Math. Textbook. Answer Keys. Chapter 1 Whole Numbers. 1.2: Place Value. Part A

Transcription

1 Answer Keys Part A Textbook MATH TEXTBOOK Math Marshall Cavendish Education Chapter Whole Numbers Page Quick Check Ninety-five thousand, seven hundred eighteen 8,, +, , 9 9,99 9,,9 9, 9 + =, 9 = + = 9 = Pages,, Six hundred thousand Seven hundred thousand 8, Nine hundred thousand,,, five hundred thousand fifty thousand seven thousand six hundred seventy six, five hundred fifty-seven thousand, six hundred seventy-six 8,; six hundred eighty-six thousand, forty-four Three hundred twenty-five thousand, one hundred seventy-six Four hundred thirty-eight thousand, eight hundred thirty-four Nine hundred six thousand, ninety-six Six hundred eighty thousand, eight hundred six 8 Seven hundred thousand, seven 9 Nine hundred ninety-nine thousand, nine hundred ninety-nine Four million Eight million 9,, 9,, 9 six hundred thousand five thousand three hundred seventy nine,,9,,; four million four million, six hundred five thousand, three hundred seventy-nine,,8 six million, three hundred forty thousand, five hundred eighty-one One million, two hundred thirty-four thousand, five hundred sixty-seven Two million, six hundred fiftythree thousand, three hundred fifty-six Four million, four hundred four thousand, forty-four Eight million, eight hundred eighty-eight thousand, eight hundred eighty-eight Five million, ninety thousand, nine hundred nine 8 Seven million, six thousand, sixty Page, 9,,,, two hundred fifteen thousand, nine hundred five eight hundred nineteen thousand, two six million, four hundred thirty thousand five million, nine thousand, three hundred Pages a 8 b c d,9.: Place Value Pages 8, tens ten thousands,, 8, 9 thousands hundred thousands

2 ten thousands,, a b, c ten thousands,,, 8, Page 9,, 9,,; thousands 8, 9,,,,,,.: Comparing Numbers to,, Pages Guided Practice 9 8 greater >,,89;,,98,,89;,,98 < > > <,8,88,,88 8,,,,,, 9 Pages 8,9,9 8,, 99,98,8 9,,,,98 9,,9,9 8,8,89,9 9,,,,;,,,,,;,,8 Rule: Count back by,.,; 8, Rule: Count on by,,.,,.: Rounding and Estimating Pages 9, 9,; 8, 9,, 8, 8,,,8,8 rounds to,;, rounds to,.,, 8, 9,, 9,,, a, b 9, a,99 b,99, +, = 9,,, =, 8, +, +, =, 9,,, =,,,,;,,;,;,;, 89; ; ; 8; ;,,;,,;,; 8, 8,,, 9,, 9,,;, 9,;,;, ; 8; ; ;,,;,; 8, 8,,, 8, 9,, 8,,8;, 8,;,;, ; 8; ; ;,,;,;,,,,, 8,

3 Pages,,;,, 9,,,; 8 8, 8,,;, 8, 9,, a, b,99, 8,, 8, 9,,,, 9 9 Page Put on Your Thinking Cap! Any number from to 9 and to a = 98 b = 9 c 8 and d 9 Page 8 Chapter Review/Test periods word form; million front-end estimation with adjustment compatible numbers,89, five million, eight hundred ninety-six thousand, four hundred thirteen,, + 8, + 9, +, , 9,, ten thousands > < Rule: Count back by,.,8,;,8, Rule: Count on by,,.,,;,,,,, 8, 9,,,, 8 9 three million, eight hundred fifty-one thousand, eight hundred eight square miles Canada, United States, France, Thailand, Hong Kong, Singapore Canada and United States 8 France and Thailand hundred twenty-four,,; 9,;,; ; ; 8; Five million, nine hundred five thousand, four hundred seventy-eight +; ; ; 98 ; ; 8, 9,, =, 8 =, 9 =, 9 = 9 9 =, =,8 8 = 8 = 9 = 9.: Using a Calculator Page 9 9,,99, km $,8 Page, 9,8, m. oz.: Multiplying by Tens, Hundreds, or Thousands Pages 8,,,8 To multiply a whole number by, just write a zero after the number.,, 8,,8, 8 9 8, Page Chapter Whole Number Multiplication and Division Page Quick Check 8,,;,;,;,; 9; ; ; Eight million, seven hundred fifty-three thousand, nine, 8 ; ;

