Basic Math Examples

$2 + \frac{h}{9} + h - \frac{1}{3} = \frac{1}{3}$

Step 1

Simplify $2 + \frac{h}{9} + h - \frac{1}{3}$ .

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Step 1.1

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

$\frac{h}{9} + h + 2 \cdot \frac{3}{3} - \frac{1}{3} = \frac{1}{3}$

Step 1.2

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

$\frac{h}{9} + h + \frac{2 \cdot 3}{3} - \frac{1}{3} = \frac{1}{3}$

Step 1.3

Combine the numerators over the common denominator.

$\frac{h}{9} + h + \frac{2 \cdot 3 - 1}{3} = \frac{1}{3}$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Multiply $2$ by $3$ .

$\frac{h}{9} + h + \frac{6 - 1}{3} = \frac{1}{3}$

Step 1.4.2

Subtract $1$ from $6$ .

$\frac{h}{9} + h + \frac{5}{3} = \frac{1}{3}$

Step 1.5

To write $h$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{h}{9} + h \cdot \frac{9}{9} + \frac{5}{3} = \frac{1}{3}$

Step 1.6

Combine $h$ and $\frac{9}{9}$ .

$\frac{h}{9} + \frac{h \cdot 9}{9} + \frac{5}{3} = \frac{1}{3}$

Step 1.7

Combine the numerators over the common denominator.

$\frac{h + h \cdot 9}{9} + \frac{5}{3} = \frac{1}{3}$

Step 1.8

Add $h$ and $h \cdot 9$ .

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Step 1.8.1

Reorder $h$ and $9$ .

$\frac{h + 9 \cdot h}{9} + \frac{5}{3} = \frac{1}{3}$

Step 1.8.2

Add $h$ and $9 \cdot h$ .

$\frac{10 h}{9} + \frac{5}{3} = \frac{1}{3}$

Step 2

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

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Step 2.1

Subtract $\frac{5}{3}$ from both sides of the equation.

$\frac{10 h}{9} = \frac{1}{3} - \frac{5}{3}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{10 h}{9} = \frac{1 - 5}{3}$

Step 2.3

Subtract $5$ from $1$ .

$\frac{10 h}{9} = \frac{- 4}{3}$

Step 2.4

Move the negative in front of the fraction.

$\frac{10 h}{9} = - \frac{4}{3}$

Step 3

Multiply both sides of the equation by $\frac{9}{10}$ .

$\frac{9}{10} \cdot \frac{10 h}{9} = \frac{9}{10} (- \frac{4}{3})$

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

Simplify $\frac{9}{10} \cdot \frac{10 h}{9}$ .

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Step 4.1.1.1

Cancel the common factor of $9$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{9}{10} \cdot \frac{10 h}{9} = \frac{9}{10} (- \frac{4}{3})$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{10} (10 h) = \frac{9}{10} (- \frac{4}{3})$

Step 4.1.1.2

Cancel the common factor of $10$ .

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Step 4.1.1.2.1

Factor $10$ out of $10 h$ .

$\frac{1}{10} (10 (h)) = \frac{9}{10} (- \frac{4}{3})$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{10} (10 h) = \frac{9}{10} (- \frac{4}{3})$

Step 4.1.1.2.3

Rewrite the expression.

$h = \frac{9}{10} (- \frac{4}{3})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{9}{10} (- \frac{4}{3})$ .

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Step 4.2.1.1

Cancel the common factor of $3$ .

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Step 4.2.1.1.1

Move the leading negative in $- \frac{4}{3}$ into the numerator.

$h = \frac{9}{10} \cdot \frac{- 4}{3}$

Step 4.2.1.1.2

Factor $3$ out of $9$ .

$h = \frac{3 (3)}{10} \cdot \frac{- 4}{3}$

Step 4.2.1.1.3

Cancel the common factor.

$h = \frac{3 \cdot 3}{10} \cdot \frac{- 4}{3}$

Step 4.2.1.1.4

Rewrite the expression.

$h = \frac{3}{10} \cdot - 4$

Step 4.2.1.2

Cancel the common factor of $2$ .

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Step 4.2.1.2.1

Factor $2$ out of $10$ .

$h = \frac{3}{2 (5)} \cdot - 4$

Step 4.2.1.2.2

Factor $2$ out of $- 4$ .

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

Step 4.2.1.2.3

Cancel the common factor.

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

Step 4.2.1.2.4

Rewrite the expression.

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

Step 4.2.1.3

Combine $\frac{3}{5}$ and $- 2$ .

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

Step 4.2.1.4

Simplify the expression.

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Step 4.2.1.4.1

Multiply $3$ by $- 2$ .

$h = \frac{- 6}{5}$

Step 4.2.1.4.2

Move the negative in front of the fraction.

$h = - \frac{6}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$h = - \frac{6}{5}$

Decimal Form:

$h = - 1.2$

Mixed Number Form:

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