Basic Math Examples

$\frac{7}{15} z + \frac{7}{10} = \frac{9}{10}$

Step 1

Combine $\frac{7}{15}$ and $z$ .

$\frac{7 z}{15} + \frac{7}{10} = \frac{9}{10}$

Step 2

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

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Step 2.1

Subtract $\frac{7}{10}$ from both sides of the equation.

$\frac{7 z}{15} = \frac{9}{10} - \frac{7}{10}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{7 z}{15} = \frac{9 - 7}{10}$

Step 2.3

Subtract $7$ from $9$ .

$\frac{7 z}{15} = \frac{2}{10}$

Step 2.4

Cancel the common factor of $2$ and $10$ .

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Step 2.4.1

Factor $2$ out of $2$ .

$\frac{7 z}{15} = \frac{2 (1)}{10}$

Step 2.4.2

Cancel the common factors.

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Step 2.4.2.1

Factor $2$ out of $10$ .

$\frac{7 z}{15} = \frac{2 \cdot 1}{2 \cdot 5}$

Step 2.4.2.2

Cancel the common factor.

$\frac{7 z}{15} = \frac{2 \cdot 1}{2 \cdot 5}$

Step 2.4.2.3

Rewrite the expression.

$\frac{7 z}{15} = \frac{1}{5}$

Step 3

Multiply both sides of the equation by $\frac{15}{7}$ .

$\frac{15}{7} \cdot \frac{7 z}{15} = \frac{15}{7} \cdot \frac{1}{5}$

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 $\frac{15}{7} \cdot \frac{7 z}{15}$ .

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Step 4.1.1.1

Cancel the common factor of $15$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{15}{7} \cdot \frac{7 z}{15} = \frac{15}{7} \cdot \frac{1}{5}$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{7} (7 z) = \frac{15}{7} \cdot \frac{1}{5}$

Step 4.1.1.2

Cancel the common factor of $7$ .

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Step 4.1.1.2.1

Factor $7$ out of $7 z$ .

$\frac{1}{7} (7 (z)) = \frac{15}{7} \cdot \frac{1}{5}$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{7} (7 z) = \frac{15}{7} \cdot \frac{1}{5}$

Step 4.1.1.2.3

Rewrite the expression.

$z = \frac{15}{7} \cdot \frac{1}{5}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Cancel the common factor of $5$ .

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Step 4.2.1.1

Factor $5$ out of $15$ .

$z = \frac{5 (3)}{7} \cdot \frac{1}{5}$

Step 4.2.1.2

Cancel the common factor.

$z = \frac{5 \cdot 3}{7} \cdot \frac{1}{5}$

Step 4.2.1.3

Rewrite the expression.

$z = \frac{3}{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$z = \frac{3}{7}$

Decimal Form:

$z = 0.\overline{428571}$