Basic Math Examples

$30 = \frac{5}{9} f - \frac{160}{9}$

Step 1

Rewrite the equation as $\frac{5}{9} f - \frac{160}{9} = 30$ .

$\frac{5}{9} f - \frac{160}{9} = 30$

Step 2

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

$\frac{5 f}{9} - \frac{160}{9} = 30$

Step 3

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

Tap for more steps...

Step 3.1

Add $\frac{160}{9}$ to both sides of the equation.

$\frac{5 f}{9} = 30 + \frac{160}{9}$

Step 3.2

To write $30$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{5 f}{9} = 30 \cdot \frac{9}{9} + \frac{160}{9}$

Step 3.3

Combine $30$ and $\frac{9}{9}$ .

$\frac{5 f}{9} = \frac{30 \cdot 9}{9} + \frac{160}{9}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{5 f}{9} = \frac{30 \cdot 9 + 160}{9}$

Step 3.5

Simplify the numerator.

Tap for more steps...

Step 3.5.1

Multiply $30$ by $9$ .

$\frac{5 f}{9} = \frac{270 + 160}{9}$

Step 3.5.2

Add $270$ and $160$ .

$\frac{5 f}{9} = \frac{430}{9}$

Step 4

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$5 f = 430$

Step 5

Divide each term in $5 f = 430$ by $5$ and simplify.

Tap for more steps...

Step 5.1

Divide each term in $5 f = 430$ by $5$ .

$\frac{5 f}{5} = \frac{430}{5}$

Step 5.2

Simplify the left side.

Tap for more steps...

Step 5.2.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 5.2.1.1

Cancel the common factor.

$\frac{5 f}{5} = \frac{430}{5}$

Step 5.2.1.2

Divide $f$ by $1$ .

$f = \frac{430}{5}$

Step 5.3

Simplify the right side.

Tap for more steps...

Step 5.3.1

Divide $430$ by $5$ .

$f = 86$