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STUDY LINK 61 Practice with Fractions Copyright © Wright Group/McGraw-Hill 180 73 90 93 Name Date Time Put a check mark next to each pair of equivalent fractions. 1. 2 3and 5 6 2. 13 4and 2 1 8 6 3. 2 34 0and 4 5 4. 7 3and 3 7 5. 5 86and 4 79 6. 23 8and 1 49 Find the reciprocal of each number. Multiply to check your answers. 7. 19 8. 2 5 9. 35 7 10. 1 6 Multiply. Write your answers in simplest form. Show your work. 11. 2 3º 1 1 8 12. 31 7º 27 2 Solve the number stories. 13. How much does a box containing 5 horseshoes weigh if each horseshoe weighs about 2 1 2pounds? 14. One and one-half dozen golf tees are laid in a straight line, end to end. If each tee is 2 1 8inches long, how long is the line of tees? 15. A standard-size brick is 8 inches long and 2 1 4inches high and has a depth of 3 3 4inches. What is the volume of a standard-size brick? Practice 16. 107 ( 82) 56  17. 4  (12  18)  18. 85 66 ( 48)  19. 7  ( 11   22) 

LESSON 61 Name Date Time Products and Sums of Reciprocals 181 Copyright © Wright Group/McGraw-Hill 1. Read Statement 1. Then find each reciprocal or product to help you decide whether the statement is true or false. Statement 1The product of the reciprocals of two positive numbers is equal to the reciprocal of their product. a. The reciprocal of 4 is . b. The reciprocal of 6 is . c. The product of the reciprocals from 1a and 1b is . d. The product of 4 and 6 is . e. The reciprocal of the product of 4 and 6 is . f. Repeat Problems 1a–1e using a different pair of positive numbers. g. Do you think Statement 1 is true or false for all positive numbers? Explain. 2. Read Statement 2. Then find each reciprocal or sum to help you decide whether the statement is true or false. Statement 2The sum of the reciprocals of two positive numbers is equal to the reciprocal of their sum. a. The reciprocal of 5 is . b. The reciprocal of 10 is . c. The sum of the reciprocals from 2a and 2b is . d. The sum of 5 and 10 is . e. The reciprocal of the sum of 5 and 10 is . f. Repeat Problems 2a–2e using a different pair of positive numbers. g. Do you think Statement 2 is true or false for all numbers having reciprocals? Explain.

LESSON 61 Name Date Time Finding Reciprocals 182 Copyright © Wright Group/McGraw-Hill Solve. 1. º 5 1 2. º 1 21 3. º 17 1 4. º 0.25 1 5. º 0.6 1 6. º n1 7. Explain how you solved Problem 5. For each number, fill in the circle next to the reciprocal. (There may be more than one correct answer.) 8. 5 6 9. 12 7 10. 3 11. 1.25 56 7 3 9 3 5.21 1 1 5 17 2 3 9 5 4 1.2 7 9 1 3 0.8 6 5 2.7 1.3 1 52 12. Explain how you solved Problem 10.

STUDY LINK 62 Fraction Division 183 93 Name Date Time Copyright © Wright Group/McGraw-Hill Division of Fractions Algorithm a b dc a bº d c Divide. Show your work. 1. 2 3 5 6 2. 13 4 2 18 6 3. 2 34 0 4 5 4. 7 3 3 7 5. 5 8 5 8 6. 2  1 4 7. 1 72 4 5 8. 55 66  Try This Practice 0123456789 10 cm Round each number to the underlined place. 12. 13.56 1 13. 589.35 52 14. 12.9 694 9. How many 13 0-centimeter segments are in 3 centimeters? segments 10. How many 13 0-centimeter segments are in 4 1 5centimeters? segments 11. How many 14 0-centimeter segments are in 6 4 5centimeters? segments

LESSON 62 Name Date Time Complex Fractions 184 Copyright © Wright Group/McGraw-Hill A complex fractionis a fraction whose numerator and/or denominator is also a fraction or a mixed number. Fractions such as , , and are complex fractions. To simplify a complex fraction, rewrite it as a division problem and divide. Simplify each complex fraction. Show your work. 1. 2. 3. 4. Find each missing divisor. 5. 1 41 3 4 6. 21 21 1 4 61 5  2 3  3 4  5 6 3 7 6 3  1 2 22 1 5  1 45 1 6  4 9 10 2 3 Example 1: Simplify 10  2 3 10  3 2  3 20 15 10  2 3 10 2 3 Example 2: Simplify  1 6 4 9  1 69 4  29 4  3 8  1 6  4 9 1 6  4 9 Try This

