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1-1. Variables and Expressions. Holt Algebra 1. Warm Up. Lesson Presentation. Lesson Quiz. Warm Up Add or subtract. 1. 6 + 104 2. 12(9) 3. 23 – 8 4. Multiply or divide. 5. 324 ÷ 18 6. 7. 13.5(10) 8. 18.2 ÷ 2. 108. 110. 15. 18. 6.

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  1. 1-1 Variables and Expressions Holt Algebra 1 Warm Up Lesson Presentation Lesson Quiz

  2. Warm Up Add or subtract. 1. 6 + 104 2. 12(9) 3. 23 – 8 4. Multiply or divide. 5. 324 ÷ 18 6. 7.13.5(10) 8. 18.2 ÷ 2 108 110 15 18 6 135 9.1

  3. Warmup: Draw into your math Journal Algebraic Expression Variables ALGEBRA Numerical Expression Evaluate Algebraic Equation

  4. Objectives Translate between words and algebra. Evaluate algebraic expressions.

  5. Vocabulary variable constant numerical expression algebraic expression evaluate

  6. A variable is a letter or a symbol used to represent a value that can change. A constant is a value that does not change. A numerical expressioncontains only constants and operations. An algebraic expression may contain variables, constants, and operations.

  7. a+2, 4n 6x2 x, a, b, c, t Algebraic Expression Variables ALGEBRA Numerical Expression Evaluate Algebraic Equation 3+2, 4(9) 6·52 x+2=5 So x=3 2x+3y=10

  8. You will need to translate between algebraic expressions and words to be successful in math. Plus, sum, increased by Minus, difference, less than Divided by, quotient Times, product, equal groups of

  9. Writing Math These expressions all mean “2 times y”: 2y 2(y) 2•y (2)(y) 2 x y (2)y

  10. Example 1: Translating from Algebra to Words Give two ways to write each algebra expression in words. A. 9 + r B. q – 3 the difference of q and 3 the sum of 9 and r 9 increased by r 3 less than q C. 7mD. j  6 the product of m and 7 the quotient of j and 6 m times 7 j divided by 6

  11. To translate words into algebraic expressions, look for words that indicate the action that is taking place. Put together, combine Find how much more or less Separate into equal groups Put together equal groups

  12. Example 2A: Translating from Words to Algebra John types 62 words per minute. Write an expression for the number of words he types in m minutes. m represents the number of minutes that John types. Think: m groups of 62 words 62 · m or 62m

  13. Example 2B: Translating from Words to Algebra Roberto is 4 years older than Emily, who is y years old. Write an expression for Roberto’s age y represents Emily’s age. y + 4 Think: “older than” means “greater than.”

  14. Example 2C: Translating from Words to Algebra Joey earns $5 for each car he washes. Write an expression for the number of cars Joey must wash to earn d dollars. d represents the total amount that Joey will earn. Think: How many groups of $5 are in d?

  15. To evaluatean expression is to find its value. To evaluate an algebraic expression, substitute numbers for the variables in the expression and then simplify the expression.

  16. Example 3: Evaluating Algebraic Expression Evaluate each expression for a = 4, b =7, and c = 2. A. b – c b – c = 7 – 2 Substitute 7 for b and 2 for c. Simplify. = 5 B. ac Substitute 4 for a and 2 for c. ac = 4 ·2 = 8 Simplify.

  17. Example 4a: Recycling Application Approximately eighty-five 20-ounce plastic bottles must be recycled to produce the fiberfill for a sleeping bag. Write an expression for the number of bottles needed to make s sleeping bags. The expression 85s models the number of bottles to make s sleeping bags.

  18. Example 4b: Recycling Application Continued Approximately eighty-five 20-ounce plastic bottles must be recycled to produce the fiberfill for a sleeping bag. Find the number of bottles needed to make 20, 50, and 325 sleeping bags. Evaluate 85s for s = 20, 50, and 325. To make 20 sleeping bags 1700 bottles are needed. 85(20) = 1700 To make 50 sleeping bags 4250 bottles are needed. 85(50) = 4250 To make 325 sleeping bags 27,625 bottles are needed. 85(325) = 27,625

  19. Writing Math A replacement set is a set of numbers that can be substituted for a variable. The replacement set in Example 4 is (20, 50, and 325).

