Loudoun County Public Schools



Chapter 1: Evaluate Expressions; Order of Operations; Write Expressions, Equations & InequalitiesExamplesThings to Remember & StudyFor Extra Help & Practice1.1 Powers Ex 1.1a) Write the power as a product (in expanded form).125 = 12 ? 12 ? 12 ? 12 ? 12Ex 1.1b) Simplify the product (write it in a shorter or simpler way).n ? n ? n = n3Ex 1.1c) Evaluate the power (find a numerical answer).102 = 10 ? 10 = 100base – the number that gets multiplied by itselfexponent – the little number written above the base number; tells how many times to multiply the basepower – the base and exponent togetherNEVER multiply base times exponent: 43 = 4 ? 4 ? 4 = 64 RIGHT!43 ≠ 4 ? 3 = 12 WRONG!CALCULATOR: Use the button x2 or ^ for calculating powersPg. 5: 17-37 odd (answers in yellow section SA1) Order of Operations Ex 1.2a) Evaluate the numeric expression (find the answer).3(8 – 22)Evaluate inside ( ) first3(8 – 4)Inside ( ): evaluate power first3(4)Inside ( ): subtract12MultiplyEx 1.2b) Evaluate the expression when n = 4 (find a numerical answer).3 + 5 ? n ÷ 10 = 3 + 5 ? 4 ÷ 10= 3 + 20 ÷ 10 = 3 + 2 = 5Ex 1.2c) Evaluate the expression when y = -2 (find a numerical answer).10y+5y-1= 10-2+5-2-1= -20+5-2-1= -15-3=5On the CALCULATOR:( 10 ( (-) 2 ) + 5 ) ÷ ( ( (-) 2 ) – 1 ) =Order of OperationsGrouping symbols – parentheses, brackets, fraction numerators and denominatorsPowers (exponents)Multiply & Divide from left to rightAdd & Subtract from left to rightTo evaluate an algebraic expression, use substitution (Wherever you see a variable, write its number instead). Then follow order of operations.CALCULATOR: Use ( ) around the numerator AND denominator of a fractionUse ( ) when you substitute a negative number Pg 5: 3-13 odd; 39-43 odd Pgs 10-11: 3-17 odd; 23-29 odd (answers in yellow section SA1) 1: Evaluate Expressions; Order of Operations; Write Expressions, Equations & InequalitiesTry These While Looking at ExamplesAnswersTry These Without LookingWrite the power as a product.1. 1132. t4Simplify the product.3. x ? x ? x ? y ? y ? z ? zEvaluate the power.4. 325. 536. (23)41. 11 ? 11 ? 112. t ? t ? t ? t 3. x3y2z4. 95. 1256. 16817. 3.2 ? 3.2 ? 3.28. y ? y ? y ? y ? y ? y9. r2s3t210. 11611. The error made was multiplying the base times the exponent. The correct way is:25 = 2 ? 2 ? 2 ? 2 ? 2 = 32Write the power as a product.7. (3.2)38. y6Simplify the product.9. r ? r ? s ? s ? s ? t ? tEvaluate the power.10. (14)211. Describe and correct the error:25 = 2 ? 5 = 10 Evaluate the expression.1. 7 + 5 ? 23 2. 24 ÷ (8 + 42)3. 8[20 – (9 – 5)2 ]4. 11 + r3 – 2r when r = 55. 9x+43x+1 when x = 76. The perimeter of a square with a side length of s is given by the expression 4s. What is the perimeter of a square with sides of length 7.5 meters?1. 472. 13. 324. 1265. 67226. 30 metersTo solve this, you must evaluate the expression 4s when s = 7.5 meters.The perimeter = 4 ? 7.5 = 30 meters.7. 1.58. 409. 1510. 1411. 64.78 inches12. After doing the addition inside the parentheses, the student should have done the division 14 ÷ 7 BEFORE the addition.Correct solution:(1 + 13) ÷ 7 + 7 = 14 ÷ 7 + 7 = 2 + 7 = 9Evaluate the expression.7. 1 + 52 ÷ 508. 24 + 4(3 + 1)9. 5(w – 4) when w = 710. -21+ b35b+9 when b = 311. The expression 25 + 1.17h estimates the adult height of a girl whose height at the age of 2 is h. Estimate the adult height of a girl who is 34 inches tall at age 2.12. Describe and correct the error.(1 + 13) ÷ 7 + 7 = 14 ÷ 7 + 7 = 14 ÷ 14 = 1 Chapter 1: Evaluate Expressions; Order of Operations; Write Expressions, Equations & InequalitiesExamplesThings to Remember & StudyFor Extra Help & Practice1.3 Write Expressions Translate the verbal phrase into an expression. (Rewrite in algebraic form).Ex 1.3a) The product of 6 and a number y 6y OR 6 ? y OR 6(y)Ex 1.3b) 4 less than the quantity 6 times a number n(6n ) – 4 Ex 1.3c) Write an expression for the situation.Amount you spend if you buy a shirt for $20 and jeans for j dollars. 