Questions: Perform the following operations: 1(-10/3)= -10/3 ÷ 1= 1 ÷ (-10/3)=

Solution Steps

1. For the first operation, multiplying any number by 1 results in the number itself. Therefore, \(1 \times \left(-\frac{10}{3}\right)\) is \(-\frac{10}{3}\).
2. For the second operation, dividing a number by 1 results in the number itself. Therefore, \(-\frac{10}{3} \div 1\) is \(-\frac{10}{3}\).
3. For the third operation, dividing 1 by a fraction is equivalent to multiplying 1 by the reciprocal of the fraction. Therefore, \(1 \div \left(-\frac{10}{3}\right)\) is equal to multiplying 1 by \(-\frac{3}{10}\).

The operation \(1 \times \left(-\frac{10}{3}\right)\) results in the number itself, as multiplying by 1 does not change the value. Therefore, the result is: \[ -\frac{10}{3} = -3.333 \]

The operation \(-\frac{10}{3} \div 1\) also results in the number itself, as dividing by 1 does not change the value. Therefore, the result is: \[ -\frac{10}{3} = -3.333 \]

The operation \(1 \div \left(-\frac{10}{3}\right)\) is equivalent to multiplying 1 by the reciprocal of the fraction. The reciprocal of \(-\frac{10}{3}\) is \(-\frac{3}{10}\). Therefore, the result is: \[ 1 \times \left(-\frac{3}{10}\right) = -0.3 \]

Final Answer