Solve for z 2/3z=4 1/4

$\frac{2}{3} z = 4 \frac{1}{4}$

Simplify the left side.

Combine $\frac{2}{3}$ and $z$ .

$\frac{2 z}{3} = 4 \frac{1}{4}$

Simplify the right side.

Convert $4 \frac{1}{4}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$\frac{2 z}{3} = 4 + \frac{1}{4}$

Add $4$ and $\frac{1}{4}$ .

To write $4$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{2 z}{3} = 4 \cdot \frac{4}{4} + \frac{1}{4}$

Combine $4$ and $\frac{4}{4}$ .

$\frac{2 z}{3} = \frac{4 \cdot 4}{4} + \frac{1}{4}$

Combine the numerators over the common denominator.

$\frac{2 z}{3} = \frac{4 \cdot 4 + 1}{4}$

Simplify the numerator.

Multiply $4$ by $4$ .

$\frac{2 z}{3} = \frac{16 + 1}{4}$

Add $16$ and $1$ .

$\frac{2 z}{3} = \frac{17}{4}$

Multiply both sides of the equation by $\frac{3}{2}$ .

$\frac{3}{2} \cdot \frac{2 z}{3} = \frac{3}{2} \cdot \frac{17}{4}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{3}{2} \cdot \frac{2 z}{3}$ .

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3}{2} \cdot \frac{2 z}{3} = \frac{3}{2} \cdot \frac{17}{4}$

Rewrite the expression.

$\frac{1}{2} (2 z) = \frac{3}{2} \cdot \frac{17}{4}$

Cancel the common factor of $2$ .

Factor $2$ out of $2 z$ .

$\frac{1}{2} (2 (z)) = \frac{3}{2} \cdot \frac{17}{4}$

Cancel the common factor.

$\frac{1}{2} (2 z) = \frac{3}{2} \cdot \frac{17}{4}$

Rewrite the expression.

$z = \frac{3}{2} \cdot \frac{17}{4}$

Simplify the right side.

Multiply $\frac{3}{2} \cdot \frac{17}{4}$ .

Multiply $\frac{3}{2}$ by $\frac{17}{4}$ .

$z = \frac{3 \cdot 17}{2 \cdot 4}$

Multiply $3$ by $17$ .

$z = \frac{51}{2 \cdot 4}$

Multiply $2$ by $4$ .

$z = \frac{51}{8}$

The result can be shown in multiple forms.

Exact Form:

$z = \frac{51}{8}$

Decimal Form:

$z = 6.375$

Mixed Number Form:

$z = 6 \frac{3}{8}$

Solve for z 2/3z=4 1/4

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