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To add two integers that have the exact same sign, simply combine their quantities and keep the shared sign. Visually using counters, because all tokens are the identical color, no neutral pairs are created. Therefore, adding 5 positive counters to 3 positive counters directly yields 8 positives ($$5 + 3 = 8$$), just as combining 5 negative counters with 3 negative counters directly results in 8 negatives ($$-5 + (-3) = -8$$).

Adding Integers with the Same Sign

A project manager is totaling two separate budget overruns for a department, both of which are recorded as negative integers. According to the rule for adding integers with the same sign, state the two-step procedure used to determine the final total overrun.

Procedure for Adding Same-Sign Integer Losses

Imagine you are a department supervisor training a new administrative assistant to reconcile monthly expense reports. You notice they are unsure how to total two separate line items that are both recorded as negative integers (representing two different debts). To ensure they follow the correct mathematical protocol, state the formal rule for adding two integers that have the same sign. In your response, clearly specify the action taken regarding the absolute values and how the sign of the final sum is determined.

Standard Procedure for Aggregating Consistent Data Signs

Visualizing the addition of same-sign integers involves combining counters of a single color without forming neutral pairs. For the sum $$5 + 3$$, joining 5 blue (positive) counters with 3 blue counters produces 8 blue counters, meaning $$5 + 3 = 8$$. Likewise, to evaluate $$-5 + (-3)$$, putting 5 red (negative) counters together with 3 red counters results in an accumulated 8 red counters, which demonstrates that $$-5 + (-3) = -8$$.

Adding $$5 + 3$$ and $$-5 + (-3)$$ with Counters

Applying the same-sign rule:
- $$ 1 + 4 = 5 $$: One positive counter combined with four more positive counters gives five positives.
- $$ -1 + (-4) = -5 $$: One negative counter combined with four more negative counters gives five negatives.

In both cases the addends share the same sign, so their absolute values ($$ 1 $$ and $$ 4 $$) are added to get $$ 5 $$, and the common sign is attached to the result.

Adding $$ 1 + 4 $$ and $$ -1 + (-4) $$

When you add two negative integers, the sum is always negative.

You use red counters to add two negative integers. What do you do with the counters?

Match each term to how it works when adding integers with the same sign.

When adding two integers with the same sign using counters, why are no neutral pairs formed?

Put the steps in order to add $$-5 + (-3)$$.

To add two integers with the same sign, add their _____ and keep the shared sign.

Case context:
The integers are $$-5$$ and $$-3$$. Both have the same sign.

Question:
Add $$-5$$ and $$-3$$. Describe your steps, then give the sum and its sign.

Sample answer:
Add the absolute values: $$5 + 3 = 8$$. Keep the shared sign, negative, so $$-5 + (-3) = -8$$.

Key points:
- Add the absolute values of the two integers.
- Keep the sign shared by both integers.
- $$5 + 3 = 8$$
- $$-5 + (-3) = -8$$

Rubric:
Full credit: adds absolute values, keeps the shared sign, and states the correct sum $$-8$$. Partial credit: correct sum but sign or steps unclear. No credit: incorrect sum or no explanation.

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