Resolva as expressões:

a) $ \frac{2}{3} + 2 \left( \frac{3}{2} \right)^2 - \left( -\frac{4}{3} \right)^2 = $

b) $ -\frac{5}{4} \cdot \frac{3}{7} \div \frac{1}{3} = $

c) $ \frac{2}{3} + \frac{5}{4} - 2 = \frac{5}{5} $

d) $ \left( -\frac{2}{3} \right)^2 + \frac{2}{7} - \frac{4}{7} - 3 \left( \frac{7}{5} \right) = $

Q: Resolva as expressões: a) $ \frac{2}{3} + 2 \left( \frac{3}{2} \right)^2 - \left( -\frac{4}{3} \right)^2 = $ b) $ -\frac{5}{4} \cdot \frac{3}{7} \div \frac{1}{3} = $ c) $ \frac{2}{3} + \frac{5}{4} - 2 = \frac{5}{5} $ d) $ \left( -\frac{2}{3} \right)^2 + \frac{2}{7} - \frac{4}{7} - 3 \left( \frac{7}{5} \right) = $

Vamos resolver as expressões: a) $\frac{2}{3} + 2 \left(\frac{3}{2}\right)^2 - \left(-\frac{4}{3}\right)^2$ 1. Calcule $\left(\frac{3}{2}\right)^2 = \frac{9}{4}$. 2. Calcule $\left(-\frac{4}{3}\right)^2 = \frac{16}{9}$. 3. Multiplique: $2 \times \frac{9}{4} = \frac{18}{4} = \frac{9}{2}$. 4. Some e subtraia: $\frac{2}{3} + \frac{9}{2} - \frac{16}{9}$. Para somar e subtrair, encontre o mínimo múltiplo comum (MMC) dos denominadores, que é 18. - $\frac{2}{3} = \frac{12}{18}$ - $\frac{9}{2} = \frac{81}{18}$ - $\frac{16}{9} = \frac{32}{18}$ Agora, some e subtraia: $\frac{12}{18} + \frac{81}{18} - \frac{32}{18} = \frac{61}{18}$. b) $-\frac{5}{4} \cdot \frac{3}{7} \div \frac{1}{3}$ 1. Multiplique: $-\frac{5}{4} \cdot \frac{3}{7} = -\frac{15}{28}$. 2. Divida por $\frac{1}{3}$: $-\frac{15}{28} \times 3 = -\frac{45}{28}$. c) $\frac{2}{3} + \frac{5}{4} - 2$ Encontre o MMC dos denominadores, que é 12. - $\frac{2}{3} = \frac{8}{12}$ - $\frac{5}{4} = \frac{15}{12}$ - $2 = \frac{24}{12}$ Some e subtraia: $\frac{8}{12} + \frac{15}{12} - \frac{24}{12} = -\frac{1}{12}$. d) $\left(-\frac{2}{3}\right)^2 + \frac{2}{7} \div \frac{-4}{7} - 3\left(\frac{7}{5}\right)$ 1. Calcule $\left(-\frac{2}{3}\right)^2 = \frac{4}{9}$. 2. Divida: $\frac{2}{7} \div \frac{-4}{7} = \frac{2}{7} \times \frac{-7}{4} = -\frac{1}{2}$. 3. Multiplique: $3 \times \frac{7}{5} = \frac{21}{5}$. Para somar e subtrair, encontre o MMC dos denominadores, que é 90. - $\frac{4}{9} = \frac{40}{90}$ - $-\frac{1}{2} = -\frac{45}{90}$ - $\frac{21}{5} = \frac{378}{90}$ Agora, some e subtraia: $\frac{40}{90} - \frac{45}{90} - \frac{378}{90} = -\frac{383}{90}$.

Question

Resolva as expressões:

a) $ \frac{2}{3} + 2 \left( \frac{3}{2} \right)^2 - \left( -\frac{4}{3} \right)^2 = $

b) $ -\frac{5}{4} \cdot \frac{3}{7} \div \frac{1}{3} = $

c) $ \frac{2}{3} + \frac{5}{4} - 2 = \frac{5}{5} $

d) $ \left( -\frac{2}{3} \right)^2 + \frac{2}{7} - \frac{4}{7} - 3 \left( \frac{7}{5} \right) = $

Accepted Answer

Vamos resolver as expressões:

a) $\frac{2}{3} + 2 \left(\frac{3}{2}\right)^2 - \left(-\frac{4}{3}\right)^2$

1. Calcule $\left(\frac{3}{2}\right)^2 = \frac{9}{4}$.
2. Calcule $\left(-\frac{4}{3}\right)^2 = \frac{16}{9}$.
3. Multiplique: $2 \times \frac{9}{4} = \frac{18}{4} = \frac{9}{2}$.
4. Some e subtraia: $\frac{2}{3} + \frac{9}{2} - \frac{16}{9}$.

Para somar e subtrair, encontre o mínimo múltiplo comum (MMC) dos denominadores, que é 18.

- $\frac{2}{3} = \frac{12}{18}$
- $\frac{9}{2} = \frac{81}{18}$
- $\frac{16}{9} = \frac{32}{18}$

Agora, some e subtraia:

$\frac{12}{18} + \frac{81}{18} - \frac{32}{18} = \frac{61}{18}$.

b) $-\frac{5}{4} \cdot \frac{3}{7} \div \frac{1}{3}$

1. Multiplique: $-\frac{5}{4} \cdot \frac{3}{7} = -\frac{15}{28}$.
2. Divida por $\frac{1}{3}$: $-\frac{15}{28} \times 3 = -\frac{45}{28}$.

c) $\frac{2}{3} + \frac{5}{4} - 2$

Encontre o MMC dos denominadores, que é 12.

- $\frac{2}{3} = \frac{8}{12}$
- $\frac{5}{4} = \frac{15}{12}$
- $2 = \frac{24}{12}$

Some e subtraia:

$\frac{8}{12} + \frac{15}{12} - \frac{24}{12} = -\frac{1}{12}$.

d) $\left(-\frac{2}{3}\right)^2 + \frac{2}{7} \div \frac{-4}{7} - 3\left(\frac{7}{5}\right)$

1. Calcule $\left(-\frac{2}{3}\right)^2 = \frac{4}{9}$.
2. Divida: $\frac{2}{7} \div \frac{-4}{7} = \frac{2}{7} \times \frac{-7}{4} = -\frac{1}{2}$.
3. Multiplique: $3 \times \frac{7}{5} = \frac{21}{5}$.

Para somar e subtrair, encontre o MMC dos denominadores, que é 90.

- $\frac{4}{9} = \frac{40}{90}$
- $-\frac{1}{2} = -\frac{45}{90}$
- $\frac{21}{5} = \frac{378}{90}$

Agora, some e subtraia:

$\frac{40}{90} - \frac{45}{90} - \frac{378}{90} = -\frac{383}{90}$.

Resolva as expressões: a)

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