4 Pages ( ),,,8 Page 8 Millions Hundred Ten Thousands Thousands Thousands Hundreds Tens Ones,,98 9 8,98,98,,, 9,8,98, Left speech bubble: To multiply a whole number by, just write two zeros after the number. Right speech bubble: To multiply a whole number by,, just write three zeros after the number. Page 9,, 8 9, 9 8, 8,,,, 9 8 Page 9 9, 9,,,,, ; ;, ;, ;, Pages 88; 8,8 8 8 ;, 8, 9 8, (8 ),,,,89,,8, 9,,,,9,,, 8 8 rounds to, and rounds to. ( ) 9,, 8, 8,,,,8 rounds to,, and rounds to.,, (, ) 8, 8, 9 8, Page, 9,,,8,,, 8 8, 9,, beads.: Multiplying by -Digit Numbers Pages 9 ltiply. Show your work. 9 multiply 9 by multiply 9 by add ones tens Estimate the value of 9. 9 rounds to, and rounds to. The estimate shows the answer is.,8,,8 8,8, 8 9, 9, Check!,8,98,8,,8 reasonable,8,8,,9,8,,8 8,,9 Check! 9, 9, 8,,9 reasonable 8, 9,8,98,, 9,

5 M ATH T EXTBOOK A NSWER K EY Page 9 Page,8,,,, 8, 8, 9,9,9,, 8,8, 8 9, Page 8.: Dividing by Tens, Hundreds, or Thousands,, Page, ; ; ,,, 8 9 9,,8 Page 8,,, 8,,,,;,; 8 Pages ; 9 ; 9 ; ; ,;,; ;, =, =, =, = 9 Page Page 8 8;, 8 (, ) 8 Sample answers: 8 Divisors for,: Number,,, Page Tens Ones, 8 8,,,,, Number 8, Can be divided by Answer = = = Divisors for,: Number,,, Answer, =, =,, = Divisors for : Ten Thousands Thousands Hundreds, Can be divided by, 8 Left speech bubble: To divide a multiple of by, just drop the two zeros. Right speech bubble: To divide a multiple of, by,, just drop the three zeros. C A LV E R T E D U C AT I O N Can be divided by, Answer, =, =,, =

6 Divisors for : Number Can be divided by Answer = = = Divisors for 88,: Number Can be divided by Answer 88, 8 88, 8 =, 88, 88, = 88,, 88,, = Page ,8 =, =.: Dividing by -Digit Numbers Pages R small 8 The quotient is and the remainder is. 9 big 9 The quotient is and the remainder is. R R 8 R The quotient is 8 and the remainder is. R 8 R 8 R 9 8 R The quotient is and the remainder is. R 9 R R 8 R The quotient is 9 and the 9 remainder is. 9 9 R 9 R R 8 R 8 R The quotient, 9 is 9 and the hundred remainder is. tens R R R 9 8 R Page 89 Math Journal Step : Round to the nearest ten. Then estimate the quotient. rounds to. = The quotient is about. Step : Check if the estimated quotient is too big or too small. 8 9 The estimated quotient,, is too big. Use as a quotient. Step : Work out the division using as a quotient. 8 The quotient is and the remainder is.

7 R R R 8 R 8 8 R R 9 9 R R R.: Order of Operations Pages Page 9 The answers are the same. Number sentence Partner A s answers Partner B s answers Page 9 8, 8 8.: Real-World Problems: Multiplication and Division Pages 9 = R; There are bags of potatoes. pounds of potatoes are left.,,,;, Amount paid number of payments amount for each payment $8 $ Then, fi nd the cost of the car. Cost of car total amount paid amount she still has to pay $ $,9 Cost of the car: $ ( $8) $,9 Which operation will you use to fi nd how $ much she would pay for each of the payments? $ $ She would pay $ for each of the equal payments. Total number of hours h Parking fee for the fi rst hour $ Parking fee for the second hour $ Parking fee from A.M. to P.M. $ $ Total parking fee $ $ $ $ Mr. Lee paid $. Page barrels; gallons of water are left stamps small boxes a packages b $ c $,. cans a $. b ounces Pages ;,, 8

