Basic Math Examples

$\frac{5}{11} h + \frac{7}{9} = \frac{2}{9}$

Step 1

Combine $\frac{5}{11}$ and $h$ .

$\frac{5 h}{11} + \frac{7}{9} = \frac{2}{9}$

Step 2

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

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Step 2.1

Subtract $\frac{7}{9}$ from both sides of the equation.

$\frac{5 h}{11} = \frac{2}{9} - \frac{7}{9}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{5 h}{11} = \frac{2 - 7}{9}$

Step 2.3

Subtract $7$ from $2$ .

$\frac{5 h}{11} = \frac{- 5}{9}$

Step 2.4

Move the negative in front of the fraction.

$\frac{5 h}{11} = - \frac{5}{9}$

Step 3

Multiply both sides of the equation by $\frac{11}{5}$ .

$\frac{11}{5} \cdot \frac{5 h}{11} = \frac{11}{5} (- \frac{5}{9})$

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 $\frac{11}{5} \cdot \frac{5 h}{11}$ .

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Step 4.1.1.1

Cancel the common factor of $11$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{11}{5} \cdot \frac{5 h}{11} = \frac{11}{5} (- \frac{5}{9})$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{5} (5 h) = \frac{11}{5} (- \frac{5}{9})$

Step 4.1.1.2

Cancel the common factor of $5$ .

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Step 4.1.1.2.1

Factor $5$ out of $5 h$ .

$\frac{1}{5} (5 (h)) = \frac{11}{5} (- \frac{5}{9})$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{5} (5 h) = \frac{11}{5} (- \frac{5}{9})$

Step 4.1.1.2.3

Rewrite the expression.

$h = \frac{11}{5} (- \frac{5}{9})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{11}{5} (- \frac{5}{9})$ .

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Step 4.2.1.1

Cancel the common factor of $5$ .

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Step 4.2.1.1.1

Move the leading negative in $- \frac{5}{9}$ into the numerator.

$h = \frac{11}{5} \cdot \frac{- 5}{9}$

Step 4.2.1.1.2

Factor $5$ out of $- 5$ .

$h = \frac{11}{5} \cdot \frac{5 (- 1)}{9}$

Step 4.2.1.1.3

Cancel the common factor.

$h = \frac{11}{5} \cdot \frac{5 \cdot - 1}{9}$

Step 4.2.1.1.4

Rewrite the expression.

$h = 11 (\frac{- 1}{9})$

Step 4.2.1.2

Combine $11$ and $\frac{- 1}{9}$ .

$h = \frac{11 \cdot - 1}{9}$

Step 4.2.1.3

Simplify the expression.

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Step 4.2.1.3.1

Multiply $11$ by $- 1$ .

$h = \frac{- 11}{9}$

Step 4.2.1.3.2

Move the negative in front of the fraction.

$h = - \frac{11}{9}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$h = - \frac{11}{9}$

Decimal Form:

$h = - 1.\overline{2}$

Mixed Number Form:

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