SKILL Are You Ready? 55 Order of Operations Teaching Skill 55 Objective Use the correct order of operations to evaluate expressions. Alternative Teaching Strategy Objective Use the correct order of operations to evaluate expressions. Explain to students that order of operations gives us a set of rules as to which operations are carried out first when an expression involves more than one operation. Some students may benefit from manipulating numbers and the order of operations. Write the following numbers on the board: 2, 3, 4, 5, and 6. Tell students that you are going to use each number exactly once, along with one set of parentheses and one each of , , , and to arrive at a final result of 4. Review the correct order of operations with students and the trick for remembering the order. Direct students’ attention to the first example. Demonstrate why having a set of rules is necessary by working out the problem left to right instead of using the correct order of operations. (8 2 3 6 3 18) Ask: Do you get the same result? (No) Write: 6 (2 3 4) 5. Work through the correct order of operations to demonstrate that the result is 4. Have students consider the second and third examples. Before working through the examples, ask a volunteer to list the operations they see in each problem, in the order in which they would be performed. 6 (2 3 4) 5 6 (6 4) 5 6 10 5 62 4 Instruct students to repeat this exercise using the same numbers and the same rules to arrive at a result of 3. Point out that they can have as many, or as few, numbers inside the parentheses as they need. (Students may arrive at different results; one possible result is (2 3) 5 6 4.) Have students complete the exercises. PRACTICE ON YOUR OWN In exercises 1–12, students evaluate expressions using order of operations. If students have trouble reaching an answer, have them work in pairs. As students become more comfortable, use larger numbers and mix up the operations. For example, require the use of one exponent, two additions, and two subtractions. Be sure to specify whether any parentheses are allowed. CHECK Determine that students know how to use the correct order of operations to evaluate expressions. Students who successfully complete the Practice on Your Own and Check are ready to move on to the next skill. Sample problems: COMMON ERRORS Students may always work from left to right and forget to follow the correct order of operations. 1) Use the numbers 1, 2, 3, 4, and 5 with one exponent, and one each of , , and to arrive at a result of 13. No parentheses 3 allowed. Possible answer: 5 4 2 1. Students who made more than 2 errors in the Practice on Your Own, or who were not successful in the Check section, may benefit from the Alternative Teaching Strategy. 2) Use the numbers 2, 3, 4, 6, and 10 with one exponent, one set of parentheses, and one each of , , and to arrive at a result 2 of 14. Possible answer: 3 10 (6 4). Copyright © by Holt, Rinehart and Winston. All rights reserved. 121 Holt Algebra 1 Name Date SKILL Are You Ready? 55 Order of Operations Class The Correct Order of Operations 1. Parentheses 2. Exponents 3. Multiply / Divide 4. Add / Subtract (left to right) (left to right) One way to remember the correct order: Please excuse my dear Aunt Sally. Example 1 Evaluate 8 2 3. Example 2 2 Evaluate (6 4) 5. Example 3 3 Evaluate 2 4 3 6. 8 6 10 2 5 84 36 2 100 5 8 12 6 20 20 6 14 Practice on Your Own Evaluate each expression. 1. (5 1) 3 2. 8 8 16 3. 6 5 1 4. 24 3 5 5. (8 10) 3 6. 20 1 7 7. 7 2 1 8. 72 2 3 9. 21 15 ÷ 3 10. 8 7 5 11. 3 6 2 9 12. (4 2) 2 9 Check Find the absolute value of each expression. 13. (6 10) 4 14. 40 4 10 15. 5 10 2 16. 15 3 10 17. 4 8 4 2 18. 8 5 3 6 Copyright © by Holt, Rinehart and Winston. All rights reserved. 122 Holt Algebra 1 SKILL Are You Ready? 