Algebra Examples

$[\begin{array}{c} - 12 & - 15 & 15 \\ - 9 & - 3 \sqrt{2} & - \frac{1}{2} \end{array}] - [\begin{array}{c} - 24 & 24 & 8 \\ 40 & 72 & \frac{16}{3} \end{array}]$

Step 1

Subtract the corresponding elements.

$[\begin{array}{c} - 12 + 24 & - 15 - 24 & 15 - 8 \\ - 9 - 40 & - 3 \sqrt{2} - 72 & - \frac{1}{2} - \frac{16}{3} \end{array}]$

Step 2

Simplify each element.

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Step 2.1

Add $- 12$ and $24$ .

$[\begin{array}{c} 12 & - 15 - 24 & 15 - 8 \\ - 9 - 40 & - 3 \sqrt{2} - 72 & - \frac{1}{2} - \frac{16}{3} \end{array}]$

Step 2.2

Subtract $24$ from $- 15$ .

$[\begin{array}{c} 12 & - 39 & 15 - 8 \\ - 9 - 40 & - 3 \sqrt{2} - 72 & - \frac{1}{2} - \frac{16}{3} \end{array}]$

Step 2.3

Subtract $8$ from $15$ .

$[\begin{array}{c} 12 & - 39 & 7 \\ - 9 - 40 & - 3 \sqrt{2} - 72 & - \frac{1}{2} - \frac{16}{3} \end{array}]$

Step 2.4

Subtract $40$ from $- 9$ .

$[\begin{array}{c} 12 & - 39 & 7 \\ - 49 & - 3 \sqrt{2} - 72 & - \frac{1}{2} - \frac{16}{3} \end{array}]$

Step 2.5

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$[\begin{array}{c} 12 & - 39 & 7 \\ - 49 & - 3 \sqrt{2} - 72 & - \frac{1}{2} \cdot \frac{3}{3} - \frac{16}{3} \end{array}]$

Step 2.6

To write $- \frac{16}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$[\begin{array}{c} 12 & - 39 & 7 \\ - 49 & - 3 \sqrt{2} - 72 & - \frac{1}{2} \cdot \frac{3}{3} - \frac{16}{3} \cdot \frac{2}{2} \end{array}]$

Step 2.7

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.7.1

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

$[\begin{array}{c} 12 & - 39 & 7 \\ - 49 & - 3 \sqrt{2} - 72 & - \frac{3}{2 \cdot 3} - \frac{16}{3} \cdot \frac{2}{2} \end{array}]$

Step 2.7.2

Multiply $2$ by $3$ .

$[\begin{array}{c} 12 & - 39 & 7 \\ - 49 & - 3 \sqrt{2} - 72 & - \frac{3}{6} - \frac{16}{3} \cdot \frac{2}{2} \end{array}]$

Step 2.7.3

Multiply $\frac{16}{3}$ by $\frac{2}{2}$ .

$[\begin{array}{c} 12 & - 39 & 7 \\ - 49 & - 3 \sqrt{2} - 72 & - \frac{3}{6} - \frac{16 \cdot 2}{3 \cdot 2} \end{array}]$

Step 2.7.4

Multiply $3$ by $2$ .

$[\begin{array}{c} 12 & - 39 & 7 \\ - 49 & - 3 \sqrt{2} - 72 & - \frac{3}{6} - \frac{16 \cdot 2}{6} \end{array}]$

Step 2.8

Combine the numerators over the common denominator.

$[\begin{array}{c} 12 & - 39 & 7 \\ - 49 & - 3 \sqrt{2} - 72 & \frac{- 3 - 16 \cdot 2}{6} \end{array}]$

Step 2.9

Simplify the numerator.

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Step 2.9.1

Multiply $- 16$ by $2$ .

$[\begin{array}{c} 12 & - 39 & 7 \\ - 49 & - 3 \sqrt{2} - 72 & \frac{- 3 - 32}{6} \end{array}]$

Step 2.9.2

Subtract $32$ from $- 3$ .

$[\begin{array}{c} 12 & - 39 & 7 \\ - 49 & - 3 \sqrt{2} - 72 & \frac{- 35}{6} \end{array}]$

Step 2.10

Move the negative in front of the fraction.

$[\begin{array}{c} 12 & - 39 & 7 \\ - 49 & - 3 \sqrt{2} - 72 & - \frac{35}{6} \end{array}]$