Answer:
1. Multiplication as Repeated Addition
2. Applying the Rule to Negative Numbers
3. Applying the Rule to Two Negative Numbers
Explanation:
The rule that "minus times minus equals plus" is a fundamental concept in mathematics known as the product of two negative numbers. It may seem counterintuitive at first, but there are several reasons why this rule holds true.
1. Multiplication as Repeated Addition: To understand why minus times minus equals plus, we can think of multiplication as repeated addition. When we multiply a positive number by another positive number, we are essentially adding the first number repeatedly. For example, 3 x 2 means adding 3 two times: 3 + 3 = 6.
2. Applying the Rule to Negative Numbers: Now let's consider negative numbers. When we multiply a positive number by a negative number, we are essentially adding the positive number repeatedly but in the opposite direction. For example, 3 x (-2) means adding 3 two times, but in the opposite direction: -3 + (-3) = -6.
3. Applying the Rule to Two Negative Numbers: When we multiply a negative number by another negative number, we can think of it as adding the negative number repeatedly but in the opposite direction twice. For example, (-3) x (-2) means adding -3 two times, but in the opposite direction each time: -3 + (-3) = -6.
However, there is another way to think about this situation. When we multiply a negative number by another negative number, we can also interpret it as the opposite of adding a positive number repeatedly. In this case, multiplying two negative numbers results in a positive number. For example, (-3) x (-2) means the opposite of adding 3 two times: -(-3 + (-3)) = 6.
In summary, the rule that minus times minus equals plus holds true because multiplication can be thought of as repeated addition, and multiplying two negative numbers can be interpreted as adding a positive number repeatedly or as the opposite of adding a positive number repeatedly. This concept is fundamental in mathematics and is consistent with the rules of arithmetic.