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Signed Numbers

Chapter 9. Signed Numbers. § 9.1. Adding Signed Numbers. – 5. – 4. – 3. – 2. – 1. 0. 1. 2. 3. 4. 5. – 4.8. 1.5. Negative numbers. Positive numbers. The Number Line. A number line is a line on which each point is associated with a number.

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Signed Numbers

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  1. Chapter 9 Signed Numbers

  2. § 9.1 Adding Signed Numbers

  3. – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 – 4.8 1.5 Negative numbers Positive numbers The Number Line A number line is a line on which each point is associated with a number. The set of positive numbers, negative numbers, and zero is the set of signed numbers.

  4. – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 “greater than” “less than” Ordering Numbers Signed numbers are named in order on the number line. Smaller numbers are on the left. – 4 < – 1 2 > – 1 Example: Replace the ? with or >. > 3 ? –2 Since 3 lies to the right of –2, we know that 3 > –2.

  5. – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 Symbol for absolute value Distance of 4 Distance of 5 Absolute Value The absolute value of a number is the distance between that number and zero on a number line. | –4| = 4 |5| = 5

  6. –3 + –11 We add the absolute values of the numbers 3 and 11. Adding Two Numbers with Same Signs Addition Rule for Two Numbers with the Same Sign To add two numbers with the same sign: • Add the absolute value of the numbers. • Use the common sign in the answer. Example: Add (– 3) + (– 11). – 14 A negative sign is used because we added two negative numbers.

  7. 5 + – 9 We subtract the absolute values of the numbers 5 and 9. Adding Two Numbers with Different Signs Addition Rule for Two Numbers with Different Signs To add two numbers with different signs: • Subtract the absolute value of the numbers. • Use the sign of the number with the larger absolute value. Example: Add 5 + (– 9). – 4 A negative sign is used because the sign of the larger number is negative.

  8. – 24 + 38 – 36 + 4 We subtract the absolute values of the numbers 24 and 38. Adding Two Numbers with Different Signs Example: Add (–24) + (38). 14 The answer is positive because the sign of the larger number is positive. Example: Add (– 36) + 4. – 32

  9. – 56 + 14 14 + – 56 – 42 – 42 Adding Two Numbers with Different Signs Commutative Property of Addition For any real numbers a and b, a + b = b + a. Example: This morning, the temperature in Alaska was –56°F. This afternoon, the temperature rose 14°F. What was the new temperature? Because addition is commutative, we could also have added the temperatures this way:

  10. – 50 – 70 – 64 – 64 Adding Three or More Signed Numbers Example: Add (–56) + 6 + (–14). Because addition is commutative, the numbers can be added in any way. (–56) + 6 + (–14) (–56) + (–14) + 6 or + (–14) + 6

  11. 4,950 3,550 + 2,575 – 2,345 + –725 –3,070 11,075 $8,005 profit Adding Three or More Signed Numbers Associative Property of Addition For any real numbers a,b, and c, (a + b) + c = a + (b + c). Example: The following table represents the profit and loss for the past five months at Sally’s Boutique. Find the overall profit. It is usually easier to add the positive numbers and the negative numbers separately.

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