Division of Fractions Algorithm a b dc a bº d c Name Date Time Dividing Fractions and Mixed Numbers 185 Copyright © Wright Group/McGraw-Hill Divide. Show your work. 1. 7 8 3 6 2. 1 11 5 1 3 3. 7 6 15 2 4. 6  2 3 5. 4 52  6. 18 4 18 4 7. 12 5 13 0 8. 1 362 1 4 9. 23 4 6 8 10. 5 71 3 5 11. 7 5 1 3 12. 34 58 1 2 Try This LESSON 62

Copyright © Wright Group/McGraw-Hill 186 95 96 Name Date Time Subtraction of Signed Numbers For any numbers aand b, abaOPP(b),or aba(b). 1. Rewrite each subtraction problem as an addition problem. Then solve the problem. a. 46 19  b. 43 17  c. 5 (6.8)  d. 21 (21)  2. Subtract. a. 72 (43)  b. 4 (39) c. (17 0)1 1 2 d. 4.8 (3.6)  e. 2 1 2 3 4 f. (5 6) (1 3) g. 12.3 5.9  h. 8.5 (2.7)  3. Fill in the missing numbers. a. 19 17  b. 43 26  c. 1 21 3 4 d.  (2 4 5)3 17 0 e. 17.6 13.9 f. 83.5 62.7  g. 5 3 46 13 6 h. 9.6 10 Practice 4. 100 10 x; x 5. 10 x100 billion; x 6. 100 million 10 x; x 7. 10 x0.00001; x STUDY LINK 63

Name Date Time Modeling Subtraction with Signed Numbers 187 Copyright © Wright Group/McGraw-Hill Cut out the and tiles on Math Masters,page 188. Use your tiles to work through each example. Use your tiles to solve each problem. Record the model you used on the back of this page. 1. 6 (2)  2. 3 (2)  3. 7 (4)  4. 4 (5)  Example 1:2 (4) Step 1Use tiles to represent 2.Step 2Because there are no negative tiles to subtract, add 4 zero pairs. Step 3Subtract 4. Step 4Count the remaining tiles. 6 () tiles are left, so 2(4)6. Example 2:2 (3) Step 1Use tilesStep 2Because there are not to represent 2. enough negative tiles to subtract, add 1 more zero pair. Step 3Subtract 3. Step 4Count the remaining tiles. 1 () tile is left, so2(3)1. LESSON 63

LESSON 63 Name Date Time Positive and Negative Tiles 188 Copyright © Wright Group/McGraw-Hill

Name Date Time The Absolute Value of a Number 189 Copyright © Wright Group/McGraw-Hill The absolute value of a number is its distance from 0 on the number line. Use the symbol to indicate absolute value. For example, the absolute value of 3 is written 3. On the number line above, both 3 and 3 are 3 units from 0. So, 33 and 33. Because absolute value tells the distance and not the direction from 0, the absolute value of any number (except 0) is positive. The absolute value of 0 is 0. You can use absolute value to find sums of positive and negative numbers. The sum of two positive numbers is the sum of their absolute values. Example:3 5 358. The sum of two negative numbers is the opposite of the sum of their absolute values. Example:3 5 OPP(35) OPP(3 5) OPP(8) 8 To add two numbers with different signs, first find their absolute values. Then subtract the lesser absolute value from the greater absolute value. Give the result the sign of the number with the greater absolute value. 0 1 2 3 4 1234 3 units 3 units Example 1:4 7 4477 Subtract: 7 4 3 Because the negative number has the greater absolute value, the sum is negative. 4 7 3Example 2:2 8 2288 Subtract: 8 2 6 Because the positive number has the greater absolute value, the sum is positive. 2 8 6 1. Describe how Example 1 would be different if you found the sum 4 7. 2. Describe how to find the sum 4 (4) using absolute values. LESSON 63

