Same Sign Rule
With addition or subtraction, when you're calculating numbers with the same sign, keep the sign and add the numbers.
Four Steps for the Same Sign Rule
1) Ask yourself whether the number is positive or negative.
2) Write the sign in step one, followed by a set of parenthesis.
3) Put the numbers inside the parenthesis and put plus signs in between them.
4) Add the numbers, then take away the parenthesis.
Mixed Sign Rule
With addition or subtraction, when you're calculating numbers with different signs, keep the sign of the larger number, then ignore the signs and subtract the smaller number from the larger one.
Four Steps for the Mixed Sign Rule
1) Ignore the signs and pick the largest number.
2) Write the sign for the largest number down, followed by a set of parenthesis.
3) Again, ignoring the signs, place the largest number in the parentheses followed by the smallest, and put a minus sign between them.
4) Subtract the smaller number from the largest number, then take away the parenthesis.
How to Solve a Problem with Lots of Numbers with Mixed Signs
1) Combine all the positive numbers in one group and all the negative numbers in another group, creating two problems.
2) Use the Same Sign Rule to solve each problem.
3) Combine the results from the two problems using the Mixed Sign Rule.
What is the Neighbor Sign Rule?
Sometimes problems are written in a way where positive and negative signs are next to each other (e.g. 3 + (-5) or 3 + -5)) The Neighbor Sign Rules show us how to handle these cases.
Neighbor Sign Rule
If the signs are both the same, they get combined into a positive. If the signs are different, they get combined into a negative.
When a Problem Contains Neighbor Signs, Same Signs, and Mixed Signs, in What Order Should I Apply the Three Rules?
1) Use the Neighbor Sign Rule.
2) Combine the positive numbers in one group and the negative numbers in another group, creating two groups.
2) Solve both problems using the Same Sign Rule.
3) Combine the results of the two problems using the Mixed Sign Rule.
When you multiply two numbers with the same sign, the answer is positive. When you multiply two numbers with different signs, the answer is negative.
Muliplication Rule for More Than Two Numbers
If the number of negative signs in the problem is even, the answer will be positive. If the number of negative signs is odd, the answer will be negative.