Finite Math Examples

$\sin (30) [\begin{array}{c} 5 & 2 & 4 \\ 7 & 4 & 8 \\ 12 & 9 & 18 \\ 10 & 7 & 1 \end{array}]$

Step 1

The exact value of $\sin (30)$ is $\frac{1}{2}$ .

$\frac{1}{2} [\begin{array}{c} 5 & 2 & 4 \\ 7 & 4 & 8 \\ 12 & 9 & 18 \\ 10 & 7 & 1 \end{array}]$

Step 2

Multiply $\frac{1}{2}$ by each element of the matrix.

$[\begin{array}{c} \frac{1}{2} \cdot 5 & \frac{1}{2} \cdot 2 & \frac{1}{2} \cdot 4 \\ \frac{1}{2} \cdot 7 & \frac{1}{2} \cdot 4 & \frac{1}{2} \cdot 8 \\ \frac{1}{2} \cdot 12 & \frac{1}{2} \cdot 9 & \frac{1}{2} \cdot 18 \\ \frac{1}{2} \cdot 10 & \frac{1}{2} \cdot 7 & \frac{1}{2} \cdot 1 \end{array}]$

Step 3

Simplify each element in the matrix.

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Step 3.1

Combine $\frac{1}{2}$ and $5$ .

$[\begin{array}{c} \frac{5}{2} & \frac{1}{2} \cdot 2 & \frac{1}{2} \cdot 4 \\ \frac{1}{2} \cdot 7 & \frac{1}{2} \cdot 4 & \frac{1}{2} \cdot 8 \\ \frac{1}{2} \cdot 12 & \frac{1}{2} \cdot 9 & \frac{1}{2} \cdot 18 \\ \frac{1}{2} \cdot 10 & \frac{1}{2} \cdot 7 & \frac{1}{2} \cdot 1 \end{array}]$

Step 3.2

Cancel the common factor of $2$ .

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Step 3.2.1

Cancel the common factor.

Step 3.2.2

Rewrite the expression.

$[\begin{array}{c} \frac{5}{2} & 1 & \frac{1}{2} \cdot 4 \\ \frac{1}{2} \cdot 7 & \frac{1}{2} \cdot 4 & \frac{1}{2} \cdot 8 \\ \frac{1}{2} \cdot 12 & \frac{1}{2} \cdot 9 & \frac{1}{2} \cdot 18 \\ \frac{1}{2} \cdot 10 & \frac{1}{2} \cdot 7 & \frac{1}{2} \cdot 1 \end{array}]$

Step 3.3

Cancel the common factor of $2$ .

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Step 3.3.1

Factor $2$ out of $4$ .

$[\begin{array}{c} \frac{5}{2} & 1 & \frac{1}{2} \cdot (2 (2)) \\ \frac{1}{2} \cdot 7 & \frac{1}{2} \cdot 4 & \frac{1}{2} \cdot 8 \\ \frac{1}{2} \cdot 12 & \frac{1}{2} \cdot 9 & \frac{1}{2} \cdot 18 \\ \frac{1}{2} \cdot 10 & \frac{1}{2} \cdot 7 & \frac{1}{2} \cdot 1 \end{array}]$

Step 3.3.2

Cancel the common factor.

$[\begin{array}{c} \frac{5}{2} & 1 & \frac{1}{2} \cdot (2 \cdot 2) \\ \frac{1}{2} \cdot 7 & \frac{1}{2} \cdot 4 & \frac{1}{2} \cdot 8 \\ \frac{1}{2} \cdot 12 & \frac{1}{2} \cdot 9 & \frac{1}{2} \cdot 18 \\ \frac{1}{2} \cdot 10 & \frac{1}{2} \cdot 7 & \frac{1}{2} \cdot 1 \end{array}]$

Step 3.3.3

Rewrite the expression.

$[\begin{array}{c} \frac{5}{2} & 1 & 2 \\ \frac{1}{2} \cdot 7 & \frac{1}{2} \cdot 4 & \frac{1}{2} \cdot 8 \\ \frac{1}{2} \cdot 12 & \frac{1}{2} \cdot 9 & \frac{1}{2} \cdot 18 \\ \frac{1}{2} \cdot 10 & \frac{1}{2} \cdot 7 & \frac{1}{2} \cdot 1 \end{array}]$

Step 3.4

Combine $\frac{1}{2}$ and $7$ .