Copyright © Wright Group/McGraw-Hill 190 º, / of Signed Numbers 97 Name Date Time Solve. 1. 12 º 5  2. 63 / 7  3. 24 (4)  4. 9 º 54 5. 50 / 10 6. 6 º 5 º 8  7. 48 / (62)  8. (8 º 5) 12  9. 50 º (23)  10. 6 º (12 15)  11. (90 10) (45)  12. 56 / (7) / (4)  13. º (7) º (4) 56 14. 40 9 A Multiplication Property The product of two numbers with the same sign is positive. The product of two numbers with different signs is negative.A Division Property The quotient of two numbers with the same sign is positive. The quotient of two numbers with different signs is negative. Try This 15. 2 3º (5 6) 16. (8 º (3))(8 º (9))  17. 0.25 º (8)  18. (3 4)  (1 2) 19. Evaluate each expression for b 7. a. (9 º b)27  b. 11 º (b)  c. b / (14)  d. b(b16)  STUDY LINK 64

Name Date Time A Multiplication Story 191 Copyright © Wright Group/McGraw-Hill In many fairy tales and children’s stories, there are good characters and bad characters. For example, in the story “Little Red Riding Hood,” the grandmother is a good character; the wolf is a bad character. You can use these character situations to remember a multiplication property for positive and negative numbers. When something good () happens to a good () character, we think it is good (). When something bad () happens to a good () character, we think it is bad (). When something good () happens to a bad () character, we think it is bad (). When something bad () happens to a bad () character, we think it is good (). Example:Solve 4 5 ? Think, “When something bad (4) happens to a good (5) character, we think it is bad ().” So, 4 5 20. LESSON 64

LESSON 64 Name Date Time Patterns with Signed Numbers 192 Copyright © Wright Group/McGraw-Hill 1. Multiply each number in the far left column by each number in the top row. Look for patterns. Use your calculator as few times as possible to complete the table. 2. Use the patterns from the table above to predict the products below. Then check each prediction with your calculator. 3. Divide each number in the far left column by each number in the top row. Look for patterns. Use your calculator as few times as possible to complete the table. Write your own number pattern in last row.  11 1111,111 11 111 1,111 11,111  11 111 Prediction111,111 Actual111,111 Divisor 99 9999,999 12 34 45 67

STUDY LINK 65 Turn-Around Patterns 193 105 Name Date Time Copyright © Wright Group/McGraw-Hill xy 1 x 1 y xºyyºxxyyx 79 1 7 1 9 63 212 39 2 3 5 6 2.71.9 2 2 23 Fill in the missing numbers in the tables. Look for patterns in the results. 1. Which patterns did you find in your completed table? 2. Which patterns did you find in your completed table? xyOPP(x) OPP(y)xyyxxyyx 797 –9 –16 212 39 2 3 5 6 2.71.9 2 2 23

LESSON 6 5 Name Date Time Properties of Numbers 194 Copyright © Wright Group/McGraw-Hill For each statement below, indicate whether it is always true or can be false. If the statement can be false, give an example. True or false? Example 1. a b dc ba  dc  2. a bdc ba  dc  3. a b dc ba  dc  4. a b dc ba  dc  5. Explain why giving only one example for a true statement is not enough to prove that it is true. Try This 6. Correct each false statement in Problems 1–4 so the statement is true for all special cases. Give one example for each statement.

LESSON 6 5 Name Date Time Renaming Repeating Decimals 195 Copyright © Wright Group/McGraw-Hill You can use a power-of-10 strategy when renaming a repeating decimal as a fraction. Work through each of the examples shown below. Rename each repeating decimal as a fraction. 1. 0.7–  2. 0.25—  3. Compare the denominators in the examples to the denominators of your answers for Problems 1 and 2. Use any patterns you notice to mentally rename 0.5– and 0.32— . Check your answers with a calculator. a. 0.5–  b. 0.32—  Example 1:Rename 0.3– as a fraction. Let 1x0.3333… If 1x0.333..., Because one digit repeats, multiply both then 10x3.33... . sides by 10 to eliminate the repeating digits to the right of the decimal point. 10x3.333 Subtract1x0.333 9x3 Divide to solve for x. 9 9x 3 9 Simplify.x 3 9 1 3 0.3– renamed as a fraction is 1 3. Example 2:Rename 0.45— as a fraction. Let 1x0.4545… If 1x0.454545..., Because two digits repeat, multiply both then 100x45.45... . sides by 100 to eliminate the repeating digits to the right of the decimal point. 100x45.4545 Subtract.1x0.4545 99x45 Divide to solve for x. 9 99 9x  4 95 9 Simplify.x 4 95 9 15 1 0.45— renamed as a fraction is 15 1.

