Use the properties of operations and rules for multiplying and dividing signed numbers to solve:
Sure! I can help you solve problems using the properties of operations and rules for multiplying and dividing signed numbers. Please provide me with the specific problem you would like me to solve.
To solve problems involving the properties of operations and rules for multiplying and dividing signed numbers, you need to understand the following rules:
Rule 1: When you multiply or divide two numbers with the same sign, the result is always positive.
Rule 2: When you multiply or divide two numbers with different signs, the result is always negative.
Now, let's solve some problems using these rules:
Problem 1: (-4) x (-3)
To solve this problem, multiply the two numbers:
(-4) x (-3) = 12
Since both numbers are negative (same sign), the result is positive.
Problem 2: 6 ÷ (-2)
To solve this problem, divide the two numbers:
6 ÷ (-2) = -3
Since the numbers have different signs, the result is negative.
Problem 3: (-8) ÷ 4
To solve this problem, divide the two numbers:
(-8) ÷ 4 = -2
Since the numbers have different signs, the result is negative.
Problem 4: (-9) x 2 ÷ (-3)
To solve this problem, follow the order of operations (multiplication before division):
(-9) x 2 ÷ (-3) = -18 ÷ (-3) = 6
First, multiply (-9) and 2 to get -18. Then, divide -18 by -3 to get 6. Both operations involve numbers with the same sign, so the result is positive.
Remember to always follow the order of operations (parentheses, exponents, multiplication/division from left to right, and addition/subtraction from left to right) when solving more complex problems.
For this response, I will be using the following rules for multiplying and dividing signed numbers:
1. When multiplying or dividing two numbers with the same sign, the result is positive.
2. When multiplying or dividing two numbers with different signs, the result is negative.
Let's solve an example using these rules:
Problem: Solve -4 x (-5)
Solution: Since we have two negative numbers, we can apply rule #1. By multiplying -4 and -5, we get: -4 x -5 = 20.
Therefore, -4 x (-5) equals 20.
Here's another example:
Problem: Solve -9 ÷ (-3)
Solution: We have two negative numbers, so we can use rule #1. By dividing -9 by -3, we get: -9 ÷ -3 = 3.
Therefore, -9 ÷ (-3) equals 3.