Basic Math Examples

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

Step 1

Simplify the right side.

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Step 1.1

Convert $1 \frac{2}{3}$ to an improper fraction.

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Step 1.1.1

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

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

Step 1.1.2

Add $1$ and $\frac{2}{3}$ .

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Step 1.1.2.1

Write $1$ as a fraction with a common denominator.

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

Step 1.1.2.2

Combine the numerators over the common denominator.

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

Step 1.1.2.3

Add $3$ and $2$ .

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

Step 2

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

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Step 2.1

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

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

Step 2.2

Combine the numerators over the common denominator.

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

Step 2.3

Add $5$ and $1$ .

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

Step 2.4

Divide $6$ by $3$ .

$z = 2$