MATH TUTORING
OPERATIONS WITH INTEGERS: EASY WAYS TO DEAL WITH “NEGATIVE-POSITIVE” NUMBERS
Victoria is an 8-th grader. At the moment she is struggling with calculating the slope of linear equations. Although Victoria knows how to find the slope, she experiences difficulties in pure calculations. Every time she has to subtract a negative number from a negative she gets the wrong result. At first I thought that my student was just not paying attention; however, when the same miscalculation happened three times in a row, I realized that we had to put aside the slope and focus on a very important topic: Operations with integers.
The rules for adding or subtracting integers are simple:
The same sign: ADD!!! If both integers are positive, the sum is positive. When both numbers are negative, the result is negative.
2 + 3 = 5 -4 – 3 = -7
-2 + – 3 = -5 -2 – 2 = -4
-4 + -6 = -10 -4 – 6 = -10
-5 + -9 = -14 -10 – 3 = -13
Opposite signs: SUBTRACT a smaller number from a bigger one! If a bigger number is positive, the result is positive. If a bigger number is negative, the result is negative.
– 2 + 1 = -1
-8 + 4 = – 4
-2 + 2 = 0
-4 + 4 = 0
-8 + 6 = -2
-10 + 10 = 0
Remember: two negatives in a row turn into positive!!!
10 – ( – 5) is the same as 10 + 5
10 –( – 5) = 15
10 –(- 10) = 20
12 – -11 = 23
1 – -2 = 3
Now, time for practice! (After you are done, check your answers and calculate percent. I hope you’ll get 100%)
Test #1
- -5 + – 12 = 10) -144 – 6 =
- -7 + -7 = 11) -1 – 2 =
- -1 + – 8 = 12) -0.5 – 1 =
- 2 + 100 = 13) -4 – 100 =
- -2 + – 100 = 14) -30 – 70 =
- 13 +(- 7) = 15) -7 – 13 =
- -3 –( – 2) = 16) -7 – (-11) =
- 100 + -100 = 17) 102 – (-100) =
- -9 – (- 1) = 18) -15 + 2 =
Answers:
- -17; 2) -14; 3) -9; 4) 102; 5) -102; 6) 6; 7) -1; 8) 0; 9) -8;
- 10) -150; 11) -3; 12) -1.5; 13) -104; 14) -100; 15) -20; 16) 4; 17)202; 18) -13