Algebra Examples

$z = \frac{5}{8} a b$

Step 1

Rewrite the equation as $\frac{5}{8} \cdot (a b) = z$ .

$\frac{5}{8} \cdot (a b) = z$

Step 2

Multiply both sides of the equation by $\frac{8}{5}$ .

$\frac{8}{5} (\frac{5}{8} \cdot (a b)) = \frac{8}{5} z$

Step 3

Simplify both sides of the equation.

Tap for more steps...

Step 3.1

Simplify the left side.

Tap for more steps...

Step 3.1.1

Simplify $\frac{8}{5} (\frac{5}{8} \cdot (a b))$ .

Tap for more steps...

Step 3.1.1.1

Multiply $\frac{5}{8} (a b)$ .

Tap for more steps...

Step 3.1.1.1.1

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

$\frac{8}{5} (\frac{a \cdot 5}{8} b) = \frac{8}{5} z$

Step 3.1.1.1.2

Combine $\frac{a \cdot 5}{8}$ and $b$ .

$\frac{8}{5} \cdot \frac{a \cdot 5 b}{8} = \frac{8}{5} z$

Step 3.1.1.2

Cancel the common factor of $8$ .

Tap for more steps...

Step 3.1.1.2.1

Cancel the common factor.

$\frac{8}{5} \cdot \frac{a \cdot 5 b}{8} = \frac{8}{5} z$

Step 3.1.1.2.2

Rewrite the expression.

$\frac{1}{5} (a \cdot 5 b) = \frac{8}{5} z$

Step 3.1.1.3

Cancel the common factor of $5$ .

Tap for more steps...

Step 3.1.1.3.1

Factor $5$ out of $a \cdot 5 b$ .

$\frac{1}{5} (5 (a b)) = \frac{8}{5} z$

Step 3.1.1.3.2

Cancel the common factor.

$\frac{1}{5} (5 (a b)) = \frac{8}{5} z$

Step 3.1.1.3.3

Rewrite the expression.

$a b = \frac{8}{5} z$

Step 3.2

Simplify the right side.

Tap for more steps...

Step 3.2.1

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

$a b = \frac{8 z}{5}$

Step 4

Divide each term in $a b = \frac{8 z}{5}$ by $b$ and simplify.

Tap for more steps...

Step 4.1

Divide each term in $a b = \frac{8 z}{5}$ by $b$ .

$\frac{a b}{b} = \frac{\frac{8 z}{5}}{b}$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Cancel the common factor of $b$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor.

$\frac{a b}{b} = \frac{\frac{8 z}{5}}{b}$

Step 4.2.1.2

Divide $a$ by $1$ .

$a = \frac{\frac{8 z}{5}}{b}$

Step 4.3

Simplify the right side.

Tap for more steps...

Step 4.3.1

Multiply the numerator by the reciprocal of the denominator.

$a = \frac{8 z}{5} \cdot \frac{1}{b}$

Step 4.3.2

Multiply $\frac{8 z}{5}$ by $\frac{1}{b}$ .

$a = \frac{8 z}{5 b}$