$[\begin{array}{c} \frac{5}{2} & 1 & 2 \\ \frac{7}{2} & \frac{1}{2} \cdot 4 & \frac{1}{2} \cdot 8 \\ \frac{1}{2} \cdot 12 & \frac{1}{2} \cdot 9 & \frac{1}{2} \cdot 18 \\ \frac{1}{2} \cdot 10 & \frac{1}{2} \cdot 7 & \frac{1}{2} \cdot 1 \end{array}]$

Step 3.5

Cancel the common factor of $2$ .

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Step 3.5.1

Factor $2$ out of $4$ .

$[\begin{array}{c} \frac{5}{2} & 1 & 2 \\ \frac{7}{2} & \frac{1}{2} \cdot (2 (2)) & \frac{1}{2} \cdot 8 \\ \frac{1}{2} \cdot 12 & \frac{1}{2} \cdot 9 & \frac{1}{2} \cdot 18 \\ \frac{1}{2} \cdot 10 & \frac{1}{2} \cdot 7 & \frac{1}{2} \cdot 1 \end{array}]$

Step 3.5.2

Cancel the common factor.

$[\begin{array}{c} \frac{5}{2} & 1 & 2 \\ \frac{7}{2} & \frac{1}{2} \cdot (2 \cdot 2) & \frac{1}{2} \cdot 8 \\ \frac{1}{2} \cdot 12 & \frac{1}{2} \cdot 9 & \frac{1}{2} \cdot 18 \\ \frac{1}{2} \cdot 10 & \frac{1}{2} \cdot 7 & \frac{1}{2} \cdot 1 \end{array}]$

Step 3.5.3

Rewrite the expression.

$[\begin{array}{c} \frac{5}{2} & 1 & 2 \\ \frac{7}{2} & 2 & \frac{1}{2} \cdot 8 \\ \frac{1}{2} \cdot 12 & \frac{1}{2} \cdot 9 & \frac{1}{2} \cdot 18 \\ \frac{1}{2} \cdot 10 & \frac{1}{2} \cdot 7 & \frac{1}{2} \cdot 1 \end{array}]$

Step 3.6

Cancel the common factor of $2$ .

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Step 3.6.1

Factor $2$ out of $8$ .

$[\begin{array}{c} \frac{5}{2} & 1 & 2 \\ \frac{7}{2} & 2 & \frac{1}{2} \cdot (2 (4)) \\ \frac{1}{2} \cdot 12 & \frac{1}{2} \cdot 9 & \frac{1}{2} \cdot 18 \\ \frac{1}{2} \cdot 10 & \frac{1}{2} \cdot 7 & \frac{1}{2} \cdot 1 \end{array}]$

Step 3.6.2

Cancel the common factor.

$[\begin{array}{c} \frac{5}{2} & 1 & 2 \\ \frac{7}{2} & 2 & \frac{1}{2} \cdot (2 \cdot 4) \\ \frac{1}{2} \cdot 12 & \frac{1}{2} \cdot 9 & \frac{1}{2} \cdot 18 \\ \frac{1}{2} \cdot 10 & \frac{1}{2} \cdot 7 & \frac{1}{2} \cdot 1 \end{array}]$

Step 3.6.3

Rewrite the expression.

$[\begin{array}{c} \frac{5}{2} & 1 & 2 \\ \frac{7}{2} & 2 & 4 \\ \frac{1}{2} \cdot 12 & \frac{1}{2} \cdot 9 & \frac{1}{2} \cdot 18 \\ \frac{1}{2} \cdot 10 & \frac{1}{2} \cdot 7 & \frac{1}{2} \cdot 1 \end{array}]$

Step 3.7

Cancel the common factor of $2$ .

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Step 3.7.1

Factor $2$ out of $12$ .

$[\begin{array}{c} \frac{5}{2} & 1 & 2 \\ \frac{7}{2} & 2 & 4 \\ \frac{1}{2} \cdot (2 (6)) & \frac{1}{2} \cdot 9 & \frac{1}{2} \cdot 18 \\ \frac{1}{2} \cdot 10 & \frac{1}{2} \cdot 7 & \frac{1}{2} \cdot 1 \end{array}]$

Step 3.7.2

Cancel the common factor.

