Álgebra linear Exemplos

[\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}]

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

Etapa 1

Adicione os elementos correspondentes.

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

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

Etapa 2

Simplifique cada elemento.

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Etapa 2.1

Para escrever

\frac{8}{3}

$\frac{8}{3}$ como fração com um denominador comum, multiplique por

\frac{14}{14}

$\frac{14}{14}$ .

[\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}]

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

Etapa 2.2

Para escrever

- \frac{19}{14}

$- \frac{19}{14}$ como fração com um denominador comum, multiplique por

\frac{3}{3}

$\frac{3}{3}$ .

[\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}]

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

Etapa 2.3

Escreva cada expressão com um denominador comum de

42

$42$ , multiplicando cada um por um fator apropriado de

1

$1$ .

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Etapa 2.3.1

Multiplique

\frac{8}{3}

$\frac{8}{3}$ por

\frac{14}{14}

$\frac{14}{14}$ .

[\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}]

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

Etapa 2.3.2

Multiplique

3

$3$ por

14

$14$ .

[\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}]

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

Etapa 2.3.3

Multiplique

\frac{19}{14}

$\frac{19}{14}$ por

\frac{3}{3}

$\frac{3}{3}$ .

[\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}]

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

Etapa 2.3.4

Multiplique

14

$14$ por

3

$3$ .

[\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}]

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

[\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}]

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

Etapa 2.4

Combine os numeradores em relação ao denominador comum.

[\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}]

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

Etapa 2.5

Simplifique o numerador.

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Etapa 2.5.1

Multiplique

8

$8$ por

14

$14$ .

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

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

Etapa 2.5.2

Multiplique

- 19

$- 19$ por

3

$3$ .

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

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

Etapa 2.5.3

Subtraia

57

$57$ de

112

$112$ .

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

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

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

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

Etapa 2.6

Para escrever

\frac{8}{3}

$\frac{8}{3}$ como fração com um denominador comum, multiplique por

\frac{28}{28}

$\frac{28}{28}$ .

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

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

Etapa 2.7

Para escrever

\frac{57}{28}

$\frac{57}{28}$ como fração com um denominador comum, multiplique por

\frac{3}{3}

$\frac{3}{3}$ .

[\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}]

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

Etapa 2.8

Escreva cada expressão com um denominador comum de

84

$84$ , multiplicando cada um por um fator apropriado de

1

$1$ .

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Etapa 2.8.1

Multiplique

\frac{8}{3}

$\frac{8}{3}$ por

\frac{28}{28}

$\frac{28}{28}$ .

[\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}]

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

Etapa 2.8.2

Multiplique

3

$3$ por

28

$28$ .

[\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}]

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

Etapa 2.8.3

Multiplique

\frac{57}{28}

$\frac{57}{28}$ por

\frac{3}{3}

$\frac{3}{3}$ .

[\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}]

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

Etapa 2.8.4

Multiplique

28

$28$ por

3

$3$ .

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

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

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

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

Etapa 2.9

Combine os numeradores em relação ao denominador comum.

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

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

Etapa 2.10

Simplifique o numerador.

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Etapa 2.10.1

Multiplique

8

$8$ por

28

$28$ .

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

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

Etapa 2.10.2

Multiplique

57

$57$ por

3

$3$ .

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

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

Etapa 2.10.3

Some

224

$224$ e

171

$171$ .

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

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

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

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

Etapa 2.11

Para escrever

\frac{8}{3}

$\frac{8}{3}$ como fração com um denominador comum, multiplique por

\frac{28}{28}

$\frac{28}{28}$ .

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

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

Etapa 2.12

Para escrever

- \frac{19}{28}

$- \frac{19}{28}$ como fração com um denominador comum, multiplique por

\frac{3}{3}

$\frac{3}{3}$ .

[\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}]

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

Etapa 2.13

Escreva cada expressão com um denominador comum de

84

$84$ , multiplicando cada um por um fator apropriado de

1

$1$ .

Toque para ver mais passagens...

Etapa 2.13.1

Multiplique

\frac{8}{3}

$\frac{8}{3}$ por

\frac{28}{28}

$\frac{28}{28}$ .

[\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}]

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

Etapa 2.13.2

Multiplique

3

$3$ por

28

$28$ .

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

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

Etapa 2.13.3

Multiplique

\frac{19}{28}

$\frac{19}{28}$ por

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Etapa 2.13.4

Multiplique

28

$28$ por

3

$3$ .

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

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

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

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

Etapa 2.14

Combine os numeradores em relação ao denominador comum.

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

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

Etapa 2.15

Simplifique o numerador.

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Etapa 2.15.1

Multiplique

8

$8$ por

28

$28$ .

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

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

Etapa 2.15.2

Multiplique

- 19

$- 19$ por

3

$3$ .

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

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

Etapa 2.15.3

Subtraia

57

$57$ de

224

$224$ .

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

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

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

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

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

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