Linear Algebra Examples

$[\begin{array}{c} \frac{8}{3} \\ \frac{8}{3} \\ \frac{8}{3} \end{array}] + [\begin{array}{c} - \frac{19}{14} \\ \frac{57}{28} \\ - \frac{19}{28} \end{array}]$

Step 1

Add the corresponding elements.

$[\begin{array}{c} \frac{8}{3} - \frac{19}{14} \\ \frac{8}{3} + \frac{57}{28} \\ \frac{8}{3} - \frac{19}{28} \end{array}]$

Step 2

Simplify each element.

Tap for more steps...

Step 2.1

To write $\frac{8}{3}$ as a fraction with a common denominator, multiply by $\frac{14}{14}$ .

$[\begin{array}{c} \frac{8}{3} \cdot \frac{14}{14} - \frac{19}{14} \\ \frac{8}{3} + \frac{57}{28} \\ \frac{8}{3} - \frac{19}{28} \end{array}]$

Step 2.2

To write $- \frac{19}{14}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$[\begin{array}{c} \frac{8}{3} \cdot \frac{14}{14} - \frac{19}{14} \cdot \frac{3}{3} \\ \frac{8}{3} + \frac{57}{28} \\ \frac{8}{3} - \frac{19}{28} \end{array}]$

Step 2.3

Write each expression with a common denominator of $42$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 2.3.1

Multiply $\frac{8}{3}$ by $\frac{14}{14}$ .

$[\begin{array}{c} \frac{8 \cdot 14}{3 \cdot 14} - \frac{19}{14} \cdot \frac{3}{3} \\ \frac{8}{3} + \frac{57}{28} \\ \frac{8}{3} - \frac{19}{28} \end{array}]$

Step 2.3.2

Multiply $3$ by $14$ .

$[\begin{array}{c} \frac{8 \cdot 14}{42} - \frac{19}{14} \cdot \frac{3}{3} \\ \frac{8}{3} + \frac{57}{28} \\ \frac{8}{3} - \frac{19}{28} \end{array}]$

Step 2.3.3

Multiply $\frac{19}{14}$ by $\frac{3}{3}$ .

$[\begin{array}{c} \frac{8 \cdot 14}{42} - \frac{19 \cdot 3}{14 \cdot 3} \\ \frac{8}{3} + \frac{57}{28} \\ \frac{8}{3} - \frac{19}{28} \end{array}]$

Step 2.3.4

Multiply $14$ by $3$ .

$[\begin{array}{c} \frac{8 \cdot 14}{42} - \frac{19 \cdot 3}{42} \\ \frac{8}{3} + \frac{57}{28} \\ \frac{8}{3} - \frac{19}{28} \end{array}]$

Step 2.4

Combine the numerators over the common denominator.

$[\begin{array}{c} \frac{8 \cdot 14 - 19 \cdot 3}{42} \\ \frac{8}{3} + \frac{57}{28} \\ \frac{8}{3} - \frac{19}{28} \end{array}]$

Step 2.5

Simplify the numerator.

Tap for more steps...

Step 2.5.1

Multiply $8$ by $14$ .

$[\begin{array}{c} \frac{112 - 19 \cdot 3}{42} \\ \frac{8}{3} + \frac{57}{28} \\ \frac{8}{3} - \frac{19}{28} \end{array}]$

Step 2.5.2

Multiply $- 19$ by $3$ .

$[\begin{array}{c} \frac{112 - 57}{42} \\ \frac{8}{3} + \frac{57}{28} \\ \frac{8}{3} - \frac{19}{28} \end{array}]$

Step 2.5.3

Subtract $57$ from $112$ .

$[\begin{array}{c} \frac{55}{42} \\ \frac{8}{3} + \frac{57}{28} \\ \frac{8}{3} - \frac{19}{28} \end{array}]$

Step 2.6

To write $\frac{8}{3}$ as a fraction with a common denominator, multiply by $\frac{28}{28}$ .

$[\begin{array}{c} \frac{55}{42} \\ \frac{8}{3} \cdot \frac{28}{28} + \frac{57}{28} \\ \frac{8}{3} - \frac{19}{28} \end{array}]$

Step 2.7

To write $\frac{57}{28}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$[\begin{array}{c} \frac{55}{42} \\ \frac{8}{3} \cdot \frac{28}{28} + \frac{57}{28} \cdot \frac{3}{3} \\ \frac{8}{3} - \frac{19}{28} \end{array}]$

Step 2.8

Write each expression with a common denominator of $84$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 2.8.1

Multiply $\frac{8}{3}$ by $\frac{28}{28}$ .

