Homework Corrections (page 1 of 2) A#13 / 1-1 Homework Worksheet 1. possible answers: a) the difference of 4 and y; y less than 4 b) the quotient of r and 5; r divided by 5 2. t + 20 3. a) 1 b) 30 4. algebraic expression: 2x; possible real-world situation: Two algebra classes each have x number of students, so 2x represents the number of algebra students in both classes.

Homework Corrections (page 2 of 2) A#13 / 1-1 Homework Worksheet 5. x x + 12 1 13 2 14 3 15 4 16

Warm Up Simplify. 1. |-3| 2. -|4| 1. |-3| 2. -|4| Write an improper fraction to represent each mixed number. 4. Write a mixed number to represent each improper fraction. 6.

Lesson Objective: I will be able to … Add real numbers Page 5 Lesson Objective: I will be able to … Add real numbers Subtract real numbers Language Objective: I will be able to … Read, write, and listen about vocabulary, key concepts, and examples

Classwork Assignment #14 Adding, Subtracting, Multiplying, and Dividing Real Numbers with Algebra Tiles Worksheet

All the numbers on a number line are called real numbers All the numbers on a number line are called real numbers. You can use a number line to model addition and subtraction of real numbers. Addition To model addition of a positive number, move right. To model addition of a negative number move left. Subtraction To model subtraction of a positive number, move left. To model subtraction of a negative number move right.

Example 1: Adding and Subtracting Numbers on a Number line Page 6 Add or subtract using a number line. A. –4 + (–7) To add –7, move left 7 units. + (–7) Start at 0. Move left to –4. –4 –4+ (–7) = –11 11 10 9 8 7 6 5 4 3 2 1 To subtract –6, move right 6 units. B. 3 – (–6) Start at 0. Move right to 3. –6 + 3 3 – (–6) = 9 -3 -2 -1 1 2 3 4 5 6 7 8 9

8 7 6 5 4 3 2 1 1 2 Your Turn 1 Subtract using a number line: Page 6 Subtract using a number line: –5 – (–6.5) To subtract negative 6.5 move right 6.5 units. –5 Start at 0. Move left to –5. – (–6.5) 8 7 6 5 4 3 2 1 1 2 –5 – (–6.5) = 1.5

5 units 5 units - 6 - 5 - 4 - 3 - 2 - 1 1 2 3 4 5 6 |–5| = 5 |5| = 5 Page 5 The absolute value of a number is the distance from zero on a number line. The absolute value of 5 is written as |5|. 5 units 5 units - 6 - 5 - 4 - 3 - 2 - 1 1 2 3 4 5 6 |–5| = 5 |5| = 5

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Example 2: Adding Real Numbers Page 6 Example 2: Adding Real Numbers Add. When the signs of numbers are different, find the difference of the absolute values: A. Use the sign of the number with the greater absolute value. The sum is negative. B. x + (–68) for x = 52 x + (–68) = 52 + (–68) First substitute 52 for x. When the signs of the numbers are different, find the difference of the absolute values. 68 – 52 = 16 Use the sign of the number with the greater absolute value. –16 The sum is negative.

Your Turn 2 Add. y + (–2) for y = –6 y + (–2) = (–6) + (–2) = –8 Page 7 Add. y + (–2) for y = –6 y + (–2) = (–6) + (–2) First substitute –6 for y. When the signs are the same, find the sum of the absolute values: 6 + 2 = 8. Both numbers are negative, so the sum is negative. = –8

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Example 3: Subtracting Real Numbers Page 7 Example 3: Subtracting Real Numbers Subtract. A. –6.7 – 4.1 = –6.7 + (–4.1) To subtract 4.1, add –4.1. When the signs of the numbers are the same, find the sum of the absolute values: 6.7 + 4.1 = 10.8. = –10.8 Both numbers are negative, so the sum is negative. B. 5 – (–4) = 5 + 4 To subtract –4 add 4. = 9 Find the sum of the absolute values.

Example 3 Continued Subtract. C. First substitute for z. To subtract Page 7 Subtract. C. First substitute for z. To subtract , add . Rewrite with a denominator of 10. When the signs of the numbers are the same, find the sum of the absolute values: . = Write the answer in the simplest form. Both numbers are negative, so the sum is negative.

Both numbers are positive so, the sum is positive. 4 Your Turn 3 Page 7 Subtract: To subtract add . –3 1 2 3 When the signs of the numbers are the same, find the sum of the absolute values: = 4. 3 1 2 + Both numbers are positive so, the sum is positive. 4

Cornell Notes Fill in the Essential Question: “How do I add and subtract with real numbers?” Write two or three main ideas from this lesson in the Notes section. Write a Question for each main idea. (The answer to the question should be the main idea.) Summarize the answers to your questions in the Summary section. Page 8