  20. Adding and Subtracting Real Numbers 1-2 Holt Algebra 1 Warm Up Lesson Presentation Lesson Quiz

  21. 2 2 2 2 3 5 Warm Up Simplify. 1. –4 –|4| 2. |–3| 3 Write an improper fraction to represent each mixed number. 6 2 14 55 3. 4 4. 7 3 7 3 7 Write a mixed number to represent each improper fraction. 12 24 5. 6. 5 9

  22. Objectives Add real numbers. Subtract real numbers.

  23. Vocabulary absolute value opposites additive inverse

  24. 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.

  25. 11 10 7 6 5 4 3 2 1 9 8 0 Example 1A: Adding and Subtracting Numberson a Number line Add or subtract using a number line. –4 + (–7) Start at 0. Move left to –4. To add –7, move left 7 units. + (–7) –4 –4+ (–7) = –11

  26. -3 -2 -1 0 1 2 3 4 5 6 8 9 7 Example 1B: Adding and Subtracting Numbers on a Number line Add or subtract using a number line. 3 – (–6) Start at 0. Move right to 3. To subtract –6, move right6units. –6 + 3 3 – (–6) = 9

  27. 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 5units - - - - - 6 5 - 1 0 1 2 3 4 5 6 4 3 2 |–5| = 5 |5| = 5

  28. When the signs of numbers are different, find the difference of the absolute values: Example 2A: Adding Real Numbers Add. Use the sign of the number with the greater absolute value. The sum is negative.

  29. Example 2B:Adding Real Numbers 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. (–6) + (–2) –8 Both numbers are negative, so the sum is negative.

  30. Two numbers are opposites if their sum is 0. A number and its opposite are on opposite sides of zero on a number line, but are the same distance from zero. They have the same absolute value.

  31. A number and its opposite are additive inverses. To subtract signed numbers, you can use additive inverses. Subtracting 6 is the same as adding the inverse of 6. Additive inverses 11 – 6 = 5 11 + (–6) = 5 Subtracting a number is the same as adding the opposite of the number.

  32. Example 3A:Subtracting Real Numbers Subtract. –6.7 – 4.1 –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.

  33. Example 3B:Subtracting Real Numbers Subtract. 5 – (–4) 5 − (–4) = 5 + 4 To subtract –4 add 4. Find the sum of the absolute values. 9

  34. First substitute for z. , add . To subtract Rewrite with a denominator of 10. Example 3C:Subtracting Real Numbers Subtract.

  35. When the signs of the numbers are the same, find the sum of the absolute values: . Example 3C Continued Write the answer in the simplest form. Both numbers are negative, so the sum is negative.

  36. Example 4: Oceanography Application An iceberg extends 75 feet above the sea. The bottom of the iceberg is at an elevation of –247 feet. What is the height of the iceberg? Find the difference in the elevations of the top of the iceberg and the bottom of the iceberg. elevationat bottom of iceberg –247 elevation at top of iceberg 75 Minus – 75 – (–247) 75 – (–247) = 75 + 247 To subtract –247, add 247. Find the sum of the absolute values. = 322 The height of the iceberg is 322 feet.

  37. Lesson Quiz: Part I Give two ways to write each algebraic expression in words. 1. j – 3 2. 4p 3. Mark is 5 years older than Juan, who is y years old. Write an expression for Mark’s age. The difference of j and 3; 3 less than j. 4 times p; The product of 4 and p. y + 5

  38. d 1 e 2 Lesson Quiz: Part II Evaluate each expression for c = 6, d = 5, and e = 10. 4. 5.c + d Shemika practices basketball for 2 hours each day. 11 6. Write an expression for the number of hours she practices in d days. 7. Find the number of hours she practices in 5, 12, and 20 days. 2d 10 hours; 24 hours; 40 hours

  39. Lesson Quiz Add or subtract using a number line. –2 2. –5 – (–3) 1. –2 + 9 7 Add or subtract. 3. –23 + 42 19 4. 4.5 – (–3.7) 8.2 5. 6. The temperature at 6:00 A.M. was –23°F. At 3:00 P.M. it was 18°F. Find the difference in the temperatures. 41°F

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