Question

Find the quotient. $$56 \div\left(-2 \frac{4}{7}\right)$$

Short answer

-\(\frac{196}{9}\)

Step-by-step solution

Convert Mixed Number to Improper Fraction

First, convert \(-2 \frac{4}{7}\) to an improper fraction. An improper fraction is a fraction in which the numerator is greater than the denominator. To convert a mixed number into an improper fraction, multiply the denominator by the whole number part, then add the numerator. So, \(-2 \frac{4}{7} = -2*7 + 4 = -14 + 4 = -18/7 \). Therefore, the problem becomes \(56 \div \frac{-18}{7}\).

Preparation for Division

Recall that dividing by a fraction is the same as multiplying by its reciprocal. Accordingly, flip \(\frac{-18}{7}\) to get \(-\frac{7}{18}\). The operation now becomes a multiplication: \(56 \times -\frac{7}{18}\).

Perform Multiplication

Proceed to multiply 56 by \(\frac{-7}{18}\). This results in \(-\frac{392}{18}\).

Simplify Fraction

Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor. In this case, both 392 and 18 can be divided by 2, making the resulting fraction \(-\frac{196}{9}\).