Basic Math Examples

$\frac{1}{5} h - \frac{2}{3} = - \frac{2}{5}$

Step 1

Combine $\frac{1}{5}$ and $h$ .

$\frac{h}{5} - \frac{2}{3} = - \frac{2}{5}$

Step 2

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

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Step 2.1

Add $\frac{2}{3}$ to both sides of the equation.

$\frac{h}{5} = - \frac{2}{5} + \frac{2}{3}$

Step 2.2

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

$\frac{h}{5} = - \frac{2}{5} \cdot \frac{3}{3} + \frac{2}{3}$

Step 2.3

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

$\frac{h}{5} = - \frac{2}{5} \cdot \frac{3}{3} + \frac{2}{3} \cdot \frac{5}{5}$

Step 2.4

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

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Step 2.4.1

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

$\frac{h}{5} = - \frac{2 \cdot 3}{5 \cdot 3} + \frac{2}{3} \cdot \frac{5}{5}$

Step 2.4.2

Multiply $5$ by $3$ .

$\frac{h}{5} = - \frac{2 \cdot 3}{15} + \frac{2}{3} \cdot \frac{5}{5}$

Step 2.4.3

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

$\frac{h}{5} = - \frac{2 \cdot 3}{15} + \frac{2 \cdot 5}{3 \cdot 5}$

Step 2.4.4

Multiply $3$ by $5$ .

$\frac{h}{5} = - \frac{2 \cdot 3}{15} + \frac{2 \cdot 5}{15}$

Step 2.5

Combine the numerators over the common denominator.

$\frac{h}{5} = \frac{- 2 \cdot 3 + 2 \cdot 5}{15}$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $- 2$ by $3$ .

$\frac{h}{5} = \frac{- 6 + 2 \cdot 5}{15}$

Step 2.6.2

Multiply $2$ by $5$ .

$\frac{h}{5} = \frac{- 6 + 10}{15}$

Step 2.6.3

Add $- 6$ and $10$ .

$\frac{h}{5} = \frac{4}{15}$

Step 3

Multiply both sides of the equation by $5$ .

$5 \frac{h}{5} = 5 (\frac{4}{15})$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $5$ .

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Step 4.1.1.1

Cancel the common factor.

$5 \frac{h}{5} = 5 (\frac{4}{15})$

Step 4.1.1.2

Rewrite the expression.

$h = 5 (\frac{4}{15})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Cancel the common factor of $5$ .

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Step 4.2.1.1

Factor $5$ out of $15$ .

$h = 5 \frac{4}{5 (3)}$

Step 4.2.1.2

Cancel the common factor.

$h = 5 \frac{4}{5 \cdot 3}$

Step 4.2.1.3

Rewrite the expression.

$h = \frac{4}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$h = \frac{4}{3}$

Decimal Form:

$h = 1.\overline{3}$

Mixed Number Form:

$h = 1 \frac{1}{3}$