9 Dear Family, During the next few weeks, our math class will relate both fractions and money to place value and will learn how to rename fractions as decimals. We will also add fractional parts of 10 and 100 and compare decimals through hundredths. decimal A number with one or more digits to the right of the decimal point decimal point A symbol used to separate dollars from cents in money amounts and to separate the ones and tenths places in a decimal equivalent decimals Two or more decimals that name the same amount hundredth One of one hundred equal parts tenth One of ten equal parts You can expect to see homework that provides practice with naming decimals in different ways, including renaming as fractions. Here is a sample of how your child will be taught to write a decimal as a fraction. Write Hundredths as a Fraction This is how we will use place value to help write a decimal as a fraction. Ones 0 . . Tenths Hundredths 6 4 decimal point © Houghton Mifflin Harcourt Publishing Company Think: 0.64 is the same as 6 tenths and 4 hundredths, or 64 hundredths. A place-value chart can be used to help visually organize numbers in relation to the decimal place. The chart can be used to pair the numbers with words, and may enable a smooth transition between standard form, word form, and the decimal or fraction. 64 So, 0.64 5 ___ 100 . Activity Use the relationship between dollars and cents and work together to express the value of a penny, nickel, dime, and quarter as a decimal and as a fraction of a dollar. Then make small groups of coins and help your child write the value of each group as a decimal and as a fraction. Chapter 9 P169 9 Querida familia, Durante las próximas semanas, en la clase de matemáticas relacionaremos tanto las fracciones como el dinero con el valor posicional y aprenderemos a convertir fracciones en decimales. También sumaremos partes fraccionales de 10 y de 100 y compararemos decimales hasta los centésimos. decimal Un número con uno o más dígitos a la derecha del punto decimal punto decimal Un símbolo usado para separar dólares de centavos en cantidades de dinero y para separar el lugar de las unidades y los décimos en decimales decimales equivalentes Dos o más decimales que nombran la misma cantidad centésimo Una de cien partes iguales décimo Una de diez partes iguales Llevaré a la casa tareas para practicar la expresión de decimales de diferentes maneras, incluso la conversión en fracciones. Este es un ejemplo de la manera como aprenderemos a escribir un decimal como una fracción. Escribir centésimos como una fracción Unidades . Décimos Centésimos . 4 0 6 punto decimal Piensa: 0.64 es lo mismo que 6 décimos y cuatro centésimos, o 64 centésimos. Una tabla de valor posicional se puede usar para ayudar a organizar visualmente números en relación con el lugar decimal. La tabla puede usarse para emparejar números con palabras y para facilitar la transición del uso de la forma normal a la forma en palabras y a la fracción decimal. 64 . Por tanto, 0.64 5 ____ 100 Actividad Usen la relación entre dólares y centavos y trabajen juntos para expresar el valor de una moneda de uno, de cinco, de diez y de veinticinco centavos en forma decimal y como una fracción de dólar. Luego hagan pequeños grupos de monedas y ayude a su hijo/a a escribir el valor de cada grupo en forma decimal y como fracción. P170 © Houghton Mifflin Harcourt Publishing Company Así es como usaremos el valor posicional para escribir un decimal como una fracción Lesson 9.1 Name COMMON CORE STANDARD MACC.4.NF.3.6 Relate Tenths and Decimals Understand decimal notation for fractions, and compare decimal fractions. Write the fraction or mixed number and the decimal shown by the model. 