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negative A plus sign or a positive sign has no effect on the number. The number stays positive. A negative sign or a subtraction sign will reverse a number to negative. A negative sign and a subtraction sign on the same number will reverse a number to negative and then back to positive. This is because the first sign (the subtraction sign) reverses it to negative and the second sign (the negative sign) reverses the reverse. This makes the number a positive.
Therefore - -7 is ... positive 5 On the last question - -7 is acting positive because of a double reverse (a subtraction sign and a negative sign on the same number).
Signs always belong to the next number. For example in the problem 5 - 7, the subtraction sign belongs to the 7. Therefore the 7 will act like a negative. The 5 has no sign and is understood to be positive.
Because of this in the problem 5 + -7, both the plus sign and the negative sign belong to...
7 a negative number On the last problem 5 + -7, both signs belonged to the 7.
Because the + sign has no effect and the negative reverses the number, 7 will act like ... a positive number 8 Because the + sign has no effect and the negative reverses the number, 7 will act like a negative.
When the numbers are acting the same (both negative or both positive) we add and keep the sign (same signs; sum them up and keep the sign).
Therefore, in the problem -3 + -5 the answer is...
-8 -2 2 10 In the problem -3 + -5 the answer is -8 because both numbers were acting negative.
When the signs are the same, add and keep the sign.
In the problem -3 -7 the answer is...
4 -4 -10 9 In the problem -3 - 7 the answer is -10 because both numbers are acting negative. -3 is clearly negative and the subtraction sign belonging to 7 make it act like a negative.
In the problem 3 - -6 the answer is...
3 -9 -3 7 In the problem 3 - -6 the answer is 9. Both the subtraction sign and the negative sign belong to the six. Both signs cause a double reverse making the 6 act like a positive. Therefore, both numbers are acting positive, add and keep the sign.
In the problem 3 + 4 the answer is ...
-7 -1 1 -1 In the problem 3 + 4 the answer is 7. Come on. What else could it be? Both numbers as positive, add and keep the sign.
Now for the fun! Absolute value is how far from zero. It ignores the signs. When numbers are acting with different signs, the largest absolute value (the greatest distance from zero ignoring the direction) rules the sign.
Which has the largest absolute value?
6 -7 1 10 Which has the largest absolute value... -1, 6, -7, or 1? -7 does because it has the greatest distance from zero. Therefore in a problem with different signs, it would rule.
Let's try again. How about the largest absolute value for these...
-15 -10 18 the same; therefore, add and keep the sign. different; therefore, subtract and take the sign of the larger absolute value. The largest absolute value for 10, -15, -10, and 18 has to be 18 because it has the greatest distance from zero.
Now let's see if the signs are acting the same or different.
In the problem -3 + 7 the signs are ...
different; therefore, subtract and take the sign of the larger absolute value. the same; therefore, add and keep the sign. In the problem -3 + 7 the signs are different; therefore, subtract and take the sign of the larger absolute value. The answer would be 4.
In the problem -6 - -3, the signs are
different; therefore, subtract and take the sign of the larger absolute value. the same; therefore, add and keep the sign. In the problem -6 - -3, the signs are different (because the subtraction sign and the negative sign on three create a double reverse and make it act positive); therefore, subtract and take the sign of the larger absolute value. The answer is -3.
In the problem -6 -7, the signs are...
the same; therefore, add and keep the sign. different; therefore, subtract and take the sign of the larger absolute value. In the problem -6 -7, the signs are the same (the subtraction sign on 7 makes it act like a negative); therefore, add and keep the sign. The answer is -13.
In the problem 5 - -3, the signs are...
the same; therefore, add and keep the sign. differently; therefore, subtract and take the sign of the larger absolute value. In the problem 5 - -3, the signs are the same (double reverses on 3 make it act positive); therefore, add and keep the sign. The answer is 8.
In the problem -5 - -3, the numbers are both acting...
differently; therefore, subtract and take the sign of the larger absolute value. the same; therefore, add and keep the sign. In the problem -5 - -3, the numbers are both acting differently (the double reverse on 3 makes it act positively); therefore, subtract and take the sign of the larger absolute value. The answer is -2.
And now one last problem of this type before we move on.
In the problem -5 + -5, the signs are...
-12 In the problem -5 + -5, the signs are the same. Add and keep the sign. The answer is -10.
-4 - 8 =
Now ask yourself are the numbers acting the same (add) or differently (subtract).
12 -4 4 -12 On the previous problem: -4 - 8 (same signs; add and keep the sign) = -12
-4 + 8 =
12 -4 4 -12 On the previous problem: -4 + 8 = (different signs find a difference; largest absolute value rules) 4.
4 - 8 =
12 -4 4 -17 On the previous problem: 4 - 8 = (different signs find a difference - larger absolute value rules the sign) -4
10 - -7 = 17 -3 3 13 On the previous problem: 10 - -7 = (double reverse on 7 make it act positive - same signs sum them up) 17.
5 - 8 = -13 -3 3 -13 On the previous problem: 5 - 8 = (different signs - find a difference - larger absolute value rules) -3.
-5 - 8 = 13 -3 3 -13 On the previous problem: -5 - 8 = (Same signs, sum them up and keep the sign) -13.
-5 + 8 = 13 -3 3 -13 On the previous problem: -5 + 8 = (different signs; find a difference - larger absolute value rules the sign) 3
5 - 8 = 13 -3 3 -13 On the previous problem: 5 - 8 = (different signs; find a difference - larger absolute value rules) -3
5 + 8 = 13 -3 3 -13 On the previous problem: 5 + 8 (same signs; sum them up - keep the sign. 13
10 - - 3 = 13 -7 7 |