Basic Math Examples

$13 - \frac{5}{3} y = 5$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Combine $y$ and $\frac{5}{3}$ .

$13 - \frac{y \cdot 5}{3} = 5$

Step 1.2

Move $5$ to the left of $y$ .

$13 - \frac{5 y}{3} = 5$

Step 2

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

Tap for more steps...

Step 2.1

Subtract $13$ from both sides of the equation.

$- \frac{5 y}{3} = 5 - 13$

Step 2.2

Subtract $13$ from $5$ .

$- \frac{5 y}{3} = - 8$

Step 3

Multiply both sides of the equation by $- \frac{3}{5}$ .

$- \frac{3}{5} (- \frac{5 y}{3}) = - \frac{3}{5} \cdot - 8$

Step 4

Simplify both sides of the equation.

Tap for more steps...

Step 4.1

Simplify the left side.

Tap for more steps...

Step 4.1.1

Simplify $- \frac{3}{5} (- \frac{5 y}{3})$ .

Tap for more steps...

Step 4.1.1.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 4.1.1.1.1

Move the leading negative in $- \frac{3}{5}$ into the numerator.

$\frac{- 3}{5} (- \frac{5 y}{3}) = - \frac{3}{5} \cdot - 8$

Step 4.1.1.1.2

Move the leading negative in $- \frac{5 y}{3}$ into the numerator.

$\frac{- 3}{5} \cdot \frac{- 5 y}{3} = - \frac{3}{5} \cdot - 8$

Step 4.1.1.1.3

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{5} \cdot \frac{- 5 y}{3} = - \frac{3}{5} \cdot - 8$

Step 4.1.1.1.4

Cancel the common factor.

$\frac{3 \cdot - 1}{5} \cdot \frac{- 5 y}{3} = - \frac{3}{5} \cdot - 8$

Step 4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{5} (- 5 y) = - \frac{3}{5} \cdot - 8$

Step 4.1.1.2

Cancel the common factor of $5$ .

Tap for more steps...

Step 4.1.1.2.1

Factor $5$ out of $- 5 y$ .

$\frac{- 1}{5} (5 (- y)) = - \frac{3}{5} \cdot - 8$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{5} (5 (- y)) = - \frac{3}{5} \cdot - 8$

Step 4.1.1.2.3

Rewrite the expression.

$- - y = - \frac{3}{5} \cdot - 8$

Step 4.1.1.3

Multiply.

Tap for more steps...

Step 4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 y = - \frac{3}{5} \cdot - 8$

Step 4.1.1.3.2

Multiply $y$ by $1$ .

$y = - \frac{3}{5} \cdot - 8$

Step 4.2

Simplify the right side.

Tap for more steps...

Step 4.2.1

Multiply $- \frac{3}{5} \cdot - 8$ .

Tap for more steps...

Step 4.2.1.1

Multiply $- 8$ by $- 1$ .

$y = 8 (\frac{3}{5})$

Step 4.2.1.2

Combine $8$ and $\frac{3}{5}$ .

$y = \frac{8 \cdot 3}{5}$

Step 4.2.1.3

Multiply $8$ by $3$ .

$y = \frac{24}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = \frac{24}{5}$

Decimal Form:

$y = 4.8$

Mixed Number Form:

$y = 4 \frac{4}{5}$