Show how to find the quotient 18 divided by (-6) by using the following:
a) the idea of division as finding a missing factor.
b) the procedures for integer division.
a) -3 because -6 * _-3_ = 18
b) -3
a) The idea of division as finding a missing factor:
To find the quotient of 18 divided by (-6) using the idea of division as finding a missing factor, we need to determine what number multiplied by (-6) gives us 18.
Let's look at the steps:
Step 1: Start with the dividend, which is 18.
Step 2: Divide 18 by (-6) to find the missing factor.
Step 3: To find the missing factor, we need to determine what number multiplied by (-6) gives us 18. In other words, we need to solve the equation (-6) * x = 18.
Step 4: Divide both sides of the equation by (-6) to isolate the variable x: x = 18 / (-6).
Step 5: Simplify the division: x = -3.
Step 6: The missing factor is -3.
Step 7: Therefore, the quotient of 18 divided by (-6) is -3.
b) The procedures for integer division:
To find the quotient of 18 divided by (-6) using the procedures for integer division, we can follow these steps:
Step 1: Write down the division problem: 18 ÷ (-6).
Step 2: Ignore the signs initially and perform the division as if the numbers were positive, so calculate 18 ÷ 6. The result is 3.
Step 3: Consider the signs. Since one number is positive and the other is negative, the quotient will be negative.
Step 4: Therefore, the quotient of 18 divided by (-6) is -3.
a) Using the idea of division as finding a missing factor:
To find the quotient when dividing 18 by (-6) using the idea of division as finding a missing factor, we need to determine what number, when multiplied by (-6), equals 18.
Since multiplying a negative number by a positive number gives a negative result, we can assume that both the quotient and the missing factor will be negative.
To find the missing factor, we can set up the equation:
x * (-6) = 18
To solve for x, we divide both sides of the equation by (-6):
x = 18 / (-6)
Dividing 18 by (-6), we get:
x = -3
Therefore, the quotient when dividing 18 by (-6) using the idea of division as finding a missing factor is -3.
b) Using the procedures for integer division:
To find the quotient when dividing 18 by (-6) using the procedures for integer division, we follow these steps:
1. Divide the absolute values of the numbers: 18 ÷ 6 = 3.
2. Determine the sign of the quotient:
- If the signs of the dividend (18) and the divisor (-6) are the same, the quotient will be positive (+).
- If the signs of the dividend and the divisor are different, the quotient will be negative (-).
In this case, the dividend is positive (+18) and the divisor is negative (-6), so the quotient will be negative.
Therefore, the quotient when dividing 18 by (-6) using the procedures for integer division is -3.