1. Think: The model is divided into 10 equal parts. Each part represents one tenth. 2. 6 ; 0.6 __ 10 ___ ___ 3. 4. ___ ___ Write the fraction or mixed number as a decimal. 1 4 7 5. ___ 6. 3___ 7. ___ 10 10 10 © Houghton Mifflin Harcourt Publishing Company _ _ _ 10. There are 10 sports balls in the equipment closet. Three are kickballs. Write the portion of the balls that are kickballs as a fraction, as a decimal, and in word form. 5 8. 6___ 10 _ 9 9. ___ 10 _ 11. Peyton has 2 pizzas. Each pizza is cut into 10 equal slices. She and her friends eat 14 slices. What part of the pizzas did they eat? Write your answer as a decimal. Chapter 9 P171 Lesson Check (MACC.4.NF.3.6) 1. Valerie has 10 CDs in her music case. Seven of the CDs are pop music CDs. What is this amount written as a decimal? 2. Which decimal amount is modeled below? A 70.0 B 7.0 C 0.7 D 0.07 A 140.0 B 14.0 C 1.4 D 0.14 Spiral Review (MACC.4.OA.2.4, MACC.4.NF.1.1, MACC.4.NF.2.3b) 3. Which number is a factor of 13? (Lesson 5.1) A 1 C 4 (Lesson 5.3) 5. How do you write the mixed number shown as a fraction greater than 1? (Lesson 7.6) P172 A 2 rows C 4 rows B 3 rows D 6 rows 6. Which of the following models has an amount shaded that is equivalent to the fraction 1_5 ? (Lesson 6.1) A C B D 6 C __ 4 __ D 4 4 © Houghton Mifflin Harcourt Publishing Company D 7 14 B ___ 4 4 photographs displayed in equal rows on a wall, with the same number of each type of art in each row. Which of the following could be the number of rows? B 3 32 A ___ 5 4. An art gallery has 18 paintings and Lesson 9.2 Name COMMON CORE STANDARD MACC.4.NF.3.6 Relate Hundredths and Decimals Understand decimal notation for fractions, and compare decimal fractions. Write the fraction or mixed number and the decimal shown by the model. 1. Think: The whole is divided into one hundred equal parts, so each part is one hundredth. 2. 77 ; 0.77 ___ 100 ___ ___ 4. 3. ___ © Houghton Mifflin Harcourt Publishing Company ___ Write the fraction or mixed number as a decimal. 11 37 98 5. ____ 6. 8 ____ 7. ____ 100 100 100 __ __ 10. There are 100 pennies in a dollar. What __ fraction of a dollar is 61 pennies? Write it as a fraction, as a decimal, and in word form. ______ ______ 50 100 8. 25 ____ __ 6 9. ____ 100 __ 11. Kylee has collected 100 souvenir thimbles from different places she has visited with her family. Twenty of the thimbles are carved from wood. Write the fraction of thimbles that are wooden as a decimal. ______ Chapter 9 P173 Lesson Check (MACC.4.NF.3.6) 1. Which decimal represents the shaded section of the model below? 2. There were 100 questions on the unit test. Alondra answered 97 of the questions correctly. What decimal represents the fraction of questions Alondra answered correctly? A 0.97 B 9.70 C 90.70 D 970.0 A 830.0 C 8.30 83.0 D 0.83 B Spiral Review (MACC.4.OA.3.5, MACC.4.NF.2.3b, MACC.4.NF.2.3d, MACC.4.NF.2.4c) 3. Which is equivalent to 7_8 ? __ 1 3 __ A 5 (Lesson 7.2) 9 6 __ 4. What is __ 10 2 10 ? (Lesson 7.4) 8 8 __ 1 1 __ 1 1 __ B 4 8 8 8 __ 1 2 __ 1 2 __ C 3 8 8 8 __ 1 2 __ 1 1 __ 1 1 __ D 2 8 8 8 8 5. Misha used _14 of a carton of 12 eggs to make an omelet. How many eggs did she use? (Lesson 8.4) A 2 6. Kurt used the rule add 4, subtract 1 to generate a pattern. The first term in his pattern is 5. Which number could be in Kurt’s pattern? (Lesson 5.6) B 3 A 4 C 4 B 6 D 6 P174 4 C ___ 10 6 D ___ 10 C 10 D 14 © Houghton Mifflin Harcourt Publishing Company 1 A ___ 10 3 B ___ 10 Lesson 9.3 Name Equivalent Fractions and Decimals COMMON CORE STANDARD MACC.4.NF.3.5 Understand decimal notation for fractions, and compare decimal fractions. Write the number as hundredths in fraction form and decimal form. 5 5 5 _______ 5 3 10 5 ____ 50 ___ 1. ___ 10 10 10 3 10 100 Think: 5 tenths is the same as 5 tenths and 0 hundredths. Write 0.50. 