51 Add and Subtract Integers Teaching Skill 51 Objective Add and subtract integers. Alternative Teaching Strategy Objective Add and subtract integers using a number line. Explain to students that adding and subtracting integers is best understood by thinking about absolute values, that is, the numbers without the negative signs. Materials needed: copies of the number lines shown below. Some students may benefit from visualizing addition and subtraction using a number line. Give each student copies of the number lines. Tell students they are going to add integers using the number lines. Review with students how to add integers with the same signs. Ask: If both signs are positive, what will be the sign of the sum? (positive) If both signs are negative, what will be the sign of the sum? (negative) Does it matter which number is larger? (No) Work through Example 1. –10 –5 –15 Review with students how to add integers with opposite signs. Stress that the sign of the sum is determined by the larger number. Work through Example 2. –10 –5 –5 0 –5 0 0 5 0 5 5 10 5 10 10 15 Write “3 (7)” on the board. Direct students’ attention to the first number line. Ask: What do each of the tick marks represent on the number lines? (one unit) Review with students how to subtract integers. Ask: What is the opposite of 5? (5) What is the opposite of 8? (8) Work through Example 3. Instruct students to place a dot on the number 3. Ask: If you were going to add 7 to 3, which direction would you move on the number line? (right) Since you are adding 7 instead, which way do you move? (left) Instruct students to move 7 units to the left. Ask: What is the result? (4) Remind students that zero is neither positive nor negative. Ask: When is the sum of two integers zero? (when the numbers are opposites, e.g. 4 and 4) Have students complete the exercises. –7 PRACTICE ON YOUR OWN In exercises 1–12, students add and subtract integers. –10 0 5 10 Next, have students use the second number line to add –13 15. Ask: Where do you place your first dot? (–13) In which direction should you move? (right) Make sure students arrive at 2 as an answer. CHECK Determine that students know how to add and subtract integers. After students have a good understanding of adding integers, explain how to use the number line to subtract integers. Have students use the third and fourth number lines to practice the following: 8 14 and 2 (9). Make sure students know to move to the left when subtracting positive numbers and to the right when subtracting negative numbers (the opposite of when adding). Students who successfully complete the Practice on Your Own and Check are ready to move on to the next skill. COMMON ERRORS Students may confuse a subtraction sign with a negative sign. Students who made more than 2 errors in the Practice on Your Own, or who were not successful in the Check section, may benefit from the Alternative Teaching Strategy. Copyright © by Holt, Rinehart and Winston. All rights reserved. –5 Have the students make up additional problems and draw their own number lines. 113 Holt Algebra 1 Name Date SKILL Are You Ready? 51 Add and Subtract Integers Class Adding Integers Same Signs Subtracting Integers Opposite Signs Step 1: Ignore the signs. Step 2: Add the two numbers. Step 3: Add the sign of the larger number to the answer. Step 1: Ignore the signs. Instead of subtracting, add Step 2: Subtract the smaller the opposite of the second number from the larger number. number and then use the rules Step 3: Add the sign of the for adding integers. larger number to the answer. Example 1: Add 3 (9). Example 2: Add 7 (12). 3 9 12 12 7 5 Since both numbers are negative, the answer is also negative. Since the larger number is negative (12 7), the answer is also negative. 3 (9) 12 7 (12) 5 Example 3: Subtract 6 (3). The opposite of 3 is 3. 639 Practice on Your Own Perform each indicated operation. 1. 11 16 2. 22 18 3. 15 (10) 4. 3 14 5. 20 (9) 6. 6 ( 5) 7. 6 (13) 8. 8 14 9. 100 95 10. 7 (10) 11. 10 (–10) 12. 25 (40) Check Perform each indicated operation. 13. 2 8 14. 10 18 15. 14 (21) 16. 7 (3) 17. 40 (35) 18. 17 4 19. 12 12 20. 18 (13) Copyright © by Holt, Rinehart and Winston. All rights reserved. 114 Holt Algebra 1 SKILL Are You Ready? 