}{5} \cdot (5 \cdot - 3)$

Step 2.2.1.1.3

Rewrite the expression.

$F - 39 = 9 \cdot - 3$

Step 2.2.1.2

Multiply $9$ by $- 3$ .

$F - 39 = - 27$

Step 3

Move all terms not containing $F$ to the right side of the equation.

Tap for more steps...

Step 3.1

Add $39$ to both sides of the equation.

$F = - 27 + 39$

Step 3.2

Add $- 27$ and $39$ .

$F = 12$