8 Number of Cars Number of Number of Are there Motorcycles Wheels Wheels? No (too many) 9 8 No (too many) No (too many) There are motorcycles. Pages 8 $ $ $8 8 pencils $ cows 9 stamps milliliters Page 9 Put On Your Thinking Cap! Method : (, 8), = 9,8 Method : (, 8) +, = 9,8 9 I can rewrite 9 as or.,,,, 9 groups, 9 (, ), 9,,, groups, 9 (, ) Pages Chapter Review/Test factors; product dividend; divisor; quotient; remainder numeric expressions order of operations,8, 8, 8,88 9 9,,8, Answers may vary. Sample answers as shown.,,, 8,98 98,9 9, about about 9 about 9 R 9 R 8 8 R 9, a,8 balloons b large packets c $8 Chapter Fractions and Mixed Numbers Pages 9 Quick Check ¾; ¼ 9; 9 ; ½ ; wholes parts = 8 9 ¾ ; ½; ⅔; ¾ ; ; ; 8; 8 ¼ ¾ 8 ⅞ 9 ¼ ½ : Adding Unlike Fractions Page 9 8 ¾ Page + ½ = ½ + = + ½ + = ½ Page Since both ⅓ and ⅜ are less than ½, their sum is less than. Since both 9 and are greater than ½, their sum is greater than. is slightly less than ½ whereas is slightly more than ½. So, we cannot tell by estimating if the sum of and is greater than or less than. Math Journal a Model b Model : The wrong number of units is shaded to show ½. Model : The wrong number of units is shaded to show. 9

9 Page Page Accept: ¾ ½ ½ + = ½ ½ + ½ = + ½ + = ½.: Subtracting Unlike Fractions Page 8 8 Page 9 ½ = ½ = ½ ½ = is less than ½. Subtracting a fraction less than ½ from will give a fraction greater than ½. So, the difference between and is greater than ½. is greater than ½. Subtracting a fraction greater than ½ from will give a fraction less than ½. So, the difference between and is less than ½. is about whereas ¼ is about. So we can estimate that the difference between and ¼ is greater than ½. ⅛ ½ 8 ½ 8 ⅓ ½ = ½ ½ = ½ =.: Fractions, Mixed Numbers, and Division Expressions Pages ; ¾; ¾; ; 9 ⅝ ; 8; 8 ; 9 ; 9 = 9½ ¾ = ¾ 9 = 9 = ½ Page ; ; 9; ; ⅓ ¾ 8 9 ½ = ½ 8 = ⅔.: Expressing Fractions, Division Expressions, and Mixed Numbers as Decimals Pages 8 8;.8 ; a yards b. yards

10 Page a quarts b. quarts a 9¾ yards b 9. yards ¾,. 8,. 9,.,.8 ¼,.,.8.: Adding Mixed Numbers Pages ½ + 9½ = + ½ = ½ 8½ + = 8½ + = + ½ = ½ Page Since ¼ and 9 are less than ½, their sum must be less than. So, the sum of ¼ and 9 must be less than. Since 9 and are greater than ½, their sum must be greater than. So, the sum of 9 and must be greater than. ⅜ is less than ½ whereas is greater than ½. We cannot tell if the sum of ⅜ and is greater than or less than. So, we cannot tell by estimating if the sum of ⅜ and is greater than or less than 9. Page 9¼ 9 9½8 8 8 ½ + ½ = 8 + = 9 + 9½ = ½.: Subtracting Mixed Numbers Pages ½ = ½ 8 8 ½ = ½ Pages 8 9 ¼ ⅝ ⅝ ½ ½ = ½ = ½.: Real-World Problems: Fractions and Mixed Numbers Pages ⅔ pounds 9 quarts 8 pounds pints pounds

11 Page Math Journal a Leah s and Marta s answers are incorrect. 8 b Page Put On Your Thinking Cap! baseball cards soccer cards basketball cards.: Multiplying Proper Fractions Page ¼ = = Pages 8 9 Chapter Review/Test least common multiple equivalent fractions; mixed number benchmark division expression ⅜ ½ ½ = + ½ + = ½ ¾ ⅓..,. ¼, ¼ 8 9 ½ + ½ = 9 ½ = ½ a ¾ pounds b ½ pounds c pounds Chapter Multiplying and Dividing Fractions and Mixed Numbers Pages Quick Check Answers vary. Sample answers as shown. ; 9 8; 9 ; 8 ½ ¼ ⅔ ¾ ½ = = Page Step Step ; yes; The products are equal. Page Finding the product of two whole numbers is the same as multiplying one number by the number of times given by the second number. So, the product of any two numbers is greater than each of the numbers.