48 Add and Subtract Fractions Teaching Skill 48 Objective Add and subtract fractions. Alternative Teaching Strategy Objective Add like fractions. Review with students the meaning of “like fractions” and “unlike fractions.” Some students may benefit from a visual model of adding like fractions. Encourage students to use a model until they are comfortable without it. Point out that adding and subtracting like fractions (fractions with the same denominators) requires simple addition or subtraction of the numerators; the denominator in the answer does not change. To create a model for fifths, have students draw a rectangle and divide it into 5 columns of equal length. Explain that each column represents one-fifth. Remind students that simplest form means no common factors in the numerator and denominator and no improper fractions. Review with students how to convert an improper fraction to a mixed number. Work through the addition example. Tell students they are going to find the 3 4 sum of __ __. Instruct students to begin 5 5 by shading 3 of the five columns in their rectangle. Review with students the steps for adding or subtracting unlike fractions. Point out that in some cases, one of the denominators may be the LCD, in which case only the other fraction must be rewritten. Work through the subtraction example. Since there are not enough fifths to shade 4 more, draw a second rectangle with 5 columns. Instruct students to shade the remaining 2 fifths in the first rectangle and 2 more in the second rectangle. Ask: When subtracting a fraction from a mixed number, what should you do first? (Convert the mixed number to an improper fraction.) Instruct students to count the shaded fifths. 7 (7) Show that the sum is __. Remind students 5 that they can rewrite this as a mixed number. 2 1__ 5 Ask: How would you model fourths? (Draw a rectangle with 4 columns.) Tenths? (Draw a rectangle with 10 columns.) Have students complete the exercises. PRACTICE ON YOUR OWN In exercises 1–8, students add and subtract fractions. CHECK Determine that students know how to add and subtract fractions. Have student practice this technique by 3 6 2 5 7 find the sums __ __ 1__ and ___ ___ 7 7 7 12 12 12 ___ 1. 12 As an extension of this exercise, have 1 7 students consider the example __ __. Ask: 4 8 Could you use this technique to add the fractions as they are written? (No) What 1 would you need to do first? Rewrite __ 4 2 __ as . Have students complete this problem. 8 Students who successfully complete the Practice on Your Own and Check are ready to move on to the next skill. COMMON ERRORS Students may add or subtract the denominators. Students who made more than 2 errors in the Practice on Your Own, or who were not successful in the Check section, may benefit from the Alternative Teaching Strategy. Copyright © by Holt, Rinehart and Winston. All rights reserved. 107 Holt Algebra 1 Name Date SKILL Are You Ready? 48 Add and Subtract Fractions Class General Operation Reminders Adding and Subtracting Fractions Like Fractions (same denominators) Unlike Fractions (different denominators) Step 1: Add or subtract the numerators. Step 2: Write the sum or difference of the numerators over the denominator. Step 3: Write the answer in simplest form. Step 1: Find the least common denominator (LCD) and then rewrite each fraction so that its denominator is the LCD. Step 2: Follow the steps for adding or subtracting like fractions. 5 1 Example 1: Add __ __. 8 8 5 1 5 6 1 __ __ _____ __ (GCF of 6 and 8 is 2.) 8 8 8 8 6 62 3 3 __ _____ __ The sum is __. 8 82 4 4 3 1 Example 2: Subtract 1__ __. 2 4 3 1 Rewrite 1__ as __. The LCD of 2 and 4 is 4. 2 2 3 __ 6 2 __ __ 2 2 4 The difference 6 __ 3 3 __ __ 3 4 4 4 is __. 4 Practice on Your Own Add or subtract. Give your answer in simplest form. 2 1 1. __ __ 5 5 5 2 2. __ __ 7 7 2 1 3. __ ___ 5 10 4 1 4. __ __ 9 3 5 2 5. 1__ __ 9 9 3 7 6. __ __ 8 4 5 2 7. 1__ __ 3 6 5 2 1 8. __ __ ___ 3 6 12 Check Add or subtract. Give your answer in simplest form. 6 3 9. __ __ 11 11 3 7 13. 1__ __ 8 8 8 2 10. __ __ 9 9 3 1 11. ___ __ 7 14 7 1 12. ___ __ 12 4 3 7 14. ___ __ 5 10 3 1 15. 1__ __ 8 4 3 1 4 16. __ ___ ___ 5 15 10 Copyright © by Holt, Rinehart and Winston. All rights reserved. 