This document provides instructions and examples for adding, subtracting, multiplying, and dividing positive and negative numbers. It begins with placing values on a number line and defining positive and negative numbers. It then covers rules for adding and subtracting, such as keeping the sign of the larger number if the signs are different. Examples are provided for applying these rules. The document finishes with rules for multiplying and dividing, such as the product of like signs being positive and different signs being negative. More examples are given to reinforce these concepts.

1. Warm Up ActivityDraw a number line like the one below. Place the following values in the proper position on the number line: a) – 9 b) 5 c) – ½ d)1 ¾ e) –2 f) 7 g) –6 h) 4 ½

2. Adding and Subtracting Positive and Negative Numbers Positive number – a number greater than 0 Example: 1 , 5 , 100 , 7500 Negative number – a number less than 0 Example: -1 , -7 , -55 , -800***Adding a negative is the same as subtracting a positive***El adición de una negativa es igual que restando un positivo5 + (–1) -> 5 – 1 ***Subtracting a negative is the same as adding a positive***Restar una negativa es igual que agregando un positivo7 – (–8) -> 7 + 8

3. Adding and Subtracting Positive and Negative Numbers Using a Number Line–7 + 5 =–7 + 5 = –2

4. Show Me the Money: Adding and Subtracting Positive and Negative NumbersThink of a negative number as being in debt or owing someone moneyThink of a positive number as getting paid or paying off debtIf you are $27 in debt and you get paid $13, how much money do you have?If you are $9 in debt and spend another $10, how much are you in debt now?

5. Rules for Adding and Subtracting Positive and Negative NumbersChange the problem to addition if it is not already an addition problem. Cambia el problema a la adición. ** subtracting a positive is the same as adding a negative ** ** subtracting a negative is the same as adding a positive**Once the problem has changed been changed to addition, determine if the signs of the numbers are the same or different.Determina si las muestras son el mismo o diferentesIf the signs are the same, add (sum) them together and keep the sign.Si las muestras son el mismo, agrega y guarda la muestraIf the signs are different, subtract (difference) the numbers and keep the sign of the larger number.Si lasmuestras son diferentes, reste y guarda la muestra del numeromasgrande.

6. Rules for Adding and Subtracting Positive and Negative NumbersChange the problem to addition if it is not already an addition problem. ** subtracting a positive is the same as adding a negative ** ** subtracting a negative is the same as adding a positive**Once the problem has changed been changed to addition, determine if the signs of the numbers are the same or different.If the signs are the same, add (sum) them together (add their absolute values) and keep the sign.If the signs are different, subtract (difference) the numbers (subtract their absolute values) and keep the sign of the larger number (the number with the larger absolute value).

7. Examples: 1) – 10 + 12 =Step 1: Is the problem written as addition?Step 2: Are the signs the same or different?Step 3: Should we add or subtract?Step 4: What is the sign of our answer?2) – 15 – (– 7) =Step 1: Is the problem written as addition?Step 2: Are the signs the same or different?Step 3: Should we add or subtract?Step 4: What is the sign of our answer?

8. Try It!1. –5 – (–8) 2. –35 + (–11)3. –10 – 6 – (–9)

9. Rules for Multiplying and DividingPositive and Negative Numbers1. The product of like signs is positive. (+)(+) = (+) (–)(–) = (+)2. The product of different signs is negative. (–)(+) = (–) (+)(–) = (–)3. The quotient of like signs is positive. (+) ÷(+) = (+) (–) ÷(–) = (+)4. The quotient of different signs is negative. (+) ÷(–) = (–) (–) ÷(+) = (–)

10. Remember the Rules: Identify the signs of the two numbers that you are multiplying and cover those two signs with your fingers.The remaining sign is the sign of your answer.

11. Remember the Rules: Think of “good” as being positive. Think of “bad” as negative .Think of “come to town” as positive. Think of “leave town” as negative. Then think of these stories: When the good guys come to town this is good. (+) (+) = (+) When the good guys leave town this is bad. (+) (–) = (–) When the bad guys come to town this is bad. (–) (+) = (–) When the bad guys leave town this is good. (–) (–) = (+)

12. Try It!1. –15 (–8) = 4. – 48 ÷ (– 6) = 5. –49 = 7 2. 36(–11) = 6. –81 = 0 3. (–10)(– 26)(–9) =