Algebra Examples

$\frac{1}{2} \cdot [\begin{array}{c} 12 & 64 \\ 78 & 30 \end{array}]$

Step 1

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

$[\begin{array}{c} \frac{1}{2} \cdot 12 & \frac{1}{2} \cdot 64 \\ \frac{1}{2} \cdot 78 & \frac{1}{2} \cdot 30 \end{array}]$

Step 2

Simplify each element in the matrix.

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Step 2.1

Cancel the common factor of $2$ .

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Step 2.1.1

Factor $2$ out of $12$ .

$[\begin{array}{c} \frac{1}{2} \cdot (2 (6)) & \frac{1}{2} \cdot 64 \\ \frac{1}{2} \cdot 78 & \frac{1}{2} \cdot 30 \end{array}]$

Step 2.1.2

Cancel the common factor.

$[\begin{array}{c} \frac{1}{2} \cdot (2 \cdot 6) & \frac{1}{2} \cdot 64 \\ \frac{1}{2} \cdot 78 & \frac{1}{2} \cdot 30 \end{array}]$

Step 2.1.3

Rewrite the expression.

$[\begin{array}{c} 6 & \frac{1}{2} \cdot 64 \\ \frac{1}{2} \cdot 78 & \frac{1}{2} \cdot 30 \end{array}]$

Step 2.2

Cancel the common factor of $2$ .

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Step 2.2.1

Factor $2$ out of $64$ .

$[\begin{array}{c} 6 & \frac{1}{2} \cdot (2 (32)) \\ \frac{1}{2} \cdot 78 & \frac{1}{2} \cdot 30 \end{array}]$

Step 2.2.2

Cancel the common factor.

$[\begin{array}{c} 6 & \frac{1}{2} \cdot (2 \cdot 32) \\ \frac{1}{2} \cdot 78 & \frac{1}{2} \cdot 30 \end{array}]$

Step 2.2.3

Rewrite the expression.

$[\begin{array}{c} 6 & 32 \\ \frac{1}{2} \cdot 78 & \frac{1}{2} \cdot 30 \end{array}]$

Step 2.3

Cancel the common factor of $2$ .

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Step 2.3.1

Factor $2$ out of $78$ .

$[\begin{array}{c} 6 & 32 \\ \frac{1}{2} \cdot (2 (39)) & \frac{1}{2} \cdot 30 \end{array}]$

Step 2.3.2

Cancel the common factor.

$[\begin{array}{c} 6 & 32 \\ \frac{1}{2} \cdot (2 \cdot 39) & \frac{1}{2} \cdot 30 \end{array}]$

Step 2.3.3

Rewrite the expression.

$[\begin{array}{c} 6 & 32 \\ 39 & \frac{1}{2} \cdot 30 \end{array}]$

Step 2.4

Cancel the common factor of $2$ .

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Step 2.4.1

Factor $2$ out of $30$ .

$[\begin{array}{c} 6 & 32 \\ 39 & \frac{1}{2} \cdot (2 (15)) \end{array}]$

Step 2.4.2

Cancel the common factor.

$[\begin{array}{c} 6 & 32 \\ 39 & \frac{1}{2} \cdot (2 \cdot 15) \end{array}]$

Step 2.4.3

Rewrite the expression.

$[\begin{array}{c} 6 & 32 \\ 39 & 15 \end{array}]$