Algebra Examples

$[\begin{array}{c} - 7 & 4 \\ 2 & - 5 \end{array}] - [\begin{array}{c} - \frac{5}{2} & - \frac{12}{3} \\ 2 & - 1 \end{array}]$

Step 1

Subtract the corresponding elements.

$[\begin{array}{c} - 7 + \frac{5}{2} & 4 + \frac{12}{3} \\ 2 - 2 & - 5 + 1 \end{array}]$

Step 2

Simplify each element.

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Step 2.1

To write $- 7$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$[\begin{array}{c} - 7 \cdot \frac{2}{2} + \frac{5}{2} & 4 + \frac{12}{3} \\ 2 - 2 & - 5 + 1 \end{array}]$

Step 2.2

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

$[\begin{array}{c} \frac{- 7 \cdot 2}{2} + \frac{5}{2} & 4 + \frac{12}{3} \\ 2 - 2 & - 5 + 1 \end{array}]$

Step 2.3

Combine the numerators over the common denominator.

$[\begin{array}{c} \frac{- 7 \cdot 2 + 5}{2} & 4 + \frac{12}{3} \\ 2 - 2 & - 5 + 1 \end{array}]$

Step 2.4

Simplify the numerator.

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Step 2.4.1

Multiply $- 7$ by $2$ .

$[\begin{array}{c} \frac{- 14 + 5}{2} & 4 + \frac{12}{3} \\ 2 - 2 & - 5 + 1 \end{array}]$

Step 2.4.2

Add $- 14$ and $5$ .

$[\begin{array}{c} \frac{- 9}{2} & 4 + \frac{12}{3} \\ 2 - 2 & - 5 + 1 \end{array}]$

Step 2.5

Move the negative in front of the fraction.

$[\begin{array}{c} - \frac{9}{2} & 4 + \frac{12}{3} \\ 2 - 2 & - 5 + 1 \end{array}]$

Step 2.6

Divide $12$ by $3$ .

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

Step 2.7

Add $4$ and $4$ .

$[\begin{array}{c} - \frac{9}{2} & 8 \\ 2 - 2 & - 5 + 1 \end{array}]$

Step 2.8

Subtract $2$ from $2$ .

$[\begin{array}{c} - \frac{9}{2} & 8 \\ 0 & - 5 + 1 \end{array}]$

Step 2.9

Add $- 5$ and $1$ .

$[\begin{array}{c} - \frac{9}{2} & 8 \\ 0 & - 4 \end{array}]$