Final answer:
The quotient of 12 / -6 is -2, which is a negative number located to the left of zero on the number line. The quotient of -15 / -3 is 5, which is a positive number located to the right of zero on the number line.
Step-by-step explanation:
The question requires us to identify the positions on the number line for the quotients of two expressions: 12 / -6 and -15 / -3. Using the rule that when a number is divided by another number, it follows the multiplication rules for the sign, we will find the quotients for both expressions.
- For 12 / -6, we are dividing a positive number by a negative number. According to the rules, the quotient will have a negative sign. Therefore, 12 / -6 = -2.
- For -15 / -3, we are dividing a negative number by a negative number. The quotient will have a positive sign. Hence, -15 / -3 = 5.
On the number line, the quotient for 12 / -6 will be at point -2 and the quotient for -15 / -3 will be at point 5.
To determine the correct locations on the number line representing the quotients of the expressions 12 / -6 and -15 / -3, we need to apply the rules for division of positive and negative numbers.
a. For 12 / -6, since the dividend (12) is positive and the divisor (-6) is negative, the quotient will be negative. Therefore, the correct location on the number line is -2.
b. For -15 / -3, both the dividend and divisor are negative, so the quotient will be positive. Therefore, the correct location on the number line is 5.