Finite Math Examples

$- 1 (\frac{3}{13}) + 5 (\frac{7}{26}) + 7 (\frac{1}{13}) + 8 (\frac{5}{13}) + 12 (\frac{1}{26})$

Step 1

Simplify each term.

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Step 1.1

Rewrite $- 1 (\frac{3}{13})$ as $- (\frac{3}{13})$ .

$- (\frac{3}{13}) + 5 (\frac{7}{26}) + 7 (\frac{1}{13}) + 8 (\frac{5}{13}) + 12 (\frac{1}{26})$

Step 1.2

Multiply $5 (\frac{7}{26})$ .

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Step 1.2.1

Combine $5$ and $\frac{7}{26}$ .

$- \frac{3}{13} + \frac{5 \cdot 7}{26} + 7 (\frac{1}{13}) + 8 (\frac{5}{13}) + 12 (\frac{1}{26})$

Step 1.2.2

Multiply $5$ by $7$ .

$- \frac{3}{13} + \frac{35}{26} + 7 (\frac{1}{13}) + 8 (\frac{5}{13}) + 12 (\frac{1}{26})$

Step 1.3

Combine $7$ and $\frac{1}{13}$ .

$- \frac{3}{13} + \frac{35}{26} + \frac{7}{13} + 8 (\frac{5}{13}) + 12 (\frac{1}{26})$

Step 1.4

Multiply $8 (\frac{5}{13})$ .

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Step 1.4.1

Combine $8$ and $\frac{5}{13}$ .

$- \frac{3}{13} + \frac{35}{26} + \frac{7}{13} + \frac{8 \cdot 5}{13} + 12 (\frac{1}{26})$

Step 1.4.2

Multiply $8$ by $5$ .

$- \frac{3}{13} + \frac{35}{26} + \frac{7}{13} + \frac{40}{13} + 12 (\frac{1}{26})$

Step 1.5

Cancel the common factor of $2$ .

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Step 1.5.1

Factor $2$ out of $12$ .

$- \frac{3}{13} + \frac{35}{26} + \frac{7}{13} + \frac{40}{13} + 2 (6) \frac{1}{26}$

Step 1.5.2

Factor $2$ out of $26$ .

$- \frac{3}{13} + \frac{35}{26} + \frac{7}{13} + \frac{40}{13} + 2 \cdot 6 \frac{1}{2 \cdot 13}$

Step 1.5.3

Cancel the common factor.

$- \frac{3}{13} + \frac{35}{26} + \frac{7}{13} + \frac{40}{13} + 2 \cdot 6 \frac{1}{2 \cdot 13}$

Step 1.5.4

Rewrite the expression.

$- \frac{3}{13} + \frac{35}{26} + \frac{7}{13} + \frac{40}{13} + 6 (\frac{1}{13})$

Step 1.6

Combine $6$ and $\frac{1}{13}$ .

$- \frac{3}{13} + \frac{35}{26} + \frac{7}{13} + \frac{40}{13} + \frac{6}{13}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{- 3 + 7 + 40 + 6}{13} + \frac{35}{26}$

Step 2.2

Simplify by adding numbers.

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Step 2.2.1

Add $- 3$ and $7$ .

$\frac{4 + 40 + 6}{13} + \frac{35}{26}$

Step 2.2.2

Add $4$ and $40$ .

$\frac{44 + 6}{13} + \frac{35}{26}$

Step 2.2.3

Add $44$ and $6$ .

$\frac{50}{13} + \frac{35}{26}$

Step 3

To write $\frac{50}{13}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{50}{13} \cdot \frac{2}{2} + \frac{35}{26}$

Step 4

Write each expression with a common denominator of $26$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{50}{13}$ by $\frac{2}{2}$ .

$\frac{50 \cdot 2}{13 \cdot 2} + \frac{35}{26}$

Step 4.2

Multiply $13$ by $2$ .

$\frac{50 \cdot 2}{26} + \frac{35}{26}$

Step 5

Combine the numerators over the common denominator.

$\frac{50 \cdot 2 + 35}{26}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $50$ by $2$ .

$\frac{100 + 35}{26}$

Step 6.2

Add $100$ and $35$ .

$\frac{135}{26}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{135}{26}$

Decimal Form:

$5.19230769 \dots$

Mixed Number Form:

$5 \frac{5}{26}$