Finite Math Examples

$1 - \frac{9}{21} \cdot \frac{8}{20} \cdot \frac{7}{19}$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $9$ and $21$ .

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Step 1.1.1

Factor $3$ out of $9$ .

$1 - \frac{3 (3)}{21} \cdot \frac{8}{20} \cdot \frac{7}{19}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $3$ out of $21$ .

$1 - \frac{3 \cdot 3}{3 \cdot 7} \cdot \frac{8}{20} \cdot \frac{7}{19}$

Step 1.1.2.2

Cancel the common factor.

$1 - \frac{3 \cdot 3}{3 \cdot 7} \cdot \frac{8}{20} \cdot \frac{7}{19}$

Step 1.1.2.3

Rewrite the expression.

$1 - \frac{3}{7} \cdot \frac{8}{20} \cdot \frac{7}{19}$

Step 1.2

Cancel the common factor of $8$ and $20$ .

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Step 1.2.1

Factor $4$ out of $8$ .

$1 - \frac{3}{7} \cdot \frac{4 (2)}{20} \cdot \frac{7}{19}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $4$ out of $20$ .

$1 - \frac{3}{7} \cdot \frac{4 \cdot 2}{4 \cdot 5} \cdot \frac{7}{19}$

Step 1.2.2.2

Cancel the common factor.

$1 - \frac{3}{7} \cdot \frac{4 \cdot 2}{4 \cdot 5} \cdot \frac{7}{19}$

Step 1.2.2.3

Rewrite the expression.

$1 - \frac{3}{7} \cdot \frac{2}{5} \cdot \frac{7}{19}$

Step 1.3

Multiply $- \frac{3}{7} \cdot \frac{2}{5}$ .

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Step 1.3.1

Multiply $\frac{2}{5}$ by $\frac{3}{7}$ .

$1 - \frac{2 \cdot 3}{5 \cdot 7} \cdot \frac{7}{19}$

Step 1.3.2

Multiply $2$ by $3$ .

$1 - \frac{6}{5 \cdot 7} \cdot \frac{7}{19}$

Step 1.3.3

Multiply $5$ by $7$ .

$1 - \frac{6}{35} \cdot \frac{7}{19}$

Step 1.4

Cancel the common factor of $7$ .

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Step 1.4.1

Move the leading negative in $- \frac{6}{35}$ into the numerator.

$1 + \frac{- 6}{35} \cdot \frac{7}{19}$

Step 1.4.2

Factor $7$ out of $35$ .

$1 + \frac{- 6}{7 (5)} \cdot \frac{7}{19}$

Step 1.4.3

Cancel the common factor.

$1 + \frac{- 6}{7 \cdot 5} \cdot \frac{7}{19}$

Step 1.4.4

Rewrite the expression.

$1 + \frac{- 6}{5} \cdot \frac{1}{19}$

Step 1.5

Multiply $\frac{- 6}{5}$ by $\frac{1}{19}$ .

$1 + \frac{- 6}{5 \cdot 19}$

Step 1.6

Multiply $5$ by $19$ .

$1 + \frac{- 6}{95}$

Step 1.7

Move the negative in front of the fraction.

$1 - \frac{6}{95}$

Step 2

Simplify the expression.

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Step 2.1

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

$\frac{95}{95} - \frac{6}{95}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{95 - 6}{95}$

Step 2.3

Subtract $6$ from $95$ .

$\frac{89}{95}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{89}{95}$

Decimal Form:

$0.93684210 \dots$