Adding Integers pp

Transcription

1 LESSON 2-1 Adding Integers pp Vocabulary integers (p. 60) opposites (p. 60) absolute value (p. 60) Additional Examples Example 1 Use a number line to find the sum. (6) You finish at, so (6) 2. Example 2 Add. 1 (2) Think: Find the of 2 and ; use the sign of. 23 Holt Pre-Algebra

2 LESSON 2-1 CONTINUED Example 3 Evaluate c 4 for c 8. c 4 ( ) 4 Replace c with. Think: Find the of 8 and ; use the sign of. Try This 1. Use a number line to find the sum. (3) Add. (4) 1 3. Evaluate d 7 for d Holt Pre-Algebra

3 LESSON 2-2 Subtracting Integers pp Additional Examples Example 1 Subtract. A ( ) Add the of 4. B. 8 (5) Same sign; use the sign of the integers. 8 (5) 8 5 Add the of 5. C. 6 (3) Same sign; use the sign of the. 6 (3) 6 3 Add the opposite of. 6 3; use the sign of. Example 2 Evaluate the expression for the given value of the variable. A. 8 j for j 6 8 j 8 ( ) Substitute for j. 8 6 Add the of 6. Same sign; use the sign of the. 25 Holt Pre-Algebra

4 LESSON 2-2 CONTINUED B. 9 y for y 4 9 y 9 ( ) Substitute 4 for. 9 4 Add the opposite of. 9 4; use the of 9. C. n 6 for n 2 n 6 6 Substitute for n. 2 (6) the opposite of 6. Same sign; use the sign of the. Try This 1. Subtract. 7 (8) 2. Evaluate the expression for the given value of the variable. 5 r for r 2 26 Holt Pre-Algebra

5 LESSON 2-3 Multiplying and Dividing Integers pp Additional Examples Example 1 Multiply or divide. A. 6(4) Signs are. Answer is. B. 8(5) Signs are the. Answer is. C are different. Answer is. D are the same. Answer is. Example 2 Simplify. A. 3(6 12) Subtract inside the. 3( ) Think: The signs are. The answer is. 27 Holt Pre-Algebra

6 LESSON 2-3 CONTINUED Example 3 Complete a table of solutions for y 3x 1 for x 2, 1, 0, 1, and 2. Plot the points on a coordinate plane. x 3x 1 y (x, y) 4 y (, ) 2 x (, ) 4 2 O (, ) 4 (, ) 6 8 (, ) 10 Try This 1. Multiply or divide. 3(2) 2. Simplify. 3(6 9) 28 Holt Pre-Algebra

7 LESSON 2-4 Solving Equations Containing Integers pp Additional Examples Example 1 Solve. A. x 3 6 x 3 6 x to both sides. x B. 5 r 9 5 r 9 x acbcd 5 r 9 Add 5 to both sides. C. 6 8 n r 6 8 n The is already isolated. n D. z 6 3 z 6 3 Add integers. (6) (6) Add to each side. z 29 Holt Pre-Algebra

8 LESSON 2-4 CONTINUED Example 2 Solve. A. 5x 35 Divide both sides by. x z B. 5 4 z 4 5 Multiply both sides by. z Try This 1. Solve. a Solve. z Holt Pre-Algebra

9 LESSON 2-5 Solving Inequalities Containing Integers pp Additional Examples Example 1 Solve and graph. A. k 3 2 k 3 2 Subtract from both sides. k 0 B. r 9 12 r 9 12 r 9 12 Add to both sides. r 15 C. u 5 3 u u to both sides. u Holt Pre-Algebra

10 LESSON 2-5 CONTINUED Example 2 Solve and graph. 3y 15 Divide each side by ; changes to. y Try This 1. Solve and graph. y Solve and graph. 8y Holt Pre-Algebra

11 LESSON 2-6 Exponents pp Vocabulary power (p. 84) exponential form (p. 84) exponent (p. 84) base (p. 84) Additional Examples Example 1 Write in exponential form. A Identify how many times is a factor. B. d d d d d d d d d d Identify how many times d is a. Example 2 Evaluate. A Find the product of 3 s. 33 Holt Pre-Algebra

12 LESSON 2-6 CONTINUED B. (3) 5 (3) 5 Find the product of 3 s. Example 3 Simplify ( ) 6(4) ( ) 6(4) Evaluate the. ( ) 6(4) Subtract inside the. 23 from left to right. from left to right. Try This 1. Write in exponential form. (3) (3) (3) (3) 2. Evaluate. (9) 3 3. Simplify ( ) Holt Pre-Algebra

13 LESSON 2-7 Properties of Exponents pp Additional Examples Example 1 Multiply. Write the product as one power. A exponents. B. n 5 n 7 exponents. Example 2 Divide. Write the product as one power. 5 A exponents. 10 B. x x 9 Subtract. Think: x 1 35 Holt Pre-Algebra

14 LESSON 2-7 CONTINUED Example 3 A light-year, or the distance light travels in one year, is almost centimeters. To convert this number to kilometers, you must divide by How many kilometers is a light-year? Subtract. A light-year is almost km. Try This 1. Multiply. Write the product as one power Divide. Write the product as one power A ship has 10 7 kilograms of grain loaded into its cargo hold. A metric ton is 10 3 kilograms. How many metric tons of grain were loaded? 36 Holt Pre-Algebra

15 LESSON 2-8 Look for a Pattern in Integer Exponents pp Additional Examples Example 1 Evaluate the powers of 10. A B C Example 2 Evaluate Write the ; change the of the exponent Holt Pre-Algebra

16 LESSON 2-8 CONTINUED Example 3 Evaluate Bases are the same, so the exponents Write the. ; change the sign of the Check: Try This 1. Evaluate the power of Evaluate (10) Evaluate Holt Pre-Algebra

17 LESSON 2-9 Scientific Notation pp Vocabulary scientific notation (p. 96) Additional Examples Example 1 Write each number in standard notation. A B Think: Move the decimal right places by the reciprocal. C Think: Move the decimal 3 places Think: Move the decimal right places. 39 Holt Pre-Algebra

18 LESSON 2-9 CONTINUED Example 2 Write in scientific notation Move the decimal to get a number between and Set up notation. Think: The decimal needs to move left to change 7.09 to , so the exponent will be. Think: The decimal needs to move places. So written in scientific notation is. Check Try This 1. Write the number in standard notation Write in scientific notation. 40 Holt Pre-Algebra

19 Chapter 2 Möbius Mobile absolute value base exponent exponential form integer opposite power scientific notation Directions 1. Cut each strip from the page before writing the definition. 2. Begin the definition on the same line as the word. 3. If a second line is needed, flip the strip toward you and continue on the top line. If a third line is needed, flip the strip back to the original side and continue on the next line. Continue this process until finished. 4. Hold the strip with the original side in view. Bring the two ends toward each other so the labels on the tabs are visible. 5. Flip the tab on the right and place it over tab A such that neither tab is visible. 6. Tape them in place. 7. Use string and the strips to build a Möbius mobile. Developed in cooperation with The Bag Ladies. 41 Holt Pre-Algebra

20 Chapter 2 Möbius Mobile Developed in cooperation with The Bag Ladies. 42 Holt Pre-Algebra