Algebra Examples

$[\begin{array}{c} \frac{1}{2} & \frac{1}{4} \\ 3 & 8 \end{array}] - [\begin{array}{c} 2 & \frac{3}{4} \\ \frac{1}{2} & 5 \end{array}]$

Step 1

Subtract the corresponding elements.

$[\begin{array}{c} \frac{1}{2} - 2 & \frac{1}{4} - \frac{3}{4} \\ 3 - \frac{1}{2} & 8 - 5 \end{array}]$

Step 2

Simplify each element.

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Step 2.1

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

$[\begin{array}{c} \frac{1}{2} - 2 \cdot \frac{2}{2} & \frac{1}{4} - \frac{3}{4} \\ 3 - \frac{1}{2} & 8 - 5 \end{array}]$

Step 2.2

Combine $- 2$ and $\frac{2}{2}$ .

$[\begin{array}{c} \frac{1}{2} + \frac{- 2 \cdot 2}{2} & \frac{1}{4} - \frac{3}{4} \\ 3 - \frac{1}{2} & 8 - 5 \end{array}]$

Step 2.3

Combine the numerators over the common denominator.

$[\begin{array}{c} \frac{1 - 2 \cdot 2}{2} & \frac{1}{4} - \frac{3}{4} \\ 3 - \frac{1}{2} & 8 - 5 \end{array}]$

Step 2.4

Simplify the numerator.

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Step 2.4.1

Multiply $- 2$ by $2$ .

$[\begin{array}{c} \frac{1 - 4}{2} & \frac{1}{4} - \frac{3}{4} \\ 3 - \frac{1}{2} & 8 - 5 \end{array}]$

Step 2.4.2

Subtract $4$ from $1$ .

$[\begin{array}{c} \frac{- 3}{2} & \frac{1}{4} - \frac{3}{4} \\ 3 - \frac{1}{2} & 8 - 5 \end{array}]$

Step 2.5

Move the negative in front of the fraction.

$[\begin{array}{c} - \frac{3}{2} & \frac{1}{4} - \frac{3}{4} \\ 3 - \frac{1}{2} & 8 - 5 \end{array}]$

Step 2.6

Combine the numerators over the common denominator.

$[\begin{array}{c} - \frac{3}{2} & \frac{1 - 3}{4} \\ 3 - \frac{1}{2} & 8 - 5 \end{array}]$

Step 2.7

Subtract $3$ from $1$ .

$[\begin{array}{c} - \frac{3}{2} & \frac{- 2}{4} \\ 3 - \frac{1}{2} & 8 - 5 \end{array}]$

Step 2.8

Cancel the common factor of $- 2$ and $4$ .

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Step 2.8.1

Factor $2$ out of $- 2$ .

$[\begin{array}{c} - \frac{3}{2} & \frac{2 (- 1)}{4} \\ 3 - \frac{1}{2} & 8 - 5 \end{array}]$

Step 2.8.2

Cancel the common factors.

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Step 2.8.2.1

Factor $2$ out of $4$ .

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

Step 2.8.2.2

Cancel the common factor.

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

Step 2.8.2.3

Rewrite the expression.

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

Step 2.9

Move the negative in front of the fraction.

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

Step 2.10

To write $3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 2.11

Combine $3$ and $\frac{2}{2}$ .

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

Step 2.12

Combine the numerators over the common denominator.

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

Step 2.13

Simplify the numerator.

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Step 2.13.1

Multiply $3$ by $2$ .

$[\begin{array}{c} - \frac{3}{2} & - \frac{1}{2} \\ \frac{6 - 1}{2} & 8 - 5 \end{array}]$

Step 2.13.2

Subtract $1$ from $6$ .

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

Step 2.14

Subtract $5$ from $8$ .

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