Question

Perform the indicated operation.

$- 75 ÷ \left(- 5\right)$

Short answer

The quotient is15

Step-by-step solution

Step-1 – Apply the concept of quotient

In mathematics, the quotient is the number obtained by dividing one number by another number.

Step-2 – Example for the quotient

For example, if we divide the number 6 by 3, the result so obtained is 2, which is the quotient. It is the answer from the division process. The quotient can be an integer or a decimal number or a fraction.

Example: 18 divide by 3, the result or quotient is 6.

$18 ÷ 3 = 6$

Step- 3 – Rules and example of Division of integers 

RULE 1: The quotient of a positive integer and a negative integer is negative.

RULE 2: The quotient of two positive integers is positive.

RULE 3: The quotient of two negative integers is positive.

Examples:

Rule 1: (– 8) ÷ (+4) = – 2

Rule 2: (+6) ÷ (– 3) = – 2

Rule 3: (+9) ÷ (+3) = +3

Rule 4: (– 6) ÷ (– 2) = +3

– Evaluate the expression: – 75 ÷ (– 5)

Rule: The quotient of two negative integers is positive.

To determine the quotient it is needed to divide $- 75 \text{by} (- 5)$

$-75÷\left(-5\right) = 15$

The quotient is $15$