Basic Math Examples

$\frac{5}{13} h + \frac{1}{7} = \frac{1}{5}$

Step 1

Combine $\frac{5}{13}$ and $h$ .

$\frac{5 h}{13} + \frac{1}{7} = \frac{1}{5}$

Step 2

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

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Step 2.1

Subtract $\frac{1}{7}$ from both sides of the equation.

$\frac{5 h}{13} = \frac{1}{5} - \frac{1}{7}$

Step 2.2

To write $\frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{5 h}{13} = \frac{1}{5} \cdot \frac{7}{7} - \frac{1}{7}$

Step 2.3

To write $- \frac{1}{7}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{5 h}{13} = \frac{1}{5} \cdot \frac{7}{7} - \frac{1}{7} \cdot \frac{5}{5}$

Step 2.4

Write each expression with a common denominator of $35$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.4.1

Multiply $\frac{1}{5}$ by $\frac{7}{7}$ .

$\frac{5 h}{13} = \frac{7}{5 \cdot 7} - \frac{1}{7} \cdot \frac{5}{5}$

Step 2.4.2

Multiply $5$ by $7$ .

$\frac{5 h}{13} = \frac{7}{35} - \frac{1}{7} \cdot \frac{5}{5}$

Step 2.4.3

Multiply $\frac{1}{7}$ by $\frac{5}{5}$ .

$\frac{5 h}{13} = \frac{7}{35} - \frac{5}{7 \cdot 5}$

Step 2.4.4

Multiply $7$ by $5$ .

$\frac{5 h}{13} = \frac{7}{35} - \frac{5}{35}$

Step 2.5

Combine the numerators over the common denominator.

$\frac{5 h}{13} = \frac{7 - 5}{35}$

Step 2.6

Subtract $5$ from $7$ .

$\frac{5 h}{13} = \frac{2}{35}$

Step 3

Multiply both sides of the equation by $\frac{13}{5}$ .

$\frac{13}{5} \cdot \frac{5 h}{13} = \frac{13}{5} \cdot \frac{2}{35}$

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 $\frac{13}{5} \cdot \frac{5 h}{13}$ .

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Step 4.1.1.1

Cancel the common factor of $13$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{13}{5} \cdot \frac{5 h}{13} = \frac{13}{5} \cdot \frac{2}{35}$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{5} (5 h) = \frac{13}{5} \cdot \frac{2}{35}$

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 $5 h$ .

$\frac{1}{5} (5 (h)) = \frac{13}{5} \cdot \frac{2}{35}$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{5} (5 h) = \frac{13}{5} \cdot \frac{2}{35}$

Step 4.1.1.2.3

Rewrite the expression.

$h = \frac{13}{5} \cdot \frac{2}{35}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $\frac{13}{5} \cdot \frac{2}{35}$ .

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Step 4.2.1.1

Multiply $\frac{13}{5}$ by $\frac{2}{35}$ .

$h = \frac{13 \cdot 2}{5 \cdot 35}$

Step 4.2.1.2

Multiply $13$ by $2$ .

$h = \frac{26}{5 \cdot 35}$

Step 4.2.1.3

Multiply $5$ by $35$ .

$h = \frac{26}{175}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$h = \frac{26}{175}$

Decimal Form:

$h = 0.14857142 \dots$