Basic Math Examples

$\frac{4}{5} h - \frac{2}{3} \cdot (b - \frac{3}{5}) = 180$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{4}{5}$ and $h$ .

$\frac{4 h}{5} - \frac{2}{3} \cdot (b - \frac{3}{5}) = 180$

Step 1.2

Apply the distributive property.

$\frac{4 h}{5} - \frac{2}{3} b - \frac{2}{3} (- \frac{3}{5}) = 180$

Step 1.3

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

$\frac{4 h}{5} - \frac{b \cdot 2}{3} - \frac{2}{3} (- \frac{3}{5}) = 180$

Step 1.4

Cancel the common factor of $3$ .

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Step 1.4.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$\frac{4 h}{5} - \frac{b \cdot 2}{3} + \frac{- 2}{3} (- \frac{3}{5}) = 180$

Step 1.4.2

Move the leading negative in $- \frac{3}{5}$ into the numerator.

$\frac{4 h}{5} - \frac{b \cdot 2}{3} + \frac{- 2}{3} \cdot \frac{- 3}{5} = 180$

Step 1.4.3

Factor $3$ out of $- 3$ .

$\frac{4 h}{5} - \frac{b \cdot 2}{3} + \frac{- 2}{3} \cdot \frac{3 (- 1)}{5} = 180$

Step 1.4.4

Cancel the common factor.

$\frac{4 h}{5} - \frac{b \cdot 2}{3} + \frac{- 2}{3} \cdot \frac{3 \cdot - 1}{5} = 180$

Step 1.4.5

Rewrite the expression.

$\frac{4 h}{5} - \frac{b \cdot 2}{3} - 2 (\frac{- 1}{5}) = 180$

Step 1.5

Combine $- 2$ and $\frac{- 1}{5}$ .

$\frac{4 h}{5} - \frac{b \cdot 2}{3} + \frac{- 2 \cdot - 1}{5} = 180$

Step 1.6

Multiply $- 2$ by $- 1$ .

$\frac{4 h}{5} - \frac{b \cdot 2}{3} + \frac{2}{5} = 180$

Step 1.7

Move $2$ to the left of $b$ .

$\frac{4 h}{5} - \frac{2 b}{3} + \frac{2}{5} = 180$

Step 2

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

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Step 2.1

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

$\frac{4 h}{5} + \frac{2}{5} = 180 + \frac{2 b}{3}$

Step 2.2

Subtract $\frac{2}{5}$ from both sides of the equation.

$\frac{4 h}{5} = 180 + \frac{2 b}{3} - \frac{2}{5}$

Step 2.3

To write $180$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{4 h}{5} = \frac{2 b}{3} + 180 \cdot \frac{5}{5} - \frac{2}{5}$

Step 2.4

Combine $180$ and $\frac{5}{5}$ .

$\frac{4 h}{5} = \frac{2 b}{3} + \frac{180 \cdot 5}{5} - \frac{2}{5}$

Step 2.5

Combine the numerators over the common denominator.

$\frac{4 h}{5} = \frac{2 b}{3} + \frac{180 \cdot 5 - 2}{5}$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $180$ by $5$ .

$\frac{4 h}{5} = \frac{2 b}{3} + \frac{900 - 2}{5}$

Step 2.6.2

Subtract $2$ from $900$ .

$\frac{4 h}{5} = \frac{2 b}{3} + \frac{898}{5}$

Step 3

Multiply both sides of the equation by $\frac{5}{4}$ .

$\frac{5}{4} \cdot \frac{4 h}{5} = \frac{5}{4} (\frac{2 b}{3} + \frac{898}{5})$

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 $\frac{5}{4} \cdot \frac{4 h}{5}$ .

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Step 4.1.1.1

Cancel the common factor of $5$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{5}{4} \cdot \frac{4 h}{5} = \frac{5}{4} (\frac{2 b}{3} + \frac{898}{5})$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{4} (4 h) = \frac{5}{4} (\frac{2 b}{3} + \frac{898}{5})$

Step 4.1.1.2

Cancel the common factor of $4$ .

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Step 4.1.1.2.1

Factor $4$ out of $4 h$ .

$\frac{1}{4} (4 (h)) = \frac{5}{4} (\frac{2 b}{3} + \frac{898}{5})$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{4} (4 h) = \frac{5}{4} (\frac{2 b}{3} + \frac{898}{5})$

Step 4.1.1.2.3

Rewrite the expression.

$h = \frac{5}{4} (\frac{2 b}{3} + \frac{898}{5})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{5}{4} (\frac{2 b}{3} + \frac{898}{5})$ .

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Step 4.2.1.1

Apply the distributive property.

$h = \frac{5}{4} \cdot \frac{2 b}{3} + \frac{5}{4} \cdot \frac{898}{5}$

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 $4$ .

$h = \frac{5}{2 (2)} \cdot \frac{2 b}{3} + \frac{5}{4} \cdot \frac{898}{5}$

Step 4.2.1.2.2

Factor $2$ out of $2 b$ .

$h = \frac{5}{2 (2)} \cdot \frac{2 (b)}{3} + \frac{5}{4} \cdot \frac{898}{5}$

Step 4.2.1.2.3

Cancel the common factor.

$h = \frac{5}{2 \cdot 2} \cdot \frac{2 b}{3} + \frac{5}{4} \cdot \frac{898}{5}$

Step 4.2.1.2.4

Rewrite the expression.

$h = \frac{5}{2} \cdot \frac{b}{3} + \frac{5}{4} \cdot \frac{898}{5}$

Step 4.2.1.3

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

$h = \frac{5 b}{2 \cdot 3} + \frac{5}{4} \cdot \frac{898}{5}$

Step 4.2.1.4

Multiply $2$ by $3$ .

$h = \frac{5 b}{6} + \frac{5}{4} \cdot \frac{898}{5}$

Step 4.2.1.5

Cancel the common factor of $5$ .

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Step 4.2.1.5.1

Cancel the common factor.

$h = \frac{5 b}{6} + \frac{5}{4} \cdot \frac{898}{5}$

Step 4.2.1.5.2

Rewrite the expression.

$h = \frac{5 b}{6} + \frac{1}{4} \cdot 898$

Step 4.2.1.6

Cancel the common factor of $2$ .

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Step 4.2.1.6.1

Factor $2$ out of $4$ .

$h = \frac{5 b}{6} + \frac{1}{2 (2)} \cdot 898$

Step 4.2.1.6.2

Factor $2$ out of $898$ .

$h = \frac{5 b}{6} + \frac{1}{2 \cdot 2} \cdot (2 \cdot 449)$

Step 4.2.1.6.3

Cancel the common factor.

$h = \frac{5 b}{6} + \frac{1}{2 \cdot 2} \cdot (2 \cdot 449)$

Step 4.2.1.6.4

Rewrite the expression.

$h = \frac{5 b}{6} + \frac{1}{2} \cdot 449$

Step 4.2.1.7

Combine $\frac{1}{2}$ and $449$ .

$h = \frac{5 b}{6} + \frac{449}{2}$