STUDY LINK 6 6 Using Order of Operations Copyright © Wright Group/McGraw-Hill 196 247 Name Date Time Please E xcuse M y D ear A unt S ally P arentheses E xponents M ultiplication D ivision A ddition S ubtraction Evaluate each expression. 1. 5 6 º 3 2  2. 4 º 9 / 2 (4 6)  3. 1 2 5 8º 1 22  4. (2.3 7.8) º 4 3  5. 427(3 (5))  6. ((2 º 4) 3) º 6 / 2  Evaluate the following expressions for m3. 7. m m6 4  8. ((4 11) º 3) / 9 º (m)  9. m 2((m 3)) 8  10. 1 2º m 5 4 3 5 11 0 Find each missing number. 11. 3 gal 7 qt 4 gal qt 12. 5 gal 3 qt qt 13. 13 pt qt pt 14. 10 c qt pt 15. 18 qt gal pt Practice Units of Capacity 2 cups (c) 1 pint (pt) 2 pints 1 quart (qt) 4 quarts 1 gallon (gal)

LESSON 6 6 Name Date Time Another Grouping Symbol 197 Copyright © Wright Group/McGraw-Hill Copyright © Wright Group/McGraw-Hill A fraction bar (sometimes referred to as the vinculum) indicates division. An expression such as (8 4) (5 2) can be written as ( (8 5 4 2) )  . A fraction bar also acts as a grouping symbol. Both the numerator and the denominator can be treated as if there were parentheses around them. Any operations in the numerator or the denominator must be performed before the division. Example:Evaluate 72  2 49 º 37  . 72  2 49 º 37  72  (2 (49 º 37 ))  72  3 16 272 3 24 Evaluate each expression. 1. 20  4 35   2. 4 6( (5 6 7 4) )   3.  4. 6[24 2 72 (7 93)]   7(8 1) (42 3) (10 7)3 A fraction bar (sometimes referred to as the vinculum) indicates division. An expression such as (8 4) (5 2) can be written as ( (8 5 4 2) )  . A fraction bar also acts as a grouping symbol. Both the numerator and the denominator can be treated as if there were parentheses around them. Any operations in the numerator or the denominator must be performed before the division. Example:Evaluate 72  2 49 º 37  . 72  2 49 º 37  72  (2 (49 º 37 ))  72  3 16 272 3 24 Evaluate each expression. 1. 20  4 35   2. 4 6( (5 6 7 4) )   3.  4. 6[24 2 72 (7 93)]   7(8 1) (42 3) (10 7)3 LESSON 66 Name Date Time Another Grouping Symbol

LESSON 6 6 Name Date Time Order of Operations 198 Copyright © Wright Group/McGraw-Hill Please E xcuse M y D ear A unt S ally P arentheses E xponents M ultiplication D ivision A ddition S ubtraction Evaluate each expression. Compare your result to a partner’s. If you don’t agree, discuss how you evaluated the expression to decide which result is correct. 1. 26 15 º 2 6  2. 18 5 10 2 3. 50 70 / 2  4. 39 1 24 / 6  5. 18 / 3 (37 13)  6. 10 28 14 5  7. 42 6 / 6 8  8. 5 3 2º 4 / 2 

STUDY LINK 6 7 Number Sentences 199 241–243 Name Date Time Copyright © Wright Group/McGraw-Hill 1. a. Draw a circle around each number sentence. 17 27 3 º 15 100 56 / 8 (54) º 20 20 (4 23) / 9 12 12 b. Choose one item that you did not circle. Explain why it is not a number sentence. 2. Tell whether each number sentence is true or false. a. 9(6 2) 0.5 b. 94 492 º 2 c. 2 64 33 / 11 d. 7025 45 3. Insert parentheses to make each number sentence true. a. 286931 b. 20 40911 c. 36 / 6 / 2 12 d. 4º8416 4. Write a number sentence for each word sentence. Tell whether the number sentence is true or false. Word sentence Number sentence True or false? a. If 14 is subtracted from 60, the result is 50. b. 90 is 3 times as much as 30. c. 21 increased by 7 is less than 40. d. The square root of 36 is greater than half of 10. Practice 5. 1.867 0.947  6. 62.49 7. 256.34.785

