§ 1.5 Addition of Real Numbers. The result of adding two or more numbers is called the sum of the numbers. You can think of gains and losses to find sums.

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§ 1.5 Addition of Real Numbers

The result of adding two or more numbers is called the sum of the numbers. You can think of gains and losses to find sums. For example, what if you had $14 in your pocket, but then lost a ten dollar bill. You would have (-10) = 4 Now…another case - what if you lost your wallet with $12 in it and then had to borrow another $5 to get through the day, but then misplaced the $5 also. Your loss of 12 followed by a loss of 5 would be represented by (-5) = -17 Now suppose you lost a twenty dollar bill, but then worked and made $16. This would be represented by (-20) + (+16) = -4 Sum of two numbers Blitzer, Introductory Algebra, 5e – Slide #2 Section 1.5

Using the Number Line to Find a Sum Let a and b represent real numbers. To find a + b using the number line, – Start at a. – If b is positive, move b units to the right. If b is negative, move b units to the left. If b is 0, stay at a. – The number where we finish on the number line represents the sum of a and b. Blitzer, Introductory Algebra, 5e – Slide #3 Section 1.5

Add 7 + (-9) using the number line. 7 + (-9) = Start at 7. Move 9 units left. Finish at -2. Adding real numbers using a number line Blitzer, Introductory Algebra, 5e – Slide #4 Section 1.5

Identity and Inverse Properties of Addition Let a be a real number, a variable or an algebraic expression. PropertyMeaningExamples Identity Property of Addition Zero can be deleted from a sum. a + 0 = a 0 + a = a = x = 2x -3y + 0 = -3y Inverse Property of Addition The sum of a real number and its additive inverse gives 0, the additive identity. a + (-a) = 0 (-a) + a = (-5) = 0 6x + (-6x) = 0 (-2y) + 2y = 0 Blitzer, Introductory Algebra, 5e – Slide #5 Section 1.5

Adding Two Numbers having the Same Sign 1. Add the absolute values. 2. Use the common sign as the sign of the sum.  Example: = -10 Add the absolute values: = 10 Use the common sign. Blitzer, Introductory Algebra, 5e – Slide #6 Section 1.5

Adding Two Numbers with Different Signs 1. Subtract the smaller absolute value from the larger absolute value. 2. Use the sign of the number with the greater absolute value.  Example: = -6 Subtract absolute values: = 6 Use the sign of the number with the greater absolute value. Blitzer, Introductory Algebra, 5e – Slide #7 Section 1.5

Example: Simplifying Algebraic Expressions with like terms. Simplify: -12x + 5x ( )x -7x Blitzer, Introductory Algebra, 5e – Slide #8 Section 1.5

Blitzer, Introductory Algebra, 5e – Slide #9 Section 1.5 Adding Real Numbers Add: -12+(-5) EXAMPLE We are adding numbers having like signs. So we just add the absolute values and take the common sign as the sign of the sum. Answer: -17 EXAMPLE Add: We are adding numbers having unlike signs. We just take the difference of the absolute values (difference is 4) and then take the sign of the number that has the largest absolute value (that’s the 14 and it is positive). Answer: +4

Blitzer, Introductory Algebra, 5e – Slide #10 Section 1.5 Rules for Addition of Real Numbers To add two real numbers with like signs, add their absolute values. Use the common sign as the sign of the sum. To add two real numbers with different signs, subtract the smaller absolute value from the greater absolute value. Use the sign of the number with the greater absolute value as the sign of the sum.