Basic Math Examples

$z \cdot 2 \frac{1}{7} = 30$

Step 1

Simplify the left side.

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Step 1.1

Simplify $z \cdot 2 \frac{1}{7}$ .

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Step 1.1.1

Convert $2 \frac{1}{7}$ to an improper fraction.

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Step 1.1.1.1

A mixed number is an addition of its whole and fractional parts.

$z \cdot (2 + \frac{1}{7}) = 30$

Step 1.1.1.2

Add $2$ and $\frac{1}{7}$ .

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Step 1.1.1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$z \cdot (2 \cdot \frac{7}{7} + \frac{1}{7}) = 30$

Step 1.1.1.2.2

Combine $2$ and $\frac{7}{7}$ .

$z \cdot (\frac{2 \cdot 7}{7} + \frac{1}{7}) = 30$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$z \cdot \frac{2 \cdot 7 + 1}{7} = 30$

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $2$ by $7$ .

$z \cdot \frac{14 + 1}{7} = 30$

Step 1.1.1.2.4.2

Add $14$ and $1$ .

$z \cdot \frac{15}{7} = 30$

Step 1.1.2

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

$\frac{z \cdot 15}{7} = 30$

Step 1.1.3

Move $15$ to the left of $z$ .

$\frac{15 z}{7} = 30$

Step 2

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

$\frac{7}{15} \cdot \frac{15 z}{7} = \frac{7}{15} \cdot 30$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

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

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Step 3.1.1.1

Cancel the common factor of $7$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{7}{15} \cdot \frac{15 z}{7} = \frac{7}{15} \cdot 30$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{15} (15 z) = \frac{7}{15} \cdot 30$

Step 3.1.1.2

Cancel the common factor of $15$ .

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Step 3.1.1.2.1

Factor $15$ out of $15 z$ .

$\frac{1}{15} (15 (z)) = \frac{7}{15} \cdot 30$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{15} (15 z) = \frac{7}{15} \cdot 30$

Step 3.1.1.2.3

Rewrite the expression.

$z = \frac{7}{15} \cdot 30$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{7}{15} \cdot 30$ .

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Step 3.2.1.1

Cancel the common factor of $15$ .

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Step 3.2.1.1.1

Factor $15$ out of $30$ .

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

Step 3.2.1.1.2

Cancel the common factor.

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

Step 3.2.1.1.3

Rewrite the expression.

$z = 7 \cdot 2$

Step 3.2.1.2

Multiply $7$ by $2$ .

$z = 14$