$[\begin{array}{c} \frac{5}{2} & 1 & 2 \\ \frac{7}{2} & 2 & 4 \\ \frac{1}{2} \cdot (2 \cdot 6) & \frac{1}{2} \cdot 9 & \frac{1}{2} \cdot 18 \\ \frac{1}{2} \cdot 10 & \frac{1}{2} \cdot 7 & \frac{1}{2} \cdot 1 \end{array}]$

Step 3.7.3

Rewrite the expression.

$[\begin{array}{c} \frac{5}{2} & 1 & 2 \\ \frac{7}{2} & 2 & 4 \\ 6 & \frac{1}{2} \cdot 9 & \frac{1}{2} \cdot 18 \\ \frac{1}{2} \cdot 10 & \frac{1}{2} \cdot 7 & \frac{1}{2} \cdot 1 \end{array}]$

Step 3.8

Combine $\frac{1}{2}$ and $9$ .

$[\begin{array}{c} \frac{5}{2} & 1 & 2 \\ \frac{7}{2} & 2 & 4 \\ 6 & \frac{9}{2} & \frac{1}{2} \cdot 18 \\ \frac{1}{2} \cdot 10 & \frac{1}{2} \cdot 7 & \frac{1}{2} \cdot 1 \end{array}]$

Step 3.9

Cancel the common factor of $2$ .

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Step 3.9.1

Factor $2$ out of $18$ .

$[\begin{array}{c} \frac{5}{2} & 1 & 2 \\ \frac{7}{2} & 2 & 4 \\ 6 & \frac{9}{2} & \frac{1}{2} \cdot (2 (9)) \\ \frac{1}{2} \cdot 10 & \frac{1}{2} \cdot 7 & \frac{1}{2} \cdot 1 \end{array}]$

Step 3.9.2

Cancel the common factor.

$[\begin{array}{c} \frac{5}{2} & 1 & 2 \\ \frac{7}{2} & 2 & 4 \\ 6 & \frac{9}{2} & \frac{1}{2} \cdot (2 \cdot 9) \\ \frac{1}{2} \cdot 10 & \frac{1}{2} \cdot 7 & \frac{1}{2} \cdot 1 \end{array}]$

Step 3.9.3

Rewrite the expression.

$[\begin{array}{c} \frac{5}{2} & 1 & 2 \\ \frac{7}{2} & 2 & 4 \\ 6 & \frac{9}{2} & 9 \\ \frac{1}{2} \cdot 10 & \frac{1}{2} \cdot 7 & \frac{1}{2} \cdot 1 \end{array}]$

Step 3.10

Cancel the common factor of $2$ .

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Step 3.10.1

Factor $2$ out of $10$ .

$[\begin{array}{c} \frac{5}{2} & 1 & 2 \\ \frac{7}{2} & 2 & 4 \\ 6 & \frac{9}{2} & 9 \\ \frac{1}{2} \cdot (2 (5)) & \frac{1}{2} \cdot 7 & \frac{1}{2} \cdot 1 \end{array}]$

Step 3.10.2

Cancel the common factor.

$[\begin{array}{c} \frac{5}{2} & 1 & 2 \\ \frac{7}{2} & 2 & 4 \\ 6 & \frac{9}{2} & 9 \\ \frac{1}{2} \cdot (2 \cdot 5) & \frac{1}{2} \cdot 7 & \frac{1}{2} \cdot 1 \end{array}]$

Step 3.10.3

Rewrite the expression.

$[\begin{array}{c} \frac{5}{2} & 1 & 2 \\ \frac{7}{2} & 2 & 4 \\ 6 & \frac{9}{2} & 9 \\ 5 & \frac{1}{2} \cdot 7 & \frac{1}{2} \cdot 1 \end{array}]$

Step 3.11

Combine $\frac{1}{2}$ and $7$ .

$[\begin{array}{c} \frac{5}{2} & 1 & 2 \\ \frac{7}{2} & 2 & 4 \\ 6 & \frac{9}{2} & 9 \\ 5 & \frac{7}{2} & \frac{1}{2} \cdot 1 \end{array}]$

Step 3.12

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

$[\begin{array}{c} \frac{5}{2} & 1 & 2 \\ \frac{7}{2} & 2 & 4 \\ 6 & \frac{9}{2} & 9 \\ 5 & \frac{7}{2} & \frac{1}{2} \end{array}]$