$[\begin{array}{c} \frac{55}{42} \\ \frac{8 \cdot 28}{3 \cdot 28} + \frac{57}{28} \cdot \frac{3}{3} \\ \frac{8}{3} - \frac{19}{28} \end{array}]$

Step 2.8.2

Multiply $3$ by $28$ .

$[\begin{array}{c} \frac{55}{42} \\ \frac{8 \cdot 28}{84} + \frac{57}{28} \cdot \frac{3}{3} \\ \frac{8}{3} - \frac{19}{28} \end{array}]$

Step 2.8.3

Multiply $\frac{57}{28}$ by $\frac{3}{3}$ .

$[\begin{array}{c} \frac{55}{42} \\ \frac{8 \cdot 28}{84} + \frac{57 \cdot 3}{28 \cdot 3} \\ \frac{8}{3} - \frac{19}{28} \end{array}]$

Step 2.8.4

Multiply $28$ by $3$ .

$[\begin{array}{c} \frac{55}{42} \\ \frac{8 \cdot 28}{84} + \frac{57 \cdot 3}{84} \\ \frac{8}{3} - \frac{19}{28} \end{array}]$

Step 2.9

Combine the numerators over the common denominator.

$[\begin{array}{c} \frac{55}{42} \\ \frac{8 \cdot 28 + 57 \cdot 3}{84} \\ \frac{8}{3} - \frac{19}{28} \end{array}]$

Step 2.10

Simplify the numerator.

Tap for more steps...

Step 2.10.1

Multiply $8$ by $28$ .

$[\begin{array}{c} \frac{55}{42} \\ \frac{224 + 57 \cdot 3}{84} \\ \frac{8}{3} - \frac{19}{28} \end{array}]$

Step 2.10.2

Multiply $57$ by $3$ .

$[\begin{array}{c} \frac{55}{42} \\ \frac{224 + 171}{84} \\ \frac{8}{3} - \frac{19}{28} \end{array}]$

Step 2.10.3

Add $224$ and $171$ .

$[\begin{array}{c} \frac{55}{42} \\ \frac{395}{84} \\ \frac{8}{3} - \frac{19}{28} \end{array}]$

Step 2.11

To write $\frac{8}{3}$ as a fraction with a common denominator, multiply by $\frac{28}{28}$ .

$[\begin{array}{c} \frac{55}{42} \\ \frac{395}{84} \\ \frac{8}{3} \cdot \frac{28}{28} - \frac{19}{28} \end{array}]$

Step 2.12

To write $- \frac{19}{28}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$[\begin{array}{c} \frac{55}{42} \\ \frac{395}{84} \\ \frac{8}{3} \cdot \frac{28}{28} - \frac{19}{28} \cdot \frac{3}{3} \end{array}]$

Step 2.13

Write each expression with a common denominator of $84$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 2.13.1

Multiply $\frac{8}{3}$ by $\frac{28}{28}$ .

$[\begin{array}{c} \frac{55}{42} \\ \frac{395}{84} \\ \frac{8 \cdot 28}{3 \cdot 28} - \frac{19}{28} \cdot \frac{3}{3} \end{array}]$

Step 2.13.2

Multiply $3$ by $28$ .

$[\begin{array}{c} \frac{55}{42} \\ \frac{395}{84} \\ \frac{8 \cdot 28}{84} - \frac{19}{28} \cdot \frac{3}{3} \end{array}]$

Step 2.13.3

Multiply $\frac{19}{28}$ by $\frac{3}{3}$ .

$[\begin{array}{c} \frac{55}{42} \\ \frac{395}{84} \\ \frac{8 \cdot 28}{84} - \frac{19 \cdot 3}{28 \cdot 3} \end{array}]$

Step 2.13.4

Multiply $28$ by $3$ .

$[\begin{array}{c} \frac{55}{42} \\ \frac{395}{84} \\ \frac{8 \cdot 28}{84} - \frac{19 \cdot 3}{84} \end{array}]$

Step 2.14

Combine the numerators over the common denominator.

$[\begin{array}{c} \frac{55}{42} \\ \frac{395}{84} \\ \frac{8 \cdot 28 - 19 \cdot 3}{84} \end{array}]$

Step 2.15

Simplify the numerator.

Tap for more steps...

Step 2.15.1

Multiply $8$ by $28$ .

$[\begin{array}{c} \frac{55}{42} \\ \frac{395}{84} \\ \frac{224 - 19 \cdot 3}{84} \end{array}]$

Step 2.15.2

Multiply $- 19$ by $3$ .

$[\begin{array}{c} \frac{55}{42} \\ \frac{395}{84} \\ \frac{224 - 57}{84} \end{array}]$

Step 2.15.3

Subtract $57$ from $224$ .

$[\begin{array}{c} \frac{55}{42} \\ \frac{395}{84} \\ \frac{167}{84} \end{array}]$