# Lesson 1.4 - Adding Real Numbers

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### Properties :

Properties Identity Property of Addition Examples: 0 + 5 = 5 -5 + 0 = -5 Inverse Property of Addition Examples: 17 + (-17) = 0 -17 + 17 = 0

Start at –3. Move right 5 units. Start at 3. a. 3 + (–5) b. –3 + 5 3 + (–5) = –2 Use a number line to simplify each expression. Move left 5 units. ALGEBRA 1 LESSON 1-4 Adding Real Numbers 1-4 -3 + 5 = 2

### Rules :

Rules Adding Numbers With the Same Sign Add their absolute values and give the sum the same sign Examples: 2 + 6 = 8 -2 + (-6) = -8 Adding Numbers With Different Signs *Subtract the absolute values and give the answer the same sign as the greatest absolute value. Examples: -2 + 6 = 4 2 + (-6) = -4

Simplify each expression. 12 + (–23) b. –6.4 + (–8.6) The difference of the absolute values is 11. The negative addend has the greater absolute value, so the sum is negative. Since both addends are negative, add their absolute values. The sum is negative. ALGEBRA 1 LESSON 1-4 Adding Real Numbers 1-4

### You try: :

You try: Find the sum: (a.) -7 + (-4) -11 (b.) -26.3 + 8.9 -17.4

### Real World Problem Solving :

The water level in a lake rose 6 inches and then fell 11 inches. Write an addition statement to find the total change in water level. 6 + (–11) = –5   The water level fell 5 inches. ALGEBRA 1 LESSON 1-4 Real World Problem Solving 1-4

### You try: :

You try: The temperature falls 15 degrees and then rises 18 degrees. Use addition to find the change in temperature. -15 + 18 = 3, 3° is the change in temperature

### Evaluating Expressions :

Evaluate 3.6 + (–t) for t = –1.7. 3.6 + (–t) 3.6 + (–(–1.7)) Substitute –1.7 for t. 3.6 + [1.7] –(–1.7) means the opposite of –1.7, which is 1.7. 5.3 Simplify. ALGEBRA 1 LESSON 1-4 Evaluating Expressions 1-4

### You try: :

You try: Evaluate the expression for t = -7.1 -t + 7.49 -(-7.1) + 7.49 7.1 + 7.49 14.59

### Real-World Problem Solving :

A scuba diver who is 88 ft below sea level begins to ascend to the surface. Define: Let r = the number of feet the diver rises. a.  Write an expression to represent the diver’s depth below sea level after rising any number of feet. Think: 88 ft below sea level plus  feet diver rises Write: –88 + r –88 + r ALGEBRA 1 LESSON 1-4 Real-World Problem Solving 1-4

### Problem Continued: :

Problem Continued: b.  Find the new depth of the scuba diver after rising 37 ft. –88 + r –88 + 37 Substitute 37 for r. – 51 Simplify. The scuba diver is 51 ft below sea level.

### You try: :

You try: The temperature one winter morning is -14°F. Define a variable and write an expression to find the temperature after it changes. Then evaluate your expression for a decrease of 11 degrees Fahrenheit. C = change in temperature -14 + c -14 + c -14 + (-11) -25 The temperature decreased -25°F