Precalculus Examples

$[\begin{array}{c} \frac{1}{6} & \frac{1}{8} \\ - \frac{6}{5} & \frac{10}{7} \end{array}]$

Step 1

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

$\frac{1}{6} \cdot \frac{10}{7} - (- \frac{6}{5} \cdot \frac{1}{8})$

Step 2

Simplify the determinant.

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.1.1.1

Factor $2$ out of $6$ .

$\frac{1}{2 (3)} \cdot \frac{10}{7} - (- \frac{6}{5} \cdot \frac{1}{8})$

Step 2.1.1.2

Factor $2$ out of $10$ .

$\frac{1}{2 \cdot 3} \cdot \frac{2 \cdot 5}{7} - (- \frac{6}{5} \cdot \frac{1}{8})$

Step 2.1.1.3

Cancel the common factor.

$\frac{1}{2 \cdot 3} \cdot \frac{2 \cdot 5}{7} - (- \frac{6}{5} \cdot \frac{1}{8})$

Step 2.1.1.4

Rewrite the expression.

$\frac{1}{3} \cdot \frac{5}{7} - (- \frac{6}{5} \cdot \frac{1}{8})$

Step 2.1.2

Multiply $\frac{1}{3}$ by $\frac{5}{7}$ .

$\frac{5}{3 \cdot 7} - (- \frac{6}{5} \cdot \frac{1}{8})$

Step 2.1.3

Multiply $3$ by $7$ .

$\frac{5}{21} - (- \frac{6}{5} \cdot \frac{1}{8})$

Step 2.1.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.1.4.1

Move the leading negative in $- \frac{6}{5}$ into the numerator.

$\frac{5}{21} - (\frac{- 6}{5} \cdot \frac{1}{8})$

Step 2.1.4.2

Factor $2$ out of $- 6$ .

$\frac{5}{21} - (\frac{2 (- 3)}{5} \cdot \frac{1}{8})$

Step 2.1.4.3

Factor $2$ out of $8$ .

$\frac{5}{21} - (\frac{2 \cdot - 3}{5} \cdot \frac{1}{2 \cdot 4})$

Step 2.1.4.4

Cancel the common factor.

$\frac{5}{21} - (\frac{2 \cdot - 3}{5} \cdot \frac{1}{2 \cdot 4})$

Step 2.1.4.5

Rewrite the expression.

$\frac{5}{21} - (\frac{- 3}{5} \cdot \frac{1}{4})$

Step 2.1.5

Multiply $\frac{- 3}{5}$ by $\frac{1}{4}$ .

$\frac{5}{21} - \frac{- 3}{5 \cdot 4}$

Step 2.1.6

Multiply $5$ by $4$ .

$\frac{5}{21} - \frac{- 3}{20}$

Step 2.1.7

Move the negative in front of the fraction.

$\frac{5}{21} - - \frac{3}{20}$

Step 2.1.8

Multiply $- - \frac{3}{20}$ .

Tap for more steps...

Step 2.1.8.1

Multiply $- 1$ by $- 1$ .

$\frac{5}{21} + 1 (\frac{3}{20})$

Step 2.1.8.2

Multiply $\frac{3}{20}$ by $1$ .

$\frac{5}{21} + \frac{3}{20}$

Step 2.2

To write $\frac{5}{21}$ as a fraction with a common denominator, multiply by $\frac{20}{20}$ .

$\frac{5}{21} \cdot \frac{20}{20} + \frac{3}{20}$

Step 2.3

To write $\frac{3}{20}$ as a fraction with a common denominator, multiply by $\frac{21}{21}$ .

$\frac{5}{21} \cdot \frac{20}{20} + \frac{3}{20} \cdot \frac{21}{21}$

Step 2.4

Write each expression with a common denominator of $420$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 2.4.1

Multiply $\frac{5}{21}$ by $\frac{20}{20}$ .

$\frac{5 \cdot 20}{21 \cdot 20} + \frac{3}{20} \cdot \frac{21}{21}$

Step 2.4.2

Multiply $21$ by $20$ .

$\frac{5 \cdot 20}{420} + \frac{3}{20} \cdot \frac{21}{21}$

Step 2.4.3

Multiply $\frac{3}{20}$ by $\frac{21}{21}$ .

$\frac{5 \cdot 20}{420} + \frac{3 \cdot 21}{20 \cdot 21}$

Step 2.4.4

Multiply $20$ by $21$ .

$\frac{5 \cdot 20}{420} + \frac{3 \cdot 21}{420}$

Step 2.5

Combine the numerators over the common denominator.

$\frac{5 \cdot 20 + 3 \cdot 21}{420}$

Step 2.6

Simplify the numerator.

Tap for more steps...

Step 2.6.1

Multiply $5$ by $20$ .

$\frac{100 + 3 \cdot 21}{420}$

Step 2.6.2

Multiply $3$ by $21$ .

$\frac{100 + 63}{420}$

Step 2.6.3

Add $100$ and $63$ .

$\frac{163}{420}$