Final answer:
The question involves providing examples of basic arithmetic operations (addition, subtraction, multiplication, and division) using combinations of positive and negative numbers. Examples for each operation are given and explained to demonstrate how the sign of the result depends on the signs of the numbers involved in the operation.
Step-by-step explanation:
The student has asked for three examples of each basic arithmetic operation with different combinations of positive and negative numbers. Here are the examples explained step-by-step:
Addition:
When two positive numbers are added, such as 3 + 2 = 5, the result is positive.
When two negative numbers are added, like -4 + (-2) = -6, the sum is negative.
Adding numbers with opposite signs, subtract the smaller number from the larger, for instance, -5 + 3 = -2.
Multiplication:
Multiplying two positive numbers, such as 2 * 3 = 6, results in a positive product.
Multiplying two negative numbers, for example (-4) * (-3) = 12, also yields a positive product.
When numbers with opposite signs are multiplied, like (-3) * 2 = -6 or 4 * (-4) = -16, the product is negative.
Subtraction:
Subtracting a positive number from another, such as 5 - 3 = 2, simply reduces the first number by the second.
In cases like 2 - (-6) = 2 + 6 = 8, the double negative turns into a positive.
Division:
Dividing two positive numbers follows the same rule as multiplication, for instance, 15 / 3 = 5.
If both numbers are negative, such as -12 / (-4) = 3, the result is positive.
When dividing numbers with opposite signs, like 9 / (-3) = -3, the quotient is negative.