108 Holt Algebra 1 SKILL Are You Ready? 60 Evaluate Expressions Teaching Skill 60 Objective Evaluate expressions. Alternative Teaching Strategy Objective Evaluate expressions. Explain to students that evaluating an expression simply means replacing the variable with a given value and simplifying. Explain to students that most expressions can be evaluated for any given number. Create the table below on the board and have students duplicate it. Tell students they are going to evaluate an expression for several different values. Review with students the order of operations and point out that they will need to follow them to correctly simplify expressions. Also review integer operations as some expressions, and some given values, may involve negative numbers. Value Have students consider Example 1. Ask: What two operations will be used to simplify this expression? (multiplication then addition) What number replaces y ? (6) Work through the example. Simplification 2 6( )3 ___ 3 ___ 1 6( )3 ___ 3 ___ 0 6( )3 ___ 3 ___ 1 6( )3 ___ 3 ___ 2 6( )3 ___ 3 ___ Ask: Based on the center column, what expression are you evaluating? (6y 3) For what values are you evaluating the expression? (2, 1, 0, 1, and 2) Next have students consider Example 2. Ask: What two operations will be used to simplify this expression? (multiplication then subtraction) What number replaces p? (4) Stress that students must be careful when working with negatives since it is easy to overlook them when simplifying. Work through the example. Have students complete the table and check their answers. (2, 1, 0, 1, 2; 12, 6, 0, 6, 12; 9, 3, 3, 9, 15) Have students duplicate the two tables below, identify the expression, and complete the last two columns. Have students complete the practice exercises. PRACTICE ON YOUR OWN In exercises 1–9, students evaluate expressions. Value CHECK Determine that students know how to evaluate expressions. Students who successfully complete the Practice on Your Own and Check are ready to move on to the next skill. Substitution Simplification 3 4( )5 ___ 5 ___ 1 4( )5 ___ 5 ___ 2 4( )5 ___ 5 ___ 4 4( )5 ___ 5 ___ Value COMMON ERRORS Students may not follow the correct order of operations and may arrive at an incorrect result. Substitution Simplification 3 3( )2 ___ 2 ___ 2 3( )2 ___ 2 ___ 1 3( )2 ___ 2 ___ 2 3( )2 ___ 2 ___ When students are comfortable completing tables, give them several expressions and have them create their own tables using the given values 3, 2, 1, 0, 1, 2, and 3. Students who made more than 2 errors in the Practice on Your Own, or who were not successful in the Check section, may benefit from the Alternative Teaching Strategy. Copyright © by Holt, Rinehart and Winston. All rights reserved. Substitution 131 Holt Algebra 1 Name Date SKILL Are You Ready? 60 Evaluate Expressions Class To evaluate a variable expression, replace the variable(s) with the given value(s) and use the order of operations to simplify. Example 1: Evaluate 10y 3 for y 6. 10y 3 10(6) 3 Replace y with 6 since 6 is the given value. 60 3 Order of operations says to multiply first. 63 Add. Example 2: Evaluate 6p 15 for p 4. 6p 15 6(4) 15 Replace p with 4 since 4 is the given value. 24 15 Order of operations says to multiply first. 9 Subtract. Practice on Your Own Evaluate each expression for the given value of the variable. 1. 7x 1 for x 5 2. 8m 12 for m 5 3. 2y 9 for y 6 4. 6p 3 for p 4 5. 27 9x for x 2 6. 10 4q for q 3 7. 7c 11 for c 3 1 8. __t 5 for t 9 3 1 9. __m 16 for m 20 2 Check Evaluate each expression for the given value of the variable. 10. 2n 3 for n 9 11. x 7 for x 5 12. 15 3h for h 5 13. 15 7m for m 3 14. 5a 9 for a 1 1 15. __y (4) for y 12 2 Copyright © by Holt, Rinehart and Winston. All rights reserved. 132 Holt Algebra 1 SKILL Are You Ready? 