Use the properties of operations and rules for multiplying and dividing signed numbers to solve: (−4)×(7/5)×(−3/4)÷(7 1/5) l

1 answer

To solve the expression \((-4) \times \left(\frac{7}{5}\right) \times \left(-\frac{3}{4}\right) \div (7 \frac{1}{5})\), we can break it down step by step, applying the properties of operations for multiplying and dividing signed numbers.

  1. Convert the mixed number into an improper fraction: \[ 7 \frac{1}{5} = 7 + \frac{1}{5} = \frac{35}{5} + \frac{1}{5} = \frac{36}{5} \]

  2. Re-write the expression: \[ (-4) \times \left(\frac{7}{5}\right) \times \left(-\frac{3}{4}\right) \div \left(\frac{36}{5}\right) \]

  3. Replace the division with multiplication by the reciprocal: \[ (-4) \times \left(\frac{7}{5}\right) \times \left(-\frac{3}{4}\right) \times \left(\frac{5}{36}\right) \]

  4. Multiply the numbers:

    • First, combine the signs: \((-4) \times (-\frac{3}{4}) = 3\).
    • Now we will multiply everything else: \[ 3 \times \left(\frac{7}{5}\right) \times \left(\frac{5}{36}\right) \]
  5. Combine the fractions: \[ 3 \times \frac{7 \times 5}{5 \times 36} = \frac{3 \times 7}{36} = \frac{21}{36} \]

  6. Simplify the fraction: \[ \frac{21}{36} = \frac{7}{12} \]

The final answer is: \[ \frac{7}{12} \]