The order of operations is shown in the diagram below. in order, left to right Use the diagram to help you label which operation you should perform first, second, third, and so on when evaluating an expression. Example:Label the order in which you should perform the operations to evaluate the expression 9 / (8 5). Then evaluate the expression. Do the operation inside the parentheses. (8 5) 3 Divide and multiply in order from left to right. 9 / 33 12 º 448 Add and subtract in order from left to right. 3 48 51 51 11 40 9 / (8 5) 12 º 4 11 40 For each expression, label the operation you would perform first, second, third, and so on. Then evaluate the expression. 1. 7 º 2 3 2. 6 0.3 º 10  3. 6 4 º 4 2 4. (9 1) / 2 º 3 2 5. 14 28 / 7 º 2  6. 1 º 7 5 / 1  45 23 1 1 2 4 3 5 9 / (8  5)  12 º 4  11 or  º or / an () LESSON 6 7 Name Date Time Ordering Operations 200 Copyright © Wright Group/McGraw-Hill

LESSON 6 7 Name-Collection Boxes 201 Copyright © Wright Group/McGraw-Hill Name Date Name Date Name Date Name Date

STUDY LINK 6 8 Solving Simple Equations Copyright © Wright Group/McGraw-Hill 202 242 243 Name Date Time 1. Find the solution to each equation. a. b7 12 b. 53 n29 c. 45 / y 25 d. mº 2 31  1 13 5 2. Translate the word sentences below into equations. Then solve each equation. Word sentence Equation Solution a. If you divide a number by 6, the result is 10. b. Which number is 7 less than 200? c. A number multiplied by 48 is equal to 2,928. d. 27 is equal to 13 increased by which number? 3. For each problem, use parentheses and as many numbers and operations as you can to write an expression equal to the target number. You may use each number only once in an expression. Write expressions with more than two numbers. a. Numbers: 3, 9, 11, 12, 19 Target number: 36 b. Numbers: 1, 2, 6, 14, 18 Target number: 50 c. Numbers: 4, 5, 8, 14, 17 Target number: 22 d. Numbers: 6, 7, 12, 14, 20 Target number: 41 Practice Complete. 4. 540 90 9 5. 36 6 0.6 6. 11 1.21 0.11

LESSON 6 8 Name Date Time Solving Challenging Equations 203 Copyright © Wright Group/McGraw-Hill 1. xx0n5 1a8 3yy 0 g1 Which of the above sentences have a. no solution? b. more than one solution? c. a solution that is a negative number? 2. Find the solution to each equation below. a. x(x1) (x2) 90 (Hint:Think of this equation as a sum of three numbers.) b. a(a1) (a2) (a3) (a4) 90 3. Whole numbers are said to be consecutiveif they follow one another in an uninterrupted pattern. For example, 5, 6, 7, 8, 9, and 10 are six consecutive whole numbers. a. Find three consecutive whole numbers whose sum is 90. (Hint:Replace each variable xin Problem 2a with the solution of the equation.)  90 b. Find five consecutive whole numbers whose sum is 90.  90 c. Find four consecutive whole numbers whose sum is 90.  90 4. Each letter in the subtraction problem below represents a different digit from 0 through 9. The digits 3 and 5 do not appear. Replace each letter so the answer to the subtraction problem is correct. GR A P E G R A P  PLUM APPL E E L U M 

Solving Pan-Balance Problems Copyright © Wright Group/McGraw-Hill 204 250 Name Date Time Solve these pan-balance problems. In each figure, the two pans are balanced. 1. One ball weighs as much as coin(s). 2. One cube weighs as much as marble(s). 3. One xweighs as much as y(s). 4. One aweighs as much as b(s). Make up two pan-balance problems for a classmate to solve. 5. 6. 1b7a6b2a 9x5y7x15y 3 5 2 7. 605 º 11 0605  8. 72 º 72 4 9. º 30 (2 º 30) 3 10. º (x5)  Practice x5 2 STUDY LINK 6 9

Name Date Time Pan-Balance Problems 205 Copyright © Wright Group/McGraw-Hill Problems 1 and 2 each consist of two parts. You need to solve one part before you have enough information to solve the other part. You must figure out which statement to complete first—it may be either the first or the second statement. In each of the figures for Problems 1–3, the two pans are balanced. 1. One cube weighs as much as One coin weighs as much as marbles. marbles. 2. One marble weighs as much as One can weighs as much as paper clips. paper clips. 3. An empty juice glass weighs as much as 5 coins. If the juice glass is full, the juice in the glass weighs as much as coins. If the juice glass is full, the juice and the glass weigh as much as coins. full1 2 empty 16 full1 4 full1 8 22 marbles LESSON 6 9

