Finite Math Examples

$1 - (\frac{29}{39} + \frac{28}{38})$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $28$ and $38$ .

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Step 1.1.1

Factor $2$ out of $28$ .

$1 - (\frac{29}{39} + \frac{2 (14)}{38})$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $2$ out of $38$ .

$1 - (\frac{29}{39} + \frac{2 \cdot 14}{2 \cdot 19})$

Step 1.1.2.2

Cancel the common factor.

$1 - (\frac{29}{39} + \frac{2 \cdot 14}{2 \cdot 19})$

Step 1.1.2.3

Rewrite the expression.

$1 - (\frac{29}{39} + \frac{14}{19})$

Step 1.2

To write $\frac{29}{39}$ as a fraction with a common denominator, multiply by $\frac{19}{19}$ .

$1 - (\frac{29}{39} \cdot \frac{19}{19} + \frac{14}{19})$

Step 1.3

To write $\frac{14}{19}$ as a fraction with a common denominator, multiply by $\frac{39}{39}$ .

$1 - (\frac{29}{39} \cdot \frac{19}{19} + \frac{14}{19} \cdot \frac{39}{39})$

Step 1.4

Write each expression with a common denominator of $741$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{29}{39}$ by $\frac{19}{19}$ .

$1 - (\frac{29 \cdot 19}{39 \cdot 19} + \frac{14}{19} \cdot \frac{39}{39})$

Step 1.4.2

Multiply $39$ by $19$ .

$1 - (\frac{29 \cdot 19}{741} + \frac{14}{19} \cdot \frac{39}{39})$

Step 1.4.3

Multiply $\frac{14}{19}$ by $\frac{39}{39}$ .

$1 - (\frac{29 \cdot 19}{741} + \frac{14 \cdot 39}{19 \cdot 39})$

Step 1.4.4

Multiply $19$ by $39$ .

$1 - (\frac{29 \cdot 19}{741} + \frac{14 \cdot 39}{741})$

Step 1.5

Combine the numerators over the common denominator.

$1 - \frac{29 \cdot 19 + 14 \cdot 39}{741}$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Multiply $29$ by $19$ .

$1 - \frac{551 + 14 \cdot 39}{741}$

Step 1.6.2

Multiply $14$ by $39$ .

$1 - \frac{551 + 546}{741}$

Step 1.6.3

Add $551$ and $546$ .

$1 - \frac{1097}{741}$

Step 2

Simplify the expression.

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Step 2.1

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

$\frac{741}{741} - \frac{1097}{741}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{741 - 1097}{741}$

Step 2.3

Subtract $1097$ from $741$ .

$\frac{- 356}{741}$

Step 2.4

Move the negative in front of the fraction.

$- \frac{356}{741}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- \frac{356}{741}$

Decimal Form:

$- 0.48043184 \dots$