58 Connect Words and Algebra Teaching Skill 58 Objective Connect words and algebra. Alternative Teaching Strategy Objective Connect words and algebra. Point out to students that an algebraic expression (or equation) is simply a mathematical way of writing a phrase or sentence. Materials needed: multiple copies of the flashcards shown below (index cards work nicely), blank index cards Have students work in pairs. Distribute copies of the flashcards and have students shuffle the cards and divide them in half so that each student has six cards. Ask: What is the difference between an expression and an equation? (An expression does not have an equal sign while an equation does.) Tell students that associating key words with the correct operation is critical to being able to make the connection between words and algebra. 3x 1 n5 x7 1n 2 __ C 3(25) t 6(2) C 12 2.50 P 2(8) 2w 1 (6)(h) A __ 2 I (500)(2)r A 50 10w S 600 50w 2 Review with students the table of key words. Provide some real life examples. Start with the following two: (1)If your age is 10 years more than your sister’s, and your sister is 12, how do you find your age? (Add 12 plus 10.) If you receive $10 per week allowance for 8 weeks, how do you find the total amount you received? (Multiply 10 times 8.) Have students provide additional examples. Review with students key words and the operations with which the words are associated. Tell students they are going to make up phrases or situations that match the algebraic expressions and equations on the cards. Give the following example: 5n 3. Ask: How would you verbalize 5n? (5 times a number) And ⴙ 3? (increased by 3) Write the phrase on the board: “5 times a number increased by 3.” Point out that variations of this phrase are also correct, such as 3 more than 5 times a number. Review the lawn cutting example with students and then have them complete the exercises. PRACTICE ON YOUR OWN In exercises 1–6, students write algebraic expressions and equations. CHECK Determine that students know how to write algebraic expressions and equations. COMMON ERRORS Students may not know the key words associated with operations, and as a result may use the wrong operation. Next, write the equation C 40 5(d ) on the board. Remind students that variables typically represent something that makes sense. For example, C might represent cost and d number of days. Or, provide the following scenario: There are 40 cookies in a bag and Tom eats 5 cookies per day. C 40 5(d ) could be the number of cookies remaining at the end of any given day. Students who made more than 1 error in the Practice on Your Own, or who were not successful in the Check section, may benefit from the Alternative Teaching Strategy. Instruct students to take turns making up situations to match the cards they have. As an extension of the exercise, have students make flashcards and continue. Students who successfully complete the Practice on Your Own and Check are ready to move on to the next skill. Copyright © by Holt, Rinehart and Winston. All rights reserved. 127 Holt Algebra 1 Name Date SKILL Are You Ready? 58 Connect Words and Algebra Class To connect words and algebra, you must understand the operations involved and how to represent them. Key words are helpful in determining the operations. Key Words Operation or Representation a number; an unknown quantity any variable, such as x or n Twice, three times, etc. multiplication (2n, 3n, etc.) sum; more than; increased by addition () difference; less than; decreased by subtraction () each; per multiplication is; equals Example: Jared must cut 6 lawns over the weekend. Each of the lawns takes 2 hours to cut. Write an equation representing the total time t to cut all 6 lawns. Answer: Since each lawn takes 2 hours, multiply 2 times the number of lawns to get the total time: t 6(2). Practice on Your Own 1. Write an expression that represents the quantity 5 more than a number. 2. Write a phrase that could be modeled by the expression x 15. 3. John bought 3 CDs and 2 DVDs. Each CD costs $9.95, and each DVD costs $14.98. Write an equation representing the total cost C. 4. A triangle has sides of length 7, 10, and s. Write an equation representing the perimeter P of the triangle. 