Pergunta

Simplify. Write your answer as a proper or improper fraction in simplest form. (frac (27)/(11))((3)/(7))=(square )/(square )
Solução

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ThiagoProfissional · Tutor por 6 anos
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To simplify the given expression, we need to divide the fraction $\frac{27}{11}$ by the fraction $\frac{3}{7}$.<br /><br />To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by swapping the numerator and denominator.<br /><br />So, the reciprocal of $\frac{3}{7}$ is $\frac{7}{3}$.<br /><br />Now, we can rewrite the given expression as:<br /><br />$\frac{\frac{27}{11}}{\frac{3}{7}} = \frac{27}{11} \times \frac{7}{3}$<br /><br />To multiply fractions, we multiply the numerators together and the denominators together.<br /><br />Multiplying the numerators: $27 \times 7 = 189$<br /><br />Multiplying the denominators: $11 \times 3 = 33$<br /><br />Therefore, the simplified expression is:<br /><br />$\frac{\frac{27}{11}}{\frac{3}{7}} = \frac{189}{33}$<br /><br />To simplify the fraction $\frac{189}{33}$, we can divide both the numerator and denominator by their greatest common divisor (GCD).<br /><br />The GCD of 189 and 33 is 3.<br /><br />Dividing the numerator by 3: $189 \div 3 = 63$<br /><br />Dividing the denominator by 3: $33 \div 3 = 11$<br /><br />Therefore, the simplified fraction is:<br /><br />$\frac{189}{33} = \frac{63}{11}$<br /><br />So, the final answer is:<br /><br />$\frac{\frac{27}{11}}{\frac{3}{7}} = \frac{63}{11}$
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