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3) \( \frac{7}{6} \div \frac{5}{6}-\left(\frac{1}{30}\right) \)

Ask by Thornton Bernard. in Angola
Feb 11,2025

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Tutor-Verified Answer

Answer

A resposta é 41/30.

Solution

Primeiro, realizamos a divisão:   (7/6) ÷ (5/6) = (7/6) × (6/5) = 7/5 Em seguida, subtraímos 1/30:   7/5 – 1/30 Para subtrair, encontramos o denominador comum. Note que:   7/5 = (7×6)/(5×6) = 42/30 Portanto:   42/30 – 1/30 = (42 – 1) / 30 = 41/30 Resposta: 41/30

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To solve the expression \( \frac{7}{6} \div \frac{5}{6}-\left(\frac{1}{30}\right) \), we start by dividing the two fractions. Dividing by a fraction is the same as multiplying by its reciprocal: \[ \frac{7}{6} \div \frac{5}{6} = \frac{7}{6} \times \frac{6}{5} = \frac{7 \times 6}{6 \times 5} = \frac{7}{5} \] Now we subtract \( \frac{1}{30} \) from \( \frac{7}{5} \). To do that, we need a common denominator. The least common multiple of 5 and 30 is 30. So we convert \( \frac{7}{5} \): \[ \frac{7}{5} = \frac{7 \times 6}{5 \times 6} = \frac{42}{30} \] Now we can subtract: \[ \frac{42}{30} - \frac{1}{30} = \frac{42 - 1}{30} = \frac{41}{30} \] Therefore, the final result is: \[ \frac{41}{30} \]

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