Question

integer rules - subtraction
change to adding:
change signs - keep the first, change addition to subtraction, change last sign to its opposite. (keep, flip, change)
-6 - (-3)=-6+(+3)=-3
6 - (+3)=6+(-3)=3
-6 - (+3)=-6+(-3)=-9
6 - (-3)=6+(+3)=9
-9 - -4 = __ -9 - 4 = 9 - 4 = 9 - -4 = __
-6 - -2 = __ -6 - 2 = 6 - 2 = 6 - -2 = __
-3 - -5 = __ -3 - 5 = 3 - 5 = 3 - -5 = __
-7 - -7 = __ -7 - 7 = 7 - 7 = 7 - -7 = __
0 - -8 = __ 0 - 8 = __
(now mix up the order of the signs) ...
1 - -7 = __ -1 - 7 = -1 - -7 = 1 - 7 = __
-8 - 2 = __ 8 - -2 = 8 - 2 = -8 - -2 = __

1. in your own words, what are the steps you need to take to subtract two integers? ____
2. can you use these same steps and rules to subtract integers of any size? ____

Explanation:

Step1: Recall integer - subtraction rule

Change subtraction to addition by keeping the first number, changing the subtraction sign to an addition sign, and changing the sign of the second number.

Step2: Solve the subtraction problems

• For \(-9-(-4)\), it becomes \(-9 + 4=-5\).
• For \(-9 - 4\), it becomes \(-9+( - 4)=-13\).
• For \(9 - 4\), it is \(9+( - 4)=5\).
• For \(9-(-4)\), it is \(9 + 4 = 13\).
• For \(-6-(-2)\), it is \(-6 + 2=-4\).
• For \(-6 - 2\), it is \(-6+( - 2)=-8\).
• For \(6 - 2\), it is \(6+( - 2)=4\).
• For \(6-(-2)\), it is \(6 + 2 = 8\).
• For \(-3-(-5)\), it is \(-3 + 5 = 2\).
• For \(-3 - 5\), it is \(-3+( - 5)=-8\).
• For \(3 - 5\), it is \(3+( - 5)=-2\).
• For \(3-(-5)\), it is \(3 + 5 = 8\).
• For \(-7-(-7)\), it is \(-7 + 7 = 0\).
• For \(-7 - 7\), it is \(-7+( - 7)=-14\).
• For \(7 - 7\), it is \(7+( - 7)=0\).
• For \(7-(-7)\), it is \(7 + 7 = 14\).
• For \(0-(-8)\), it is \(0 + 8 = 8\).
• For \(0 - 8\), it is \(0+( - 8)=-8\).
• For \(1-(-7)\), it is \(1 + 7 = 8\).
• For \(-1 - 7\), it is \(-1+( - 7)=-8\).
• For \(-1-(-7)\), it is \(-1 + 7 = 6\).
• For \(1 - 7\), it is \(1+( - 7)=-6\).
• For \(-8 - 2\), it is \(-8+( - 2)=-10\).
• For \(8-(-2)\), it is \(8 + 2 = 10\).
• For \(8 - 2\), it is \(8+( - 2)=6\).
• For \(-8-(-2)\), it is \(-8 + 2=-6\).

Step3: Answer question 1

Keep the first integer as it is. Change the subtraction operation to addition. Change the sign of the second integer to its opposite. Then perform the addition operation.

Step4: Answer question 2

Yes, these steps and rules can be used to subtract integers of any size. The rules are based on the fundamental properties of integers and the relationship between addition and subtraction, and they work for all integers regardless of their magnitude.

Answer:

-9-(-4)=-5; -9 - 4=-13; 9 - 4 = 5; 9-(-4)=13; -6-(-2)=-4; -6 - 2=-8; 6 - 2 = 4; 6-(-2)=8; -3-(-5)=2; -3 - 5=-8; 3 - 5=-2; 3-(-5)=8; -7-(-7)=0; -7 - 7=-14; 7 - 7 = 0; 7-(-7)=14; 0-(-8)=8; 0 - 8=-8; 1-(-7)=8; -1 - 7=-8; -1-(-7)=6; 1 - 7=-6; -8 - 2=-10; 8-(-2)=10; 8 - 2 = 6; -8-(-2)=-6

1. Keep the first integer, change subtraction to addition, change the sign of the second integer, then add.
2. Yes