12 8 Finding the product of two proper fractions is the same as finding a fractional part of another fraction. A proper fraction is always less than, so a fractional part of a proper fraction will always be less than the original fractions. Page 8 ⅓ ½ ¼ ⅜.: Real-World Problems: Multiplying with Proper Fractions Page Method gal gal a She gives of the strawberries to her neighbor. b She has of the strawberries left. Method a of Janice's strawberries is left after she makes jam with of them. She gives of the strawberries to her neighbor. b She has of the strawberries left. Page ½ ⅓ ⅓ yard ⅓ ¼ ⅓ The model shows that: units gal unit gal units gal a Michelle uses gallon of paint. b There is gallon of paint left. Method a Michelle uses gallon of paint. b There is gallon of paint left. jam The model shows that: Number of units given to the neighbor Total number of units in whole.: Multiplying Improper Fractions by Fractions Page ½ = = 9 = ½ = = 8 8 = ¾ 9 = 9 = 9 8 = 9⅓ 8 = 8.: Multiplying Mixed Numbers and Whole Numbers Page 8 So, is the same as groups of.

13 Page 9 Step d ¼ ⅛ Page 8 ½ ⅔.: Real-World Problems: Multiplying with Mixed Numbers Pages bottle qt bottles qt bottles contain quarts of olive oil qt of olive oil $ qt of olive oil $ $ The total cost of the olive oil is $. Page 8 cups ½ ⅛ ounces ¼ pounds $. $.: Dividing a Fraction by a Whole Number Pages 8 8 ; ; Each piece is feet long. ; ⅓; Page 88 Count a the total number of parts, b the number of colored parts. ; Each piece is feet long. Page 89 9 square yards 8 9 a ⅓ pound b pound.: Real-World Problems: Multiplying and Dividing with Fractions Pages 9 9 of units units of units units plants The model shows that: units plants unit plants Kim has pumpkin plants. ;

14 ; ; ; Page 9 a tickets b 8 tickets $ minutes 9 centimeters meter apples Page 98 Math Journal Amol got the answer by dividing the denominator 9 by. division Page 99 Put On Your Thinking Cap! + ; addition Bart got the answer by adding the numerators and the denominators separately. a b students kg 8 kg kg kg Number of toy cars bought by Brad = ½ = Total number of toy cars bought = + = toy cars $ toy car $ = $ The cost of each toy car was $. Pages Chapter Review/Test improper fraction mixed number common factor reciprocal ⅔ ⅔ ⅝ 8 ⅓ 9 8 ⅜ 9 $. a square yard b square yard 98 Chapter Algebra Page Quick Check > < = 8 True 9 False Tr ue False True 9 8.: Using Letters as Numbers Pages x x x x 8 z z z z z z 8 z 9 z k ; groups of k ; k ; k groups of (any three) j ; groups of j ; j ; j groups of (any three) p ; p ; p ; p groups of (any three) 8q ; 8 q ; q 8 ; 8 groups of q (any three)

15 n 8 n n n m 8 m 8m p p p p 8 8 9, 9,9 98 Page ; ; They are equivalent expressions. ; ; They are equivalent expressions. + (+ Page Math Journal Answers vary. Pages 8 Answers vary. Sample answers as shown. w v x or x y or y (z + ) or (z + ) (a ) or a 9 + b 8 b 9 b b b b b b b + 8 x + ; 8 x ; 9 x; x ; 9 n ; 8 n ; n ; + ; 9,9,,99 8 9, 9,8.: Simplifying Algebraic Expressions Pages x y a b c a; a; a a 8 x 9 z 9y b c a 8 a a a a a a a a 9 x x y x a a b + 8 b s s + Page a 8a a x x y 8 y 9 a + b + 8 s + + r.: Inequalities and Equations Pages = > < > less than = > r = q =