STUDY LINK 6 10 Balancing Equations Copyright © Wright Group/McGraw-Hill 206 Name Date Time For Problem 1, record the result of each operation on each pan. 1. Original pan-balance equation Operation (in words) (abbreviation) Subtract 4. S 4 Multiply by 3. M 3 Add 17k.A17k For Problems 2 and 3, record the operation that was used to obtain the result on each pan balance. 2. Original pan-balance equation Operation (in words) (abbreviation) 3. Original pan-balance equation Operation (in words) (abbreviation)     k 9 q  5 2 4q  5 2  3q  1  1.5q 2q  2.5 q 7  3m  12 13  5m 13 2m  12 6 m  6 1 2  m 1 2 250–252

LESSON 6 10 Name Date Time Equations 207 Copyright © Wright Group/McGraw-Hill A pan balance is a good model for an equation. To keep the pans balanced, do the same thing to both pans. Example: You can find the value of the variable nby removing, or subtracting, 17 from the left pan and the right pan. n 17 17 98 17 n81 To check the solution, replace nwith 81. 81 17 98 true Fill in the missing numbers that will keep the pans balanced. Check each solution. 1. 76 y33  43 y 2. m45 10  m35 3. kº 5 130  k26 4. b4º31  b124 5. You can use one operation to undo another. Name the operation that will undo each of the following: a. addition b. multiplication 98  17 n y  33 76  k  5130  m  4510  b  431 

LESSON 6 10 Name Date Time Pan-Balance Equations 208 Copyright © Wright Group/McGraw-Hill Solve each equation. Record the operations you use and the equation that results. Check your solution by substituting it for the variable in the original equation. 1. Equation: Operation Resulting equation 2. Equation: Operation Resulting equation 3. Equation: Operation Resulting equation 4. Equation: Operation Resulting equation 5x  5x  29 2 10 7  y3 2  5  2.5  t2  1.5t  2m  4 29  7m  Try This

STUDY LINK 6 11 Solving Equations 209 251–252 Name Date Time Copyright © Wright Group/McGraw-Hill Solve each equation. Then check the solution. 1. 9 5k45 2k 2. 9 2m8 5.5 4m Original equation Original equation Operation Operation Check Check 3. 24x10 18x4 4. 12d9 15d9 Original equation Original equation Operation Operation Check Check 5. 6r5 712r 6. 1 3p7 12 2 3p Original equation Original equation Operation Operation Check Check k12 5k362k S 9 95k452k

STUDY LINK 6 12 Review Copyright © Wright Group/McGraw-Hill 210 Name Date Time 1. Write a number sentence for each word sentence. Word sentence Number sentence a. 15 is not equal to 3 times 7. b. 5 more than a number is 75. c. 13 more than 9 divided by 9 is less than or equal to 14. 2. Insert parentheses to make each equation true. a. 200 4 º 510 b. 16 2 25 312 3. Use the order of operations to evaluate each expression. a. 5 º 6 8 º 2  b. 20  282 c. 40 8 24 º 2  d. 42(4 º 2) 3 º 2  4. Solve each equation. a. 3x5 5x3 b. (4y 25)  y9 Solution Solution 5. Name three solutions of the inequality. Then graph the solution set. a. f  3 2 321012 Practice 6. $2.52 12 Estimate Quotient 7. 45 5 7.6 0 Estimate Quotient 8. 1209 3,7 20 Estimate Quotient 242–244 251–252

LESSON 6 12 Name Date Time Reviewing Relation Symbols and Inequalities 211 Copyright © Wright Group/McGraw-Hill 1. Translate between word and number sentences. Word sentence Number sentence a. 7 9is greater than 2 3. b. 19 ≠ 54 3 c. 20 is greater than or equal to 5 less than 5 squared. d. The product of 4 and 19 is less than 80. e. 62 plus a number yis greater than 28. f. 2. Indicate whether each inequality is true or false. a. 5 º 4 20 b. (7 3) º 6 60 c. 54 / 9 7 d. 45 9 º 5 e. 29 12  5 31 f. 18 2 º 7 6 3. Are the inequalities 17 6 9 and 9 17 6 equivalent? Explain. 2  1x 7

