Solve for z (5z)/8-1/3=2/5

$\frac{5 z}{8} - \frac{1}{3} = \frac{2}{5}$

Step 1

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

Add $\frac{1}{3}$ to both sides of the equation.

$\frac{5 z}{8} = \frac{2}{5} + \frac{1}{3}$

To write $\frac{2}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5 z}{8} = \frac{2}{5} \cdot \frac{3}{3} + \frac{1}{3}$

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{5 z}{8} = \frac{2}{5} \cdot \frac{3}{3} + \frac{1}{3} \cdot \frac{5}{5}$

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2}{5}$ by $\frac{3}{3}$ .

$\frac{5 z}{8} = \frac{2 \cdot 3}{5 \cdot 3} + \frac{1}{3} \cdot \frac{5}{5}$

Multiply $5$ by $3$ .

$\frac{5 z}{8} = \frac{2 \cdot 3}{15} + \frac{1}{3} \cdot \frac{5}{5}$

Multiply $\frac{1}{3}$ by $\frac{5}{5}$ .

$\frac{5 z}{8} = \frac{2 \cdot 3}{15} + \frac{5}{3 \cdot 5}$

Multiply $3$ by $5$ .

$\frac{5 z}{8} = \frac{2 \cdot 3}{15} + \frac{5}{15}$

Combine the numerators over the common denominator.

$\frac{5 z}{8} = \frac{2 \cdot 3 + 5}{15}$

Simplify the numerator.

Multiply $2$ by $3$ .

$\frac{5 z}{8} = \frac{6 + 5}{15}$

Add $6$ and $5$ .

$\frac{5 z}{8} = \frac{11}{15}$

Step 2

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

$\frac{8}{5} \cdot \frac{5 z}{8} = \frac{8}{5} \cdot \frac{11}{15}$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{8}{5} \cdot \frac{5 z}{8}$ .

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8}{5} \cdot \frac{5 z}{8} = \frac{8}{5} \cdot \frac{11}{15}$

Rewrite the expression.

$\frac{1}{5} (5 z) = \frac{8}{5} \cdot \frac{11}{15}$

Cancel the common factor of $5$ .

Factor $5$ out of $5 z$ .

$\frac{1}{5} (5 (z)) = \frac{8}{5} \cdot \frac{11}{15}$

Cancel the common factor.

$\frac{1}{5} (5 z) = \frac{8}{5} \cdot \frac{11}{15}$

Rewrite the expression.

$z = \frac{8}{5} \cdot \frac{11}{15}$

Simplify the right side.

Multiply $\frac{8}{5} \cdot \frac{11}{15}$ .

Multiply $\frac{8}{5}$ by $\frac{11}{15}$ .

$z = \frac{8 \cdot 11}{5 \cdot 15}$

Multiply $8$ by $11$ .

$z = \frac{88}{5 \cdot 15}$

Multiply $5$ by $15$ .

$z = \frac{88}{75}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$z = \frac{88}{75}$

Decimal Form:

$z = 1.17\overline{3}$

Mixed Number Form:

$z = 1 \frac{13}{75}$

Solve for z (5z)/8-1/3=2/5

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