16 Page < > = < = > < 8 < 9 < > j = k = m = 8 n =.: Real-World Problems: Algebra Pages 9 a m + ; m + m + = m + b a y + b (y + ); (y + ) (y + ) a > Lenny b y y Pages 9 a r b r c years old a x dollars b ( x) dollars c $ a z b z + c 9z + a < 9; The steel pipe is longer. b p = a m dollars b $8 a q quart b. quarts Page Math Journal Answers vary. No, it is not correct. a does not stand for apple. It stands for an unknown number. So a can be any number. The correct way to think of a + a = a is that any number added to itself is equal to twice the number. Put On Your Thinking Cap! Solution: Let the number that Grace thinks of be m. () m = m () m + () m + m = Grace will get. Pages Chapter Review/Test variable algebraic expression evaluate inequality; equation solve x + 8 x 8 x 9 x 8 a a a a + 8 < 9 > = > p = p = p = 8 p = a men: m = m; children: m, b, a Andy b 8 Chapter Area of a Triangle Pages 9 Quick Check b and c; d and f; a and e Ye s No cm in. in. 9 cm 8 cm 9 ft.: Base and Height of a Triangle Page CB; AD JH; GK MN; LO RT; ST BE; AC QR; PQ XU; YZ Page Step They are all perpendicular to the base. Pages AC; BD RS; PQ height ZW; XY base BC AB CF AC BE BC AD ZW.: Finding the Area of a Triangle Pages 9 -Step JEFK HEFI DG height

17 -Step WQRV UQRT PS height The area of triangle DEF is half the area of the corresponding rectangle HEFI or half its base times height. The area of triangle PQR is half the area of the corresponding rectangle UQRT or half its base times height. The formula for area of triangle applies to acute and obtuse triangles. Step. cm Step yes Page cm 8 in. cm 8 yd 88 ft 9 m Pages 8 cm 9 in. 9 yd 8 m 9 cm 8 in. ft 8 in. 9 yd Page They are equal; heights; area Put On Your Thinking Cap! A cm 8 cm B Area of triangle ABD = 8 = cm Area of triangle ABE = E = cm Page Chapter Review/Test perpendicular base; height area acute triangle BC; AD QR; PS FD; ED 8 MN; PO 9 cm D C in. m ft 8 cm cm cm Chapter Ratio Page 8 Quick Check 8 9 out of parts out of 8 parts : Finding Ratio Pages : : blue pennants to or there are The ratio : tells us that there are yellow pennants yellow pennants to blue pennants. : : : : : : The ratio : tells us that there are yellow pennants to blue pennants or there are blue pennants to yellow pennants. 8 Pages : 8; : 9;. Sample answers: Ratio Mass of mussels to mass of lobsters : Mass of shrimp to mass of scallops : 8 Mass of crabs and lobsters to mass of scallops : and shrimp Mass of lobsters to mass of shellfish in total : 9 Mass of shellfish in total to mass of scallops 9 : 8 A B A B A : B = : and B : A = : or A : B = : and 8

18 B : A = : Accept : and : or : and :. : :.: Equivalent Ratios Pages 8 8 : ; ; : ; ; : : ; : ; : : : Page 8 Step Answers vary. Step They are equivalent ratios. Step These ratios are also equivalent ratios because the number of cubes in each group is the common factor of the terms of the ratios. Page 8 : : 8 They are equivalent ratios. : 9 : 8 : 9 : 9 8.: Real-World Problems: Ratios Pages 8 88 : : = : The ratio of the total number of umbrellas and raincoats sold to the number of raincoats sold is :. = ; The number of umbrellas sold was. : = : ; The ratio of the number of umbrellas sold to the number of raincoats sold is :. + 8 = 8; Gerald donated a total of 8 quarters. 8 : = : ; The ratio of the total number of quarters Gerald donated to the number of dimes he donated is :. The total number of quarters Gerald donated is = ; Gerald donated a total of coins. 8 : = : ; The ratio of the total number of quarters Gerald donated to the number of coins he donated is :. 9 + = ; The total number of stamps in Stanley s collection is. 9 : = : 9; The ratio of the number of U.S. stamps to the total number of stamps Stanley has is : 9. 8 ml Portion Portion? ml units ml unit ml units ml The total volume of both portions is milliliters. Method : : The volume of portion is milliliters. The total volume of both portions is milliliters. Page 89 Math Journal Answers vary. : : : cm 8 :.: Ratio in Fraction Form Page 9 : or : or It is the first term of the same ratio in ratio form. It is the second term of the same ratio in ratio form. The first term of a ratio is the numerator of the same ratio in fraction form. The second term of a ratio is the denominator of the same ratio in fraction form. 9