LESSON 6 12 Name Date Time Graphing Compound Inequalities 212 Copyright © Wright Group/McGraw-Hill Graph all solutions of each inequality. 1. 1 x 8 (Hint:1 x 8 means x 1 and x 8. For a number to be a solution, it must make both number sentences true.) 2. 3 y2 7 3. m2 4. x29 Write an inequality for each graph. 5. 6. 7. 10987654321012345678910 10987654321012345678910 10987654321012345678910 10987654321012345678910 10987654321012345678910 10987654321012345678910 10987654321012345678910

Copyright © Wright Group/McGraw-Hill Name Date Time Probability and Discrete Mathematics All of us are aware that the world is filled with uncertainties. As Ben Franklin wrote, “Nothing is certain except death and taxes!” Of course, there are some things we can be sure of: The sun will rise tomorrow, for example. We also know that there are degrees of uncertainty—some things are more likely to happen than others. There are occurrences that, although uncertain, can be predicted with reasonable accuracy. While predictions are usually most reliable when they deal with general trends, it is possible and often helpful to predict the outcomes of specific situations. In Unit 7, your child will learn how to simulate a situation with random outcomes and how to determine the likelihood of various outcomes. Additionally, the class will analyze games of chance to determine whether or not they are fair; that is, whether or not all players have the same chance of winning. We will be looking at two tools for analyzing probability situations: tree diagrams (familiar from single-elimination sports tournaments) and Venn diagrams (circle diagrams that show relationships between overlapping groups). One lesson concerns strategies for taking multiple-choice tests based on probability. Should test-takers guess at answers they don’t know? Your child will learn some of the advantages and disadvantages of guessing on this type of test. left- handed 84.865 152right- eyed 41 Venn diagram Please keep this Family Letter for reference as your child works through Unit 7. 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 4 1 4 1 4 1 4 Tree diagram STUDY LINK 6 13 Unit 7: Family Letter 213

Copyright © Wright Group/McGraw-Hill Vocabulary Important terms in Unit 7: equally likely outcomes Outcomesof a chance experiment or situation that have the same probability of happening. If all the possible outcomes are equally likely, then the probability of an event is equal to: expected outcome The average outcome over a large number of repetitions of a random experiment. For example, the expected outcome of rolling one die is the average number of dots showing over a large number of rolls. outcome A possible result of a chance experiment or situation. For example, heads and tails are the two possible outcomes of tossing a coin. probability A number from 0 through 1, giving the likelihood that an event will happen. The closer a probability is to 1, the more likely the event is to happen. probability tree diagram A drawing used to analyze a probabilitysituation that consists of two or more choices or stages. For example, the branches of the probability tree diagram below represent the fourequally likely outcomeswhen one coin is flipped two times. random number A number produced by a random experiment, such as rolling a die or spinning a spinner. For example, rolling a fair die produces random numbers because each of the six possible numbers 1, 2, 3, 4, 5, and 6 has the same chance of coming up. simulation A model of a real situation. For example, a fair coin can be used to simulate a series of games between two equally matched teams. Venn diagram A picture that uses circles or rings to show relationships among sets. The Venn diagram below shows the number of students who have a dog, a cat, or both. dog 95 6cat Students number of favorable outcomesnumber of possible outcomes H H (H,H) (H,T) (T,H) (T,T)THTT 214 Unit 7: Family Letter cont. STUDY LINK 613

