a is a positive number.
b is a negative number.
The sum of a+b is...?
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a is a positive number.
b is a negative number.
The sum of a+b is...?
We will use trial and error in order to test this:
Let's assume that the value of the positive number is greater than the value of the negative number 1 and 2.
1+(-2) = -1
The result is negative.
We will try to make the value of the second number greater than the first 2 and 1.
2+(-1)= 1
The result is positive.
That is, we can see that the result depends on the values of the two numbers, so we cannot know from the beginning what the result will be.
It is not possible to know.
What will be the sign of the result of the next exercise?
\( (-2)\cdot(-4)= \)
Because the magnitude (absolute value) of the negative number might be larger! For example: 2 + (-7) = -5. The negative number 'wins' when it's larger in absolute value.
It's all about which number is farther from zero. If |a| > |b|, the sum is positive. If |b| > |a|, the sum is negative. If they're equal, the sum is zero!
Think of it like a tug-of-war! The positive number pulls one way, the negative pulls the other. Whichever side has more 'strength' (larger absolute value) wins and determines the sign.
Yes! When you see 'a is positive, b is negative' without specific values, always test with different examples. Try cases where the positive is larger, then where the negative is larger.
Then we could determine the exact answer! For instance, if a = 4 and b = -6, then a + b = -2. But without knowing the values, any result is possible.
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