Finite Math Examples

$\frac{z}{5} - 7 = 2 \frac{3}{4}$

Step 1

Simplify the right side.

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Step 1.1

Convert $2 \frac{3}{4}$ to an improper fraction.

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Step 1.1.1

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

$\frac{z}{5} - 7 = 2 + \frac{3}{4}$

Step 1.1.2

Add $2$ and $\frac{3}{4}$ .

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Step 1.1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{z}{5} - 7 = 2 \cdot \frac{4}{4} + \frac{3}{4}$

Step 1.1.2.2

Combine $2$ and $\frac{4}{4}$ .

$\frac{z}{5} - 7 = \frac{2 \cdot 4}{4} + \frac{3}{4}$

Step 1.1.2.3

Combine the numerators over the common denominator.

$\frac{z}{5} - 7 = \frac{2 \cdot 4 + 3}{4}$

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $2$ by $4$ .

$\frac{z}{5} - 7 = \frac{8 + 3}{4}$

Step 1.1.2.4.2

Add $8$ and $3$ .

$\frac{z}{5} - 7 = \frac{11}{4}$

Step 2

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

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Step 2.1

Add $7$ to both sides of the equation.

$\frac{z}{5} = \frac{11}{4} + 7$

Step 2.2

To write $7$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{z}{5} = \frac{11}{4} + 7 \cdot \frac{4}{4}$

Step 2.3

Combine $7$ and $\frac{4}{4}$ .

$\frac{z}{5} = \frac{11}{4} + \frac{7 \cdot 4}{4}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{z}{5} = \frac{11 + 7 \cdot 4}{4}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $7$ by $4$ .

$\frac{z}{5} = \frac{11 + 28}{4}$

Step 2.5.2

Add $11$ and $28$ .

$\frac{z}{5} = \frac{39}{4}$

Step 3

Multiply both sides of the equation by $5$ .

$5 \frac{z}{5} = 5 (\frac{39}{4})$

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

Cancel the common factor of $5$ .

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Step 4.1.1.1

Cancel the common factor.

$5 \frac{z}{5} = 5 (\frac{39}{4})$

Step 4.1.1.2

Rewrite the expression.

$z = 5 (\frac{39}{4})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $5 (\frac{39}{4})$ .

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Step 4.2.1.1

Combine $5$ and $\frac{39}{4}$ .

$z = \frac{5 \cdot 39}{4}$

Step 4.2.1.2

Multiply $5$ by $39$ .

$z = \frac{195}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$z = \frac{195}{4}$

Decimal Form:

$z = 48.75$

Mixed Number Form:

$z = 48 \frac{3}{4}$