Math

QuestionUse counters to show two integers with different signs that add to a positive number. Explain your reasoning.

Studdy Solution

STEP 1

Assumptions1. We are using counters to model two integers. . The two integers have different signs, meaning one is positive and the other is negative.
3. The sum of the two integers is positive.

STEP 2

Let's choose two integers with different signs such that their sum is positive. For instance, we can choose +5 and -.

STEP 3

Now, we will use counters to model these integers.For the positive integer +5, we can represent it with5 positive counters.
For the negative integer -3, we can represent it with3 negative counters.

STEP 4

To find the sum of these two integers, we combine the positive and negative counters.When a positive counter and a negative counter are combined, they cancel each other out. This is because adding a positive number and a negative number of the same magnitude results in zero.

STEP 5

In our case, we have5 positive counters and3 negative counters.When we combine them,3 positive counters and3 negative counters will cancel each other out, leaving us with2 positive counters.

STEP 6

Therefore, the sum of +5 and -3 is +2.We know the sum is positive because we are left with positive counters.The sum of two integers with different signs will be positive if the absolute value of the positive integer is greater than the absolute value of the negative integer.
In our case, the absolute value of +5 (which is5) is greater than the absolute value of -3 (which is3), so the sum is positive.

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