Finite Math Examples

$1 - \frac{7}{15} \cdot \frac{6}{14} \cdot \frac{5}{13} \cdot \frac{4}{12}$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $7$ .

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Step 1.1.1

Move the leading negative in $- \frac{7}{15}$ into the numerator.

$1 + \frac{- 7}{15} \cdot \frac{6}{14} \cdot \frac{5}{13} \cdot \frac{4}{12}$

Step 1.1.2

Factor $7$ out of $- 7$ .

$1 + \frac{7 (- 1)}{15} \cdot \frac{6}{14} \cdot \frac{5}{13} \cdot \frac{4}{12}$

Step 1.1.3

Factor $7$ out of $14$ .

$1 + \frac{7 \cdot - 1}{15} \cdot \frac{6}{7 \cdot 2} \cdot \frac{5}{13} \cdot \frac{4}{12}$

Step 1.1.4

Cancel the common factor.

$1 + \frac{7 \cdot - 1}{15} \cdot \frac{6}{7 \cdot 2} \cdot \frac{5}{13} \cdot \frac{4}{12}$

Step 1.1.5

Rewrite the expression.

$1 + \frac{- 1}{15} \cdot \frac{6}{2} \cdot \frac{5}{13} \cdot \frac{4}{12}$

Step 1.2

Cancel the common factor of $3$ .

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Step 1.2.1

Factor $3$ out of $15$ .

$1 + \frac{- 1}{3 (5)} \cdot \frac{6}{2} \cdot \frac{5}{13} \cdot \frac{4}{12}$

Step 1.2.2

Factor $3$ out of $6$ .

$1 + \frac{- 1}{3 \cdot 5} \cdot \frac{3 \cdot 2}{2} \cdot \frac{5}{13} \cdot \frac{4}{12}$

Step 1.2.3

Cancel the common factor.

$1 + \frac{- 1}{3 \cdot 5} \cdot \frac{3 \cdot 2}{2} \cdot \frac{5}{13} \cdot \frac{4}{12}$

Step 1.2.4

Rewrite the expression.

$1 + \frac{- 1}{5} \cdot \frac{2}{2} \cdot \frac{5}{13} \cdot \frac{4}{12}$

Step 1.3

Multiply $\frac{- 1}{5}$ by $\frac{2}{2}$ .

$1 + \frac{- 1 \cdot 2}{5 \cdot 2} \cdot \frac{5}{13} \cdot \frac{4}{12}$

Step 1.4

Multiply $- 1$ by $2$ .

$1 + \frac{- 2}{5 \cdot 2} \cdot \frac{5}{13} \cdot \frac{4}{12}$

Step 1.5

Multiply $5$ by $2$ .

$1 + \frac{- 2}{10} \cdot \frac{5}{13} \cdot \frac{4}{12}$

Step 1.6

Cancel the common factor of $5$ .

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Step 1.6.1

Factor $5$ out of $10$ .

$1 + \frac{- 2}{5 (2)} \cdot \frac{5}{13} \cdot \frac{4}{12}$

Step 1.6.2

Cancel the common factor.

$1 + \frac{- 2}{5 \cdot 2} \cdot \frac{5}{13} \cdot \frac{4}{12}$

Step 1.6.3

Rewrite the expression.

$1 + \frac{- 2}{2} \cdot \frac{1}{13} \cdot \frac{4}{12}$

Step 1.7

Multiply $\frac{- 2}{2}$ by $\frac{1}{13}$ .

$1 + \frac{- 2}{2 \cdot 13} \cdot \frac{4}{12}$

Step 1.8

Multiply $2$ by $13$ .

$1 + \frac{- 2}{26} \cdot \frac{4}{12}$

Step 1.9

Cancel the common factor of $2$ .

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Step 1.9.1

Factor $2$ out of $- 2$ .

$1 + \frac{2 (- 1)}{26} \cdot \frac{4}{12}$

Step 1.9.2

Factor $2$ out of $12$ .

$1 + \frac{2 \cdot - 1}{26} \cdot \frac{4}{2 \cdot 6}$

Step 1.9.3

Cancel the common factor.

$1 + \frac{2 \cdot - 1}{26} \cdot \frac{4}{2 \cdot 6}$

Step 1.9.4

Rewrite the expression.

$1 + \frac{- 1}{26} \cdot \frac{4}{6}$

Step 1.10

Cancel the common factor of $2$ .

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Step 1.10.1

Factor $2$ out of $26$ .

$1 + \frac{- 1}{2 (13)} \cdot \frac{4}{6}$

Step 1.10.2

Factor $2$ out of $4$ .

$1 + \frac{- 1}{2 \cdot 13} \cdot \frac{2 \cdot 2}{6}$

Step 1.10.3

Cancel the common factor.

$1 + \frac{- 1}{2 \cdot 13} \cdot \frac{2 \cdot 2}{6}$

Step 1.10.4

Rewrite the expression.

$1 + \frac{- 1}{13} \cdot \frac{2}{6}$

Step 1.11

Multiply $\frac{- 1}{13}$ by $\frac{2}{6}$ .

$1 + \frac{- 1 \cdot 2}{13 \cdot 6}$

Step 1.12

Multiply $- 1$ by $2$ .

$1 + \frac{- 2}{13 \cdot 6}$

Step 1.13

Multiply $13$ by $6$ .

$1 + \frac{- 2}{78}$

Step 1.14

Cancel the common factor of $- 2$ and $78$ .

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Step 1.14.1

Factor $2$ out of $- 2$ .

$1 + \frac{2 (- 1)}{78}$

Step 1.14.2

Cancel the common factors.

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Step 1.14.2.1

Factor $2$ out of $78$ .

$1 + \frac{2 \cdot - 1}{2 \cdot 39}$

Step 1.14.2.2

Cancel the common factor.

$1 + \frac{2 \cdot - 1}{2 \cdot 39}$

Step 1.14.2.3

Rewrite the expression.

$1 + \frac{- 1}{39}$

Step 1.15

Move the negative in front of the fraction.

$1 - \frac{1}{39}$

Step 2

Simplify the expression.

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Step 2.1

Write $1$ as a fraction with a common denominator.

$\frac{39}{39} - \frac{1}{39}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{39 - 1}{39}$

Step 2.3

Subtract $1$ from $39$ .

$\frac{38}{39}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{38}{39}$

Decimal Form:

$0.\overline{974358}$