Algebra Examples

$4 h = \frac{5}{15} - \frac{3}{15}$ $4 h = \frac{2}{15}$

Step 1

Simplify.

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Step 1.1

Cancel the common factor of $3$ and $15$ .

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Step 1.1.1

Factor $3$ out of $3$ .

$4 h = \frac{5}{15} - \frac{3 (1)}{15}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $3$ out of $15$ .

$4 h = \frac{5}{15} - \frac{3 \cdot 1}{3 \cdot 5}$

Step 1.1.2.2

Cancel the common factor.

$4 h = \frac{5}{15} - \frac{3 \cdot 1}{3 \cdot 5}$

Step 1.1.2.3

Rewrite the expression.

$4 h = \frac{5}{15} - \frac{1}{5}$

Step 1.2

Reduce the expression $\frac{5}{15}$ by cancelling the common factors.

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Step 1.2.1

Factor $5$ out of $5$ .

$4 h = \frac{5 (1)}{15} - \frac{1}{5}$

Step 1.2.2

Factor $5$ out of $15$ .

$4 h = \frac{5 \cdot 1}{5 \cdot 3} - \frac{1}{5}$

Step 1.2.3

Cancel the common factor.

$4 h = \frac{5 \cdot 1}{5 \cdot 3} - \frac{1}{5}$

Step 1.2.4

Rewrite the expression.

$4 h = \frac{1}{3} - \frac{1}{5}$

Step 1.3

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$4 h = \frac{1}{3} \cdot \frac{5}{5} - \frac{1}{5}$

Step 1.4

To write $- \frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$4 h = \frac{1}{3} \cdot \frac{5}{5} - \frac{1}{5} \cdot \frac{3}{3}$

Step 1.5

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

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Step 1.5.1

Multiply $\frac{1}{3}$ by $\frac{5}{5}$ .

$4 h = \frac{5}{3 \cdot 5} - \frac{1}{5} \cdot \frac{3}{3}$

Step 1.5.2

Multiply $3$ by $5$ .

$4 h = \frac{5}{15} - \frac{1}{5} \cdot \frac{3}{3}$

Step 1.5.3

Multiply $\frac{1}{5}$ by $\frac{3}{3}$ .

$4 h = \frac{5}{15} - \frac{3}{5 \cdot 3}$

Step 1.5.4

Multiply $5$ by $3$ .

$4 h = \frac{5}{15} - \frac{3}{15}$

Step 1.6

Combine the numerators over the common denominator.

$4 h = \frac{5 - 3}{15}$

Step 1.7

Subtract $3$ from $5$ .

$4 h = \frac{2}{15}$

Step 2

Divide each term in $4 h = \frac{2}{15}$ by $4$ and simplify.

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Step 2.1

Divide each term in $4 h = \frac{2}{15}$ by $4$ .

$\frac{4 h}{4} = \frac{\frac{2}{15}}{4}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $4$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{4 h}{4} = \frac{\frac{2}{15}}{4}$

Step 2.2.1.2

Divide $h$ by $1$ .

$h = \frac{\frac{2}{15}}{4}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply the numerator by the reciprocal of the denominator.

$h = \frac{2}{15} \cdot \frac{1}{4}$

Step 2.3.2

Cancel the common factor of $2$ .

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Step 2.3.2.1

Factor $2$ out of $4$ .

$h = \frac{2}{15} \cdot \frac{1}{2 (2)}$

Step 2.3.2.2

Cancel the common factor.

$h = \frac{2}{15} \cdot \frac{1}{2 \cdot 2}$

Step 2.3.2.3

Rewrite the expression.

$h = \frac{1}{15} \cdot \frac{1}{2}$

Step 2.3.3

Multiply $\frac{1}{15}$ by $\frac{1}{2}$ .

$h = \frac{1}{15 \cdot 2}$

Step 2.3.4

Multiply $15$ by $2$ .

$h = \frac{1}{30}$

Step 3

Replace all occurrences of $h$ with $\frac{1}{30}$ in each equation.

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Step 3.1

Replace all occurrences of $h$ in $4 h = \frac{2}{15}$ with $\frac{1}{30}$ .

$4 (\frac{1}{30}) = \frac{2}{15}$

$h = \frac{1}{30}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify $4 (\frac{1}{30})$ .

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Step 3.2.1.1

Cancel the common factor of $2$ .

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Step 3.2.1.1.1

Factor $2$ out of $4$ .

$2 (2) (\frac{1}{30}) = \frac{2}{15}$

$h = \frac{1}{30}$

Step 3.2.1.1.2

Factor $2$ out of $30$ .

$2 \cdot (2 (\frac{1}{2 \cdot 15})) = \frac{2}{15}$

$h = \frac{1}{30}$

Step 3.2.1.1.3

Cancel the common factor.

$2 \cdot (2 (\frac{1}{2 \cdot 15})) = \frac{2}{15}$

$h = \frac{1}{30}$

Step 3.2.1.1.4

Rewrite the expression.

$2 (\frac{1}{15}) = \frac{2}{15}$

$h = \frac{1}{30}$

$2 (\frac{1}{15}) = \frac{2}{15}$

$h = \frac{1}{30}$

Step 3.2.1.2

Combine $2$ and $\frac{1}{15}$ .

$\frac{2}{15} = \frac{2}{15}$

$h = \frac{1}{30}$

$\frac{2}{15} = \frac{2}{15}$

$h = \frac{1}{30}$

$\frac{2}{15} = \frac{2}{15}$

$h = \frac{1}{30}$

$\frac{2}{15} = \frac{2}{15}$

$h = \frac{1}{30}$

Step 4

Remove any equations from the system that are always true.

$h = \frac{1}{30}$