5. The value of a painting begins at $12,000 and increases by $500 per year. Write an equation representing the value V of the painting at the end of any given year y. 6. David has 56 baseball cards of which he sells 3 cards per week. Write an equation representing the number of cards n he has left at the end of any given week w. Check 7. Write an expression that represents a number decreased by 6. 8. Tina bought 6 plates and 2 glasses. Each plate costs $6.99, and each glass costs $22.98. Write an equation representing the total cost C. 9. Joseph opens a checking account with $400. Each month he adds $150 to the account. Write an equation representing the total amount A in the account at the end of any given month m. Copyright © by Holt, Rinehart and Winston. All rights reserved. 128 Holt Algebra 1 Answer Key continued SKILL 53 ANSWERS: 11. 0 Practice on Your Own 12. 12 1. 5 Check 2. 18 9 3. __ 11 4. 9 13. 11 5. 20 16. 25 6. 8 17. 13 7. 13 18. 0 1 8. ___ 25 19. 1.1 Check 9. 4 10. 72 14. 2.3 15. 10 20. 1 SKILL 55 ANSWERS: Practice on Your Own 11. 7 2 12. __ 5 13. 10 1. 3 2. 4 3. 31 14. 12 4. 3 15. 6 1 16. __ 2 5. 6 6. 14 SKILL 54 ANSWERS: 7. 50 Practice on Your Own 8. 9 1. 15 9. 26 2. 8 10. 43 3. 0.4 11. 0 4. 1.19 12. 4 5. 10 Check 6. 4 13. 4 7. 0.75 14. 0 8. 0.7 15. 25 9. 6 16. 22 10. 7 17. 2 18. 58 Copyright © by Holt, Rinehart and Winston. All rights reserved. 225 Holt Algebra 1 Answer Key continued SKILL 50 ANSWERS: Check Practice on Your Own 13. 6 1. 75 14. 8 2. 800 15. 7 3. 0.02 16. 10 4. $300 17. 5 5. $144 18. 21 6. $2000 19. 0 7. 3% 20. 31 8. 4% SKILL 52 ANSWERS: Check Practice on Your Own 9. 200 1. 15 10. 500 2. 4 11. 0.015 3. 55 12. $2400 4. 8 13. $12,000 5. 63 14. 5% 6. 6 SKILL 51 ANSWERS: 7. 150 Practice on Your Own 8. 15 1. 5 9. 26 2. 4 10. 7 3. 25 11. 32 4. 17 12. 3 5. 11 Check 6. 11 13. 70 7. 19 14. 6 8. 6 15. 72 9. 5 16. 7 10. 17 17. 64 11. 0 18. 12 12. 15 19. 9 20. 12 Copyright © by Holt, Rinehart and Winston. All rights reserved. 224 Holt Algebra 1 Answer Key continued SKILL 47 ANSWERS: Practice on Your Own 4 1. ___ 15 2. 3 1 3. __ 9 1 4. 1__ 2 1 __ 5. 7 1 6. __ 11 1 7. 4__ 2 8. 6 Check 1 9. ___ 18 2 10. __ 3 5 ___ 11. 14 12. 9 1 13. ___ 12 1 14. __ 7 1 15. 1__ 2 16. 15 Check 9 9. __ 11 2 10. __ 3 5 ___ 11. 14 1 12. __ 3 1 13. 1__ 2 3 ___ 14. 1 10 3 15. __ 8 23 ___ 16. 30 SKILL 49 ANSWERS: Practice on Your Own 1. 18 2. 9 3. 280 4. 30 5. 6 6. 21 7. 33 8. 45 SKILL 48 ANSWERS: 9. 84 Practice on Your Own 3 1. __ 5 3 __ 2. 7 1 __ 3. 2 1 __ 4. 9 1 5. 1__ 3 5 __ 6. 1 8 5 __ 7. 6 1 8. 1__ 4 10. 2600 Copyright © by Holt, Rinehart and Winston. All rights reserved. Check 11. 20 12. 21 13. 240 14. 360 15. 6 16. 23 17. 81 18. 285 223 Holt Algebra 1 Answer Key continued 4. 45p 3q 5 5. 25b c 2 6. 6x y 7. 16z 12. 0 4 14. 4 2 5 15. 2 3 2 8. 8d e 9. 18t 10. w SKILL 61 ANSWERS: 2 Practice on Your Own 8 11. 22r 13. 6 4 2 1. 10m n 7 2 2. 4x y 2 2 12. 50x y 4 3. 20a b 5 4. ___3 2t Check 13. 30f 2 f 2 5. ___ 3 2 14. 27x y 15. 60h 4 6. 3p 3q 2r 3 2 2 16. 49a b 4 7. u v 4 2 17. 4p q 4c 2 8. ___ d5 18. 21u v 3 19. g 9. 144h 2k 2 8 2 2 20. 16y z 10. 1 3 2 11. 10xy z SKILL 60 ANSWERS: Practice on Your Own wz 12. ___ 9 1. 36 Check 2. 28 13. 35s t 3. 3 x 14. ___ 5y 4. 27 5. 9 6. 2 4 15. 8b 4c 4 16. 5pq 3 7. 10 5mn 17. ____ 3 8. 8 18. 36u 3w 4 9. 6 Check 10. 15 8 2 19. 10x y 7 20. __ f 11. 2 Copyright © by Holt, Rinehart and Winston. All rights reserved. 227 Holt Algebra 1 Answer Key continued SKILL 56 ANSWERS: 8. 0 Practice on Your Own 9. 11h 1. 5x 30 10. 9y 9 2. 5z 35 11. 10 10x 3. 2n 4 12. 5 5u 4. 12 4k 13. 13y 6x 5. 48 8y 14. 4 6. 6m 18 Check 7. 10p 10 15. 10x 8. 60 3c 16. 3c 9. 7q 7 17. 3a 10. 55 11t 18. 8.4z 11. 14 2b 19. 10m 11 12. 36 9w 20. 8q 5r Check SKILL 58 ANSWERS: 13. 12c 24 Practice on Your Own 14. 15 5a 1. 5 n 15. 25 25d 2. a number decreased by 15; 15 less than a number; the difference between a number and 15; etc. 16. 50 10j 17. 4x 12 3. C 3(9.95) 2(14.98) 18. 30 15y 4. P 7 10 s 19. 3g 75 5. V 12,000 500y 20. 9m 9 SKILL 57 ANSWERS: 2 6. n 56 3w Check 7. n 6 Practice on Your Own 1. 12x 8. C 6(6.99) 2(22.98) 2. 4m 9. A 400 150m 3. 7a 2 SKILL 59 ANSWERS: 4. 7t 5. 3b 6. 8d Practice on Your Own 1. 10x 2 2. 21a 7. x Copyright © by Holt, Rinehart and Winston. All rights reserved. 2 4 3. 16mn 226 Holt Algebra 1