The sum of two numbers is positive.
Therefore, the two numbers are...?
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The sum of two numbers is positive.
Therefore, the two numbers are...?
Testing through trial and error:
Let's assume both numbers are positive: 1 and 2.
1+2 = 3
Positive result.
Let's assume both numbers are negative -1 and -2
-1+(-2) = -3
Negative result.
Let's assume one number is positive and the other negative: 1 and -2.
1+(-2) = -1
Negative result.
Let's test a situation where the value of the first number is greater than the second: -1 and 2.
2+(-1) = 1
Positive result.
That is, we can see that when both numbers are positive, or in certain types of cases when one number is positive and the other negative, the sum is positive.
Answers a+c are correct.
What will be the sign of the result of the next exercise?
\( (-2)\cdot(-4)= \)
No, never! When you add two negative numbers, you're combining negative values: (-3) + (-5) = -8. The result is always more negative than either individual number.
This happens when the positive number has a larger absolute value than the negative number. For example: 7 + (-3) = 4 because 7 is greater than 3.
Absolute value is the distance from zero, ignoring the sign. So |-5| = 5 and |5| = 5. When comparing mixed numbers, the one with larger absolute value 'wins' and determines the sign of the sum.
Yes! Remember these patterns:
Because a positive sum can result from two different scenarios: either both numbers are positive (answer a), OR one number is positive and one is negative with the positive having larger absolute value (answer c).
Test concrete examples! Don't just think abstractly. Pick specific numbers like 2 and 3, or -4 and 7, then calculate their sums. This helps you see which combinations actually work.
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