50 ; 0.50 ___ 100 9 2. ___ 3. 0.2 10 4. 0.8 © Houghton Mifflin Harcourt Publishing Company Write the number as tenths in fraction form and decimal form. 40 10 5. ____ 6. ____ 100 100 6 8. Billy walks __ 10 mile to school each day. 6 Write __ as hundredths in fraction form 10 and in decimal form. 7. 0.60 9. Four states have names that begin with the letter A. This represents 0.08 of all the states. Write 0.08 as a fraction. Chapter 9 P175 Lesson Check (MACC.4.NF.3.5) 1. The fourth-grade students at Harvest School make up 0.3 of all students at the school. Which fraction is equivalent to 0.3? A B C D 3 __ 2. Kyle and his brother have a marble set. Of the marbles, 12 are blue. This 50 represents ___ 100 of all the marbles. Which 50 decimal is equivalent to ___ 100 ? A 10 30 __ 10 3 ___ 100 33 ___ 100 50 B 5.0 C 0.50 D 5,000 Spiral Review (MACC.4.OA.3.5, MACC.4.NF.1.1, MACC.4.NF.2.4c, MACC.4.NF.3.6) 45 3. Jesse won his race by 3 ___ seconds. 100 What is this number written as a decimal? (Lesson 9.2) A 0.345 B 3.45 34.5 D 345 P176 A 2 inches B 4 inches C 5 inches D 6 inches 9 5. Of Katie’s pattern blocks, __ 12 are triangles. 9 What is __ in simplest form? (Lesson 6.3) 1 A __ 4 __ B 2 3 __ C 3 4 9 D ___ 12 pictures on poster board. Each piece of tape was 3_8 inch long. How much tape did Marge use? (Lesson 8.4) 12 6. A number pattern has 75 as its first term. The rule for the pattern is subtract 6. What is the sixth term? (Lesson 5.6) A 39 B 45 C 51 D 69 © Houghton Mifflin Harcourt Publishing Company C 4. Marge cut 16 pieces of tape for mounting Lesson 9.4 Name COMMON CORE STANDARD MACC.4.NF.3.6 Relate Fractions, Decimals, and Money Understand decimal notation for fractions, and compare decimal fractions. Write the total money amount. Then write the amount as a fraction or a mixed number and as a decimal in terms of dollars. 1. 2. 18 ; 0.18 $0.18; ___ 100 ______ ______ Write as a money amount and as a decimal in terms of dollars. 25 3. ____ 100 79 4. ____ 31 5. ____ 100 __ 8 6. ____ 100 __ 42 7. ____ 100 __ 100 __ __ Write the money amount as a fraction in terms of dollars. 8. $0.87 9. $0.03 __ 10. $0.66 __ 11. $0.95 __ 12. $1.00 __ __ Write the total money amount. Then write the amount as a fraction and as a decimal in terms of dollars. © Houghton Mifflin Harcourt Publishing Company 13. 2 quarters 2 dimes ____ 14. 3 dimes 4 pennies ____ 16. Kate has 1 dime, 4 nickels, and 8 pennies. Write Kate’s total amount as a fraction in terms of a dollar. _______ 15. 8 nickels 12 pennies ____ 75 17. Nolan says he has ___ of a dollar. If he 100 only has 3 coins, what are the coins? _______ Chapter 9 P177 Lesson Check (MACC.4.NF.3.6) 1. Which of the following names the total money amount shown as a fraction in terms of a dollar? 81 2. Crystal has ___ 100 of a dollar. Which of the following could be the coins Crystal has? A 3 quarters, 1 dime, 1 penny B 2 quarters, 6 nickels, 1 penny C 2 quarters, 21 pennies D 1 quarter, 4 dimes, 1 nickel, 1 penny 43 A ___ 1 ___ B 43 10 43 C ___ 57 43 D ____ 100 Spiral Review (MACC.4.NF.1.1, MACC.4.NF.3.6) 3 (Lesson 6.2) 3 A __ 5 __ B 2 6 8 __ 9 4 D ___ 10 C 5. Which decimal is shown by the model? B P178 1.0 the pretzels. Which fraction is equivalent to _38 ? (Lesson 6.2) 9 A ___ 24 3 C ___ 16 ___ B 15 20 __ D 1 5 6. Mr. Guzman has 100 cows on his dairy farm. Of the cows, 57 are Holstein. What decimal represents the portion of cows that are Holstein? (Lesson 9.2) (Lesson 9.2) A 10.0 4. Penelope bakes pretzels. She salts _38 of C 0.1 D 0.01 A 0.43 B 0.57 C 5.7 D 57.0 © Houghton Mifflin Harcourt Publishing Company 3. Joel gives _13 of his baseball cards to his sister. Which fraction is equivalent to _1 ? Name HE8B;CÃEBL?D=ÃÄÃED;O PROBLEM SOLVING Lesson 9.5 COMMON CORE STANDARD MACC.4.MD.1.2 Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Use the act it out strategy to solve. 