Finite Math Examples

$[\begin{array}{c} \frac{3}{4} & \frac{1}{7} \\ \frac{1}{4} & \frac{6}{7} \end{array}]$

Step 1

The determinant of a $2 \times 2$ matrix can be found using the formula $| \begin{array}{c} a & b \\ c & d \end{array} | = a d - c b$ .

$\frac{3}{4} \cdot \frac{6}{7} - \frac{1}{4} \cdot \frac{1}{7}$

Step 2

Simplify the determinant.

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Step 2.1

Simplify each term.

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Step 2.1.1

Cancel the common factor of $2$ .

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Step 2.1.1.1

Factor $2$ out of $4$ .

$\frac{3}{2 (2)} \cdot \frac{6}{7} - \frac{1}{4} \cdot \frac{1}{7}$

Step 2.1.1.2

Factor $2$ out of $6$ .

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

Step 2.1.1.3

Cancel the common factor.

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

Step 2.1.1.4

Rewrite the expression.

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

Step 2.1.2

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

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

Step 2.1.3

Multiply $3$ by $3$ .

$\frac{9}{2 \cdot 7} - \frac{1}{4} \cdot \frac{1}{7}$

Step 2.1.4

Multiply $2$ by $7$ .

$\frac{9}{14} - \frac{1}{4} \cdot \frac{1}{7}$

Step 2.1.5

Multiply $- \frac{1}{4} \cdot \frac{1}{7}$ .

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Step 2.1.5.1

Multiply $\frac{1}{7}$ by $\frac{1}{4}$ .

$\frac{9}{14} - \frac{1}{7 \cdot 4}$

Step 2.1.5.2

Multiply $7$ by $4$ .

$\frac{9}{14} - \frac{1}{28}$

Step 2.2

To write $\frac{9}{14}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{9}{14} \cdot \frac{2}{2} - \frac{1}{28}$

Step 2.3

Write each expression with a common denominator of $28$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{9}{14}$ by $\frac{2}{2}$ .

$\frac{9 \cdot 2}{14 \cdot 2} - \frac{1}{28}$

Step 2.3.2

Multiply $14$ by $2$ .

$\frac{9 \cdot 2}{28} - \frac{1}{28}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{9 \cdot 2 - 1}{28}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $9$ by $2$ .

$\frac{18 - 1}{28}$

Step 2.5.2

Subtract $1$ from $18$ .

$\frac{17}{28}$