Algebra Examples

$[\begin{array}{c} \frac{1}{8} & \frac{1}{3} \\ - \frac{11}{5} & \frac{11}{2} \end{array}]$

Step 1

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

$\frac{1}{8} \cdot \frac{11}{2} - (- \frac{11}{5} \cdot \frac{1}{3})$

Step 2

Simplify the determinant.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $\frac{1}{8} \cdot \frac{11}{2}$ .

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Step 2.1.1.1

Multiply $\frac{1}{8}$ by $\frac{11}{2}$ .

$\frac{11}{8 \cdot 2} - (- \frac{11}{5} \cdot \frac{1}{3})$

Step 2.1.1.2

Multiply $8$ by $2$ .

$\frac{11}{16} - (- \frac{11}{5} \cdot \frac{1}{3})$

Step 2.1.2

Multiply $- \frac{11}{5} \cdot \frac{1}{3}$ .

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Step 2.1.2.1

Multiply $\frac{1}{3}$ by $\frac{11}{5}$ .

$\frac{11}{16} - - \frac{11}{3 \cdot 5}$

Step 2.1.2.2

Multiply $3$ by $5$ .

$\frac{11}{16} - - \frac{11}{15}$

Step 2.1.3

Multiply $- - \frac{11}{15}$ .

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Step 2.1.3.1

Multiply $- 1$ by $- 1$ .

$\frac{11}{16} + 1 (\frac{11}{15})$

Step 2.1.3.2

Multiply $\frac{11}{15}$ by $1$ .

$\frac{11}{16} + \frac{11}{15}$

Step 2.2

To write $\frac{11}{16}$ as a fraction with a common denominator, multiply by $\frac{15}{15}$ .

$\frac{11}{16} \cdot \frac{15}{15} + \frac{11}{15}$

Step 2.3

To write $\frac{11}{15}$ as a fraction with a common denominator, multiply by $\frac{16}{16}$ .

$\frac{11}{16} \cdot \frac{15}{15} + \frac{11}{15} \cdot \frac{16}{16}$

Step 2.4

Write each expression with a common denominator of $240$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.4.1

Multiply $\frac{11}{16}$ by $\frac{15}{15}$ .

$\frac{11 \cdot 15}{16 \cdot 15} + \frac{11}{15} \cdot \frac{16}{16}$

Step 2.4.2

Multiply $16$ by $15$ .

$\frac{11 \cdot 15}{240} + \frac{11}{15} \cdot \frac{16}{16}$

Step 2.4.3

Multiply $\frac{11}{15}$ by $\frac{16}{16}$ .

$\frac{11 \cdot 15}{240} + \frac{11 \cdot 16}{15 \cdot 16}$

Step 2.4.4

Multiply $15$ by $16$ .

$\frac{11 \cdot 15}{240} + \frac{11 \cdot 16}{240}$

Step 2.5

Combine the numerators over the common denominator.

$\frac{11 \cdot 15 + 11 \cdot 16}{240}$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $11$ by $15$ .

$\frac{165 + 11 \cdot 16}{240}$

Step 2.6.2

Multiply $11$ by $16$ .

$\frac{165 + 176}{240}$

Step 2.6.3

Add $165$ and $176$ .

$\frac{341}{240}$