Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

Move $5$ to the left of $h$ .

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

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 $- \frac{11}{5}$ .

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

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 $- \frac{11}{5} (- \frac{5 h}{11})$ .

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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

Move the leading negative in $- \frac{11}{5}$ into the numerator.

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

Step 4.1.1.1.2

Move the leading negative in $- \frac{5 h}{11}$ into the numerator.

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

Step 4.1.1.1.3

Factor $11$ out of $- 11$ .

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

Step 4.1.1.1.4

Cancel the common factor.

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

Step 4.1.1.1.5

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 4.1.1.3

Multiply.

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Step 4.1.1.3.1

Multiply $- 1$ by $- 1$ .

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

Step 4.1.1.3.2

Multiply $h$ by $1$ .

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

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 $- \frac{11}{5}$ into the numerator.

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

Step 4.2.1.1.2

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

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

Step 4.2.1.1.3

Factor $5$ out of $- 5$ .

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

Step 4.2.1.1.4

Cancel the common factor.

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

Step 4.2.1.1.5

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

Multiply $- 11$ by $- 1$ .

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

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:

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