a is a positive number.
b is a negative number.
What kind of number is the sum of b and a?
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a is a positive number.
b is a negative number.
What kind of number is the sum of b and a?
We will illustrate with an example:
Let's assume that a is 1 and b is -2
1+ (-2) =
1-2 = -1
Answer: Negative
Now let's assume that a is 2
and b is -1
2+(-1) =
2-1 = 1
Even though the operation is negative, the number remains positive.
That is, if the absolute value of the positive number (a) is greater than that of the negative (b), the result will still be positive.
As we do not have data regarding this information, it is impossible to know what the sum of a+b will be.
.Impossible to know.
What will be the sign of the result of the next exercise?
\( (-2)\cdot(-4)= \)
Because the magnitude matters! If the positive number a is larger than the absolute value of negative b, the sum will be positive. For example: 5 + (-2) = 3 (positive).
If |a| = |b|, then a + b = 0. For example, if a = 3 and b = -3, then 3 + (-3) = 0. The positive and negative cancel each other out.
That's exactly the point! Since we don't know the specific values of a and b, we cannot determine which absolute value is larger, so the sign is impossible to know.
All three outcomes are possible!
Yes! When adding a positive and negative number: The result takes the sign of whichever number has the larger absolute value. If we don't know the magnitudes, we can't predict the sign.
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