Finite Math Examples

$- (- 12 + 9) | \frac{9}{4} - \frac{17}{8} | + | - \frac{1}{2} |$

Step 1

Simplify each term.

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Step 1.1

Add $- 12$ and $9$ .

$- - 3 | \frac{9}{4} - \frac{17}{8} | + | - \frac{1}{2} |$

Step 1.2

Multiply $- 1$ by $- 3$ .

$3 | \frac{9}{4} - \frac{17}{8} | + | - \frac{1}{2} |$

Step 1.3

To write $\frac{9}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$3 | \frac{9}{4} \cdot \frac{2}{2} - \frac{17}{8} | + | - \frac{1}{2} |$

Step 1.4

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{9}{4}$ by $\frac{2}{2}$ .

$3 | \frac{9 \cdot 2}{4 \cdot 2} - \frac{17}{8} | + | - \frac{1}{2} |$

Step 1.4.2

Multiply $4$ by $2$ .

$3 | \frac{9 \cdot 2}{8} - \frac{17}{8} | + | - \frac{1}{2} |$

Step 1.5

Combine the numerators over the common denominator.

$3 | \frac{9 \cdot 2 - 17}{8} | + | - \frac{1}{2} |$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Multiply $9$ by $2$ .

$3 | \frac{18 - 17}{8} | + | - \frac{1}{2} |$

Step 1.6.2

Subtract $17$ from $18$ .

$3 | \frac{1}{8} | + | - \frac{1}{2} |$

Step 1.7

$\frac{1}{8}$ is approximately $0.125$ which is positive so remove the absolute value

$3 (\frac{1}{8}) + | - \frac{1}{2} |$

Step 1.8

Combine $3$ and $\frac{1}{8}$ .

$\frac{3}{8} + | - \frac{1}{2} |$

Step 1.9

$- \frac{1}{2}$ is approximately $- 0.5$ which is negative so negate $- \frac{1}{2}$ and remove the absolute value

$\frac{3}{8} + \frac{1}{2}$

Step 2

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{3}{8} + \frac{1}{2} \cdot \frac{4}{4}$

Step 3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{1}{2}$ by $\frac{4}{4}$ .

$\frac{3}{8} + \frac{4}{2 \cdot 4}$

Step 3.2

Multiply $2$ by $4$ .

$\frac{3}{8} + \frac{4}{8}$

Step 4

Combine the numerators over the common denominator.

$\frac{3 + 4}{8}$

Step 5

Add $3$ and $4$ .

$\frac{7}{8}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{8}$

Decimal Form:

$0.875$