Finite Math Examples

$1 - (\frac{16}{39} + \frac{15}{38})$

Step 1

Simplify each term.

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Step 1.1

To write $\frac{16}{39}$ as a fraction with a common denominator, multiply by $\frac{38}{38}$ .

$1 - (\frac{16}{39} \cdot \frac{38}{38} + \frac{15}{38})$

Step 1.2

To write $\frac{15}{38}$ as a fraction with a common denominator, multiply by $\frac{39}{39}$ .

$1 - (\frac{16}{39} \cdot \frac{38}{38} + \frac{15}{38} \cdot \frac{39}{39})$

Step 1.3

Write each expression with a common denominator of $1482$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{16}{39}$ by $\frac{38}{38}$ .

$1 - (\frac{16 \cdot 38}{39 \cdot 38} + \frac{15}{38} \cdot \frac{39}{39})$

Step 1.3.2

Multiply $39$ by $38$ .

$1 - (\frac{16 \cdot 38}{1482} + \frac{15}{38} \cdot \frac{39}{39})$

Step 1.3.3

Multiply $\frac{15}{38}$ by $\frac{39}{39}$ .

$1 - (\frac{16 \cdot 38}{1482} + \frac{15 \cdot 39}{38 \cdot 39})$

Step 1.3.4

Multiply $38$ by $39$ .

$1 - (\frac{16 \cdot 38}{1482} + \frac{15 \cdot 39}{1482})$

Step 1.4

Combine the numerators over the common denominator.

$1 - \frac{16 \cdot 38 + 15 \cdot 39}{1482}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $16$ by $38$ .

$1 - \frac{608 + 15 \cdot 39}{1482}$

Step 1.5.2

Multiply $15$ by $39$ .

$1 - \frac{608 + 585}{1482}$

Step 1.5.3

Add $608$ and $585$ .

$1 - \frac{1193}{1482}$

Step 2

Simplify the expression.

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Step 2.1

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

$\frac{1482}{1482} - \frac{1193}{1482}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{1482 - 1193}{1482}$

Step 2.3

Subtract $1193$ from $1482$ .

$\frac{289}{1482}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{289}{1482}$

Decimal Form:

$0.19500674 \dots$