19 Pages 9 9 ½; ½ ; : or : or : : 8 : : : : : : Page 9 Math Journal Answers vary. Pages 9 9 : or : Comparing Three Quantities Pages 9 : : Page Step : : 8 = : : Page : : : : : 8 : : : : : : : ; 8 8 8; 9 ; ; : : : :.: Real-World Problems: More Ratios Pages 8 unit cm Length of Z Total number of units The total length of the three pieces of ribbon is centimeters. units $ car paym unit $ $ Total number of units electric $ $ grocery The total amount of all three bills was $. Total number of units From the model: a The ratio of the number of coins Sally has to the number of coins Layla has to the total number of coins they have is : :. b units coins unit coins units 8 coins They have coins altogether. The ratio of the distance Raul ran to the distance he swam to Tot the total distance of the biathlon is : :. of Distance Raul ran Total distance of the biathlon The distance Raul ran is times the total distance of the biathlon. units unit units The total distance of the biathlon was meters.

20 Pages 9 : : 8 : : centimeters a 8 milliliters b, milliliters a Anna b $, a b a b c d Lilian: years old. May: years old. 8a : : 8b 8c lb 9a 9b ¾ 9c ¼ 9d square meters a : : b c d Page Math Journal Accept reasonable explanations and models. The ratio of the number of white balloons to the number of pink balloons is : or :. Answers vary. Sample: : : = 8 : :. Sample answers: : = : : = :. Rewrite the given numbers as products. = 8 = 9 = = = = = = = = = = = Identify the common factors of the given numbers. Use guess and check to find equivalent ratios whose terms are all on the list. For example, 8,, and have a common factor of. Dividing each of them by gives,, and. Page Put On Your Thinking Cap! a $ b 8 quarters $.9 Page Chapter Review/Test ratio ; terms equivalent ratios simplest form greatest common factor A A A : B = : B B 8 A : B = : 9 : : / 8/ : : 8 : : 9 : 9 ; : 8 : a cm b cm c cm Page 9,,,,8,..a: Evaluating Expressions with Parentheses, Brackets, and Braces Pages [8 ( + )] = Step : + = Step : 8 = Step : = 9 { [ ( )]} = Step : = Step : = 8 Step : 8 = Step : 9 = [9 ( + 9)] [9 ] 8 [( ) ] 8 [ ] 8 8 { [ ( )]} 8 { [ ]} 8 { } 8 8 {[ (8 )] } {[ ] } { } [ ( 8 )] [ ( )] [ 8] [ 8] 9 ( ) +[(8+ ) 9] [(8+ ) 9] [8 9] [8 ] 8

21 .: Multiplying with Whole Numbers and Proper Fractions Page Sample answer: Finding by finding groups of, so the product is greater than the factor. You could also find by finding groups of, so the product is greater than the factor. Sample answer: The product of two whole numbers (greater than ) is greater than either factor. Either way you multiply the two numbers, you are finding the number of items in several groups, which means that the product is greater than both the factors. Sample answer: The product ⅓ means to find a fractional part of, so the product is less than the factor. However, the product ⅓ means to find groups of /, so the product is greater than the factor ⅓. Sample answer: The product of a proper fraction and a whole number is less than the whole number factor (because you are finding a part of the whole number) but greater than the fractional factor (because you are finding equal groups of the fraction)..: Finding the Area of a Rectangle with Fractional Side Lengths Page 8 yd yd ft ft 9 yd ft 9 yd 8 in. 8 yd in yd 8 in...a: Dividing a Whole Number by a Unit Fraction Page jugs 8 square yards..a: Real-World Problems: Dividing a Whole Number by a Unit Fraction Page gallons He can water potted plants. 8 bottles of ceramic glaze 8 8 He can coat pieces of sculpture.