Finite Math Examples

$\frac{1.5}{1} \cdot (\frac{22}{8} - \frac{9}{2}) + (\frac{3}{7} + \frac{6}{14}) \cdot (- \frac{4}{3})$

Step 1

Simplify each term.

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Step 1.1

Divide $1.5$ by $1$ .

$1.5 \cdot (\frac{22}{8} - \frac{9}{2}) + (\frac{3}{7} + \frac{6}{14}) \cdot (- \frac{4}{3})$

Step 1.2

Cancel the common factor of $22$ and $8$ .

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Step 1.2.1

Factor $2$ out of $22$ .

$1.5 \cdot (\frac{2 (11)}{8} - \frac{9}{2}) + (\frac{3}{7} + \frac{6}{14}) \cdot (- \frac{4}{3})$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $2$ out of $8$ .

$1.5 \cdot (\frac{2 \cdot 11}{2 \cdot 4} - \frac{9}{2}) + (\frac{3}{7} + \frac{6}{14}) \cdot (- \frac{4}{3})$

Step 1.2.2.2

Cancel the common factor.

$1.5 \cdot (\frac{2 \cdot 11}{2 \cdot 4} - \frac{9}{2}) + (\frac{3}{7} + \frac{6}{14}) \cdot (- \frac{4}{3})$

Step 1.2.2.3

Rewrite the expression.

$1.5 \cdot (\frac{11}{4} - \frac{9}{2}) + (\frac{3}{7} + \frac{6}{14}) \cdot (- \frac{4}{3})$

Step 1.3

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

$1.5 \cdot (\frac{11}{4} - \frac{9}{2} \cdot \frac{2}{2}) + (\frac{3}{7} + \frac{6}{14}) \cdot (- \frac{4}{3})$

Step 1.4

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

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

$1.5 \cdot (\frac{11}{4} - \frac{9 \cdot 2}{2 \cdot 2}) + (\frac{3}{7} + \frac{6}{14}) \cdot (- \frac{4}{3})$

Step 1.4.2

Multiply $2$ by $2$ .

$1.5 \cdot (\frac{11}{4} - \frac{9 \cdot 2}{4}) + (\frac{3}{7} + \frac{6}{14}) \cdot (- \frac{4}{3})$

Step 1.5

Combine the numerators over the common denominator.

$1.5 \cdot \frac{11 - 9 \cdot 2}{4} + (\frac{3}{7} + \frac{6}{14}) \cdot (- \frac{4}{3})$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Multiply $- 9$ by $2$ .

$1.5 \cdot \frac{11 - 18}{4} + (\frac{3}{7} + \frac{6}{14}) \cdot (- \frac{4}{3})$

Step 1.6.2

Subtract $18$ from $11$ .

$1.5 \cdot \frac{- 7}{4} + (\frac{3}{7} + \frac{6}{14}) \cdot (- \frac{4}{3})$

Step 1.7

Move the negative in front of the fraction.

$1.5 \cdot (- \frac{7}{4}) + (\frac{3}{7} + \frac{6}{14}) \cdot (- \frac{4}{3})$

Step 1.8

Multiply $1.5 (- \frac{7}{4})$ .

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Step 1.8.1

Multiply $- 1$ by $1.5$ .

$- 1.5 (\frac{7}{4}) + (\frac{3}{7} + \frac{6}{14}) \cdot (- \frac{4}{3})$

Step 1.8.2

Combine $- 1.5$ and $\frac{7}{4}$ .

$\frac{- 1.5 \cdot 7}{4} + (\frac{3}{7} + \frac{6}{14}) \cdot (- \frac{4}{3})$

Step 1.8.3

Multiply $- 1.5$ by $7$ .

$\frac{- 10.5}{4} + (\frac{3}{7} + \frac{6}{14}) \cdot (- \frac{4}{3})$

Step 1.9

Divide $- 10.5$ by $4$ .

$- 2.625 + (\frac{3}{7} + \frac{6}{14}) \cdot (- \frac{4}{3})$

Step 1.10

Cancel the common factor of $6$ and $14$ .

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Step 1.10.1

Factor $2$ out of $6$ .

$- 2.625 + (\frac{3}{7} + \frac{2 (3)}{14}) \cdot (- \frac{4}{3})$

Step 1.10.2

Cancel the common factors.

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Step 1.10.2.1

Factor $2$ out of $14$ .

$- 2.625 + (\frac{3}{7} + \frac{2 \cdot 3}{2 \cdot 7}) \cdot (- \frac{4}{3})$

Step 1.10.2.2

Cancel the common factor.

$- 2.625 + (\frac{3}{7} + \frac{2 \cdot 3}{2 \cdot 7}) \cdot (- \frac{4}{3})$

Step 1.10.2.3

Rewrite the expression.

$- 2.625 + (\frac{3}{7} + \frac{3}{7}) \cdot (- \frac{4}{3})$

Step 1.11

Combine the numerators over the common denominator.

$- 2.625 + \frac{3 + 3}{7} \cdot (- \frac{4}{3})$

Step 1.12

Add $3$ and $3$ .

$- 2.625 + \frac{6}{7} \cdot (- \frac{4}{3})$

Step 1.13

Cancel the common factor of $3$ .

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Step 1.13.1

Move the leading negative in $- \frac{4}{3}$ into the numerator.

$- 2.625 + \frac{6}{7} \cdot \frac{- 4}{3}$

Step 1.13.2

Factor $3$ out of $6$ .

$- 2.625 + \frac{3 (2)}{7} \cdot \frac{- 4}{3}$

Step 1.13.3

Cancel the common factor.

$- 2.625 + \frac{3 \cdot 2}{7} \cdot \frac{- 4}{3}$

Step 1.13.4

Rewrite the expression.

$- 2.625 + \frac{2}{7} \cdot - 4$

Step 1.14

Combine $\frac{2}{7}$ and $- 4$ .

$- 2.625 + \frac{2 \cdot - 4}{7}$

Step 1.15

Multiply $2$ by $- 4$ .

$- 2.625 + \frac{- 8}{7}$

Step 1.16

Move the negative in front of the fraction.

$- 2.625 - \frac{8}{7}$

Step 2

To write $- 2.625$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$- 2.625 \cdot \frac{7}{7} - \frac{8}{7}$

Step 3

Combine fractions.

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Step 3.1

Combine $- 2.625$ and $\frac{7}{7}$ .

$\frac{- 2.625 \cdot 7}{7} - \frac{8}{7}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{- 2.625 \cdot 7 - 8}{7}$

Step 4

Simplify the numerator.

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Step 4.1

Multiply $- 2.625$ by $7$ .

$\frac{- 18.375 - 8}{7}$

Step 4.2

Subtract $8$ from $- 18.375$ .

$\frac{- 26.375}{7}$

Step 5

Divide $- 26.375$ by $7$ .

$- 3.76785714$