Copyright © Wright Group/McGraw-Hill Do-Anytime Activities To work with your child on the concepts taught in this unit and in previous units, try these interesting and rewarding activities: 1.While playing a game that uses a die, keep a tally sheet of how many times a certain number lands. For example, try to find out how many times during the game the number 5 comes up. Have your child write the probability for the chosen number. ( 1 6is the probability that any given number on a six-sided die will land.) The tally sheet should show how many times the die was rolled during the game and how many times the chosen number came up. 2.Have your child listen to the weather forecast on television and pick out the language of probability. Have him or her listen for such terms as likely, probability, (percent) chance, unlikely,and so on. 3.Watch with your child for events that occur without dependence on any other event. In human relationships, truly independent events may be difficult to isolate, but this observation alone helps to define the randomness of events. Guide your child to see the difference between dependent events and independent events. For example, “Will Uncle Mike come for dinner?” depends on whether or not he got his car fixed. However, “Will I get heads or tails when I flip this coin?” depends on no other event. In Unit 7, your child will continue to review concepts from previous units and prepare for topics in upcoming units by playing games such as: 2–4–8 and 3–6–9 Frac–Tac–Toe(Percent Versions)SeeStudent Reference Book, pages 314–316 The two versions, 2-4-8 Frac-Tac-Toeand3-6-9 Frac-Tac-Toe,help students practice conversions between fractions and percents. Two players need a deck of number cards with four each of the numbers 0–10; a gameboard, a 5 5 grid that resembles a bingo card; a Frac-Tac-ToeNumber-Card Board; markers or counters in two different colors, and a calculator. Angle TangleSeeStudent Reference Book,page 306 Two players need a protractor, straightedge, and blank sheets of paper to play this game. Mastering the estimation and measurement of angles is the goal of Angle Tangle. Name That NumberSeeStudent Reference Book,page 329 This game provides practice in using order of operations to write number sentences. Two or three players need a complete deck of number cards. Solution SearchSeeStudent Reference Book, page 332 This game provides practice solving open number sentences. Players use a complete deck of number cards as well as Solution Searchcards to solve inequalities. Building Skills through Games 215 Unit 7: Family Letter cont. STUDY LINK 613

Copyright © Wright Group/McGraw-Hill As You Help Your Child with Homework As your child brings assignments home, you may want to go over the instr\ uctions together, clarifying them as necessary. The answers listed below will guide you through some of the Unit 7 Stu\ dy Links. Study Link 7 1 1.Quarter, nickel, dime; No. There is an unequal number of each type of coin. 2. 1, 2, 4, 5, 10, and 20 Yes. Each number card is a factor of 20. 3. 37.5% 4.100% 5.25%, 50%, 75% 6. 27.12 Study Link 7 2 1.No. Sample answer: Teams should be evenly matched. A team selected at random might not have a balance of skilled and unskilled players. 2. Yes and no. Sample answer: In an elementary school, preference for the better seats should go to the youngest children so they can see the game. However, in Grades 3–6, the principal should choose seat assignments randomly. 3. Disagree. Sample answer: There is always an even chance of this spinner landing on black or white. Previous spins do not affect the outcome. 4. Agree. Sample answer: There is always a better chance that this spinner will land on white because the white area is larger. The outcome does not depend on previous spins. Study Link 7 3 1.6 ways 2.30, 26, 23, 22, 19, 18, 16, 15, 12, 9 3a. 25% 3b.33.33% Study Link 7 4 3.12 4.15 5.15 Study Link 7 5 1.Tree diagram probabilities (from top, left to right) 1 2,1 2 Box 1: 1 3,1 3,1 3,1 3,1 3,1 3 Box 2: 1 2,1 2,1 2,1 2,1 2,1 2,1 2,1 2,1 2,1 2,1 2,1 2 Box 3: 11 2,11 2,11 2,11 2,11 2,11 2,11 2,11 2,11 2,11 2,11 2,11 2 2. 12 3. a. 1 6 b. 3 3, or 100% c. 1 3 d.0% 4. 36.5 5.22.6 6.12.6 Study Link 7 6 1. a. Track b.Basketball c.22 d.8 e. 30 f.52 g.22 3. 1 4 7 0 4. 2 1 11 2 5. 8 23 0 Study Link 7 7 1. Tree diagram probabilities (from top, left to right) 1 4,1 4,1 4,1 4 R1: 1 3,1 3,1 3;R2: 1 3,1 3,1 3; R3: 1 3,1 3,1 3;G: 1 3,1 3,1 3 Bottom row probabilities: 11 2,11 2,11 2,11 2,11 2,11 2,11 2,11 2,11 2,11 2,11 2,11 2 a. 50 b.25 2. a. HHT; HTH; HTT; THH; THT; TTH b. 37.5 c.87.5 Study Link 7 8 1. C, D, A, B 2. Tree diagram with branches labeled as follows (from left to right): Swimsuits: red, white, blue Sandals: red, white; red, white; red, white a. 6 b. 2 6, or 1 3 3. a. b. 25 Sample answer: 8 students play the piano, 5 students play the guitar, 2 students play both instruments, and 10 students play neither instrument. 8 2 5 10 25 216 Piano Ms. Garcia’s Students Guitar 10 8 5 2 Unit 7: Family Letter cont. STUDY LINK 613