Michigan League of Academic Games

~Adding without a + sign~ (All Levels)

We've had a previous lesson about dividing fractions (also called double division), which is the same as multiplying. This is a similar lesson about adding using two - signs (without a + sign). Especially in the Minor and Elementary Divisions, the solutions often are simple, such as 8+2. In this case, all of the players at the table may have the same solution, which will probably lead to a forceout. But, if you have a different solution using some of the same cubes (the 8 and the 2), but also using - signs, you may have an advantage and cause one of the other players to challenge P-Flub. Your solution would be 8-(0-2), which is the same as 8+2.

The easiest way that I teach this lesson is with a number line. You can draw a number line on a paper going from -12 on the left side all the way to 12 on the right side. Write a - on the top left of the number line, because these are the negative numbers. Write a + on the far right side of the number line, because these are the positive numbers. Most of you should know that you move toward the left when you are subtracting positive numbers (such as 5-3, starting at 5 and moving 3 to the left to equal 2). Conversely, if you are adding 3+6, you would start at 3 and move 6 places to the right because you are adding.

With negative numbers, the process is a little different. In a solution such as 8-(0-2), you must do the 0-2 first because it is in parentheses. Using the same process from above, you find that 0-2 equals -2. So, the new problem is 8-(-2). If we were trying to figure out 8-2, we would start at 8 and move 2 to the left. But, because we have -2, we must move in the opposite direction (because -2 is the opposite of +2). So, we start at 8 and move 2 to the right, which is the same as 8+2, which, of course, equals 10. Other similar solutions are 7-(0-3), 5-(0-5), 6-(1-5) and 4-(2-8).

Practice problems:
1. 3-(5-9)
2. 9-(1-9)
3. 2-(0-1)
4. 6-(7-8)
5. 1-(3-6)
6. 0-(1-4)
7. 4-(0-9)
8. 3-(1-7)
9. 5-(2-6)
10. 7-(2-9)

Special thanks to Assistant Executive Director Rod Beard of University Prep Academy for this lesson.

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