20 + jADDITION ( + ) words: sum, plus, total, more than, increased bySUBTRACTION ( – ) words:difference, less than, minus, decreased byMULTIPLICATION ( ? ) words:times, product, multiplied by, ofDIVISION ( ÷ ) words:quotient, divided by, out ofMost of the time, the order of the expression is the same as the order of the wordsFor “less than” reverse the order:5 less than x is written x – 5 Use parentheses for: “quantity”, “sum of”, “difference of”, and “quotient of”Pg. 18: 3-21 odd (answers in yellow section SA1) Write Equations & InequalitiesEx 1.4a) The difference of a number z and 11 is equal to 35.z – 11 = 35Ex 1.4b) The product of 6 and a number n is at least 24.6n ≥ 24Ex 1.4c) The sum of 8 and a number k is greater than 4 and no more than 16.8 + k > 4 AND 8 + k ≤ 16These can be combined: 4 < 8 + k ≤ 16Ex 1.4d) Is 4 a solution to 3z + 7 > 20 ?3(4) + 7 > 2012 + 7 > 2019 > 20 Statement is FALSE, so 4 is NOT a solutionEQUALS ( = ) words:is, is equal to, was, hasGREATER THAN ( > ) words:is greater than, is more thanGREATER THAN OR EQUAL TO ( ≥ ) words:is no less than, is at leastLESS THAN ( < ) words:is less than, is fewer than, is smaller thanLESS THAN OR EQUAL TO ( ≤ ) words:is no more than, is at mostThe < or > sign “points” to the smaller quantityWATCH OUT! “less than” by itself means – ; “is less than” means <FIRST: Look for the equals or inequality words. NEXT: Translate the words BEFORE and AFTER the equals/bining: Write quantities in order from least to greatest.A solution to an equation or inequality must make the statement TRUE.Pg 24: 3-27 odd (answers in yellow section SA1) 1: Evaluate Expressions; Order of Operations; Write Expressions, Equations & InequalitiesTry These While Looking at ExamplesAnswersTry These Without LookingTranslate the phrase into an expression.1. 50 divided by a number h2. 5 more than twice a number wWrite an expression for the situation.3. Number of pages of a 5 page article left to read if you’ve read p pages4. Number of hours in m minutes1. 50 ÷ h OR 50h 2. 5 + 2w3. 5 – p Think: There are 5 pages altogether. I have already read p pages, so I need to subtract to find out how many pages are left. 4. m ÷ 60 Think: 1 hour is 60 minutes, 2 hours is 120 minutes, and so on. Hours = minutes ÷ 605. 15 + x 6. p2 – 3 7. dTranslate the phrase into an expression.5. The sum of 15 and a number x6. 3 less than the square of a number p7. The number of adult tickets sold at a school talent show is 5 less than 3 times the number c of children’s tickets sold. Which expression represents the number of adult tickets sold?a) 3c + 5b) 5 – 3cc) 5c + 3d) 3c – 5 Write an equation or inequality.1. The sum of 12 and the quantity 8 times a number k is equal to 48.2. The product of 4 and a number w is at most 51.3. Which is the correct way to combine these inequalities? d < 17 and d > 1a) 17 < d > 1b) 1 < d < 17c) 1 < d > 17d) 17 < d < 1Is the given number a solution?4. 2p – 1 ≥ 7 ; 35. 5d – 4 ≥ 16 ; 41. 12 + 8k = 482. 4w ≤ 513. b4. NO. Substituting 3 for p makes the statement FALSE.5. YES. Substituting 4 for d makes the statement TRUE.6. 6(m + 3) = 207. 4 + 2k ≥ k ÷ 58. d9. YES. 10. NO.Write an equation or inequality.6. 6 times the sum of m and 3 is 20.7. 4 more than twice a number k is no less than the quotient of k and 5.8. Which is the correct way to combine these inequalities? f ≥ 12 and 34 > fa) 34 < f ≥ 12b) 12 > f ≥ 34c) 12 ≤ f > 34d) 12 ≤ f < 34Is the given number a solution?9. x-53 ≤3 ; 1110. 9 + 4y = 17 ; 1 ................
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