1. Carl wants to buy a bicycle bell that costs $4.50. Carl has saved $2.75 so far. How much more money does he need to buy the bell? Use 4 $1 bills and 2 quarters to model $4.50. Remove bills and coins that have a value of $2.75. First, remove 2 $1 bills and 2 quarters. Next, exchange one $1 bill for 4 quarters and remove 1 quarter. Count the amount that is left. So, Carl needs to save $1.75 more. $1.75 ____ 2. Together, Xavier, Yolanda, and Zachary have $4.44. If each person has the same amount, how much money does each person have? ____ 3. Marcus, Nan, and Olive each have $1.65 in their pockets. They decide to combine the money. How much money do they have altogether? © Houghton Mifflin Harcourt Publishing Company ____ 4. Jessie saves $6 each week. In how many weeks will she have saved at least $50? ____ 5. Becca has $12 more than Cece. Dave has $3 less than Cece. Cece has $10. How much money do they have altogether? ____ Chapter 9 P179 Lesson Check (MACC.4.MD.1.2) 1. Four friends earned $5.20 for washing a car. They shared the money equally. How much did each friend get? A $1.05 B $1.30 C $1.60 D $20.80 2. Which represents the value of one $1 bill and 5 quarters? A $1.05 B $1.25 C $1.50 D $2.25 Spiral Review (MACC.4.OA.2.4, MACC.4.NF.1.1, MACC.4.NF.1.2, MACC.4.NF.3.6) dollar is this? (Lesson 9.4) A B C D 9 ____ 100 9 ___ 10 90 ____ 100 99 ____ 100 5. I am a prime number between 30 and 40. Which number could I be? (Lesson 5.5) A 31 B 33 C 36 D 39 P180 9 4. Michael made __ 12 of his free throws at 9 practice. What is __ in simplest form? 12 (Lesson 6.3) 1 A __ 4 3 B __ 9 __ C 1 2 3 D __ 4 1 6. Georgette is using the benchmark __ to 2 compare fractions. Which statement is correct? (Lesson 6.6) 3 __ A __ >1 8 2 2 __ <1 B __ 5 2 1 7 C ___ < __ 12 2 9 1 = __ D ___ 10 2 © Houghton Mifflin Harcourt Publishing Company 3. Bethany has 9 pennies. What fraction of a Lesson 9.6 Name Add Fractional Parts of 10 and 100 Find the sum. 2 43 1. ___ 1 ____ 10 100 100 Understand decimal notation for fractions, and compare decimal fractions. 2 Think: Write __ 10 as a fraction with a denominator of 100: 20 43 63 __ 1 __ 5 __ 100 COMMON CORE STANDARD MACC.4.NF.3.5 2 3 10 5 ____ 20 _______ 10 3 10 100 100 63 ___ 100 17 6 2. ____ 1 ___ 9 4 3. ____ 1 ___ 23 7 4. ___ 1 ____ 5. $0.48 1 $0.30 6. $0.25 1 $0.34 7. $0.66 1 $0.06 © Houghton Mifflin Harcourt Publishing Company 100 100 10 10 38 8. Ned’s frog jumped ___ 100 meter. Then his 4 frog jumped __ meter. How far did Ned’s 10 frog jump in all? 10 100 5 9. Keiko walks __ 10 kilometer from school to 19 the park. Then she walks ___ kilometer 100 from the park to her home. How far does Keiko walk in all? Chapter 9 P181 Lesson Check (MACC.4.NF.3.5) 2 1. In a fish tank, __ 10 of the fish were orange 5 and ___ of the fish were striped. What 100 fraction of the fish were orange or striped? 7 A ___ 10 52 B ____ 100 25 C ____ 100 7 D ____ 100 2. Greg spends $0.45 on an eraser and $0.30 on a pen. How much money does Greg spend in all? A $3.45 B $0.75 C $0.48 D $0.15 Spiral Review (MACC.4.NF.1.1, MACC.4.NF.2.3d, MACC.4.MD.1.2) many months will it take him to save at least $60? (Lesson 9.5) A 6 months B 7 months C 8 months D 9 months 5. A carpenter has a board that is 8 feet long. He cuts off two pieces. One piece is 3 1_2 feet long and the other is 2 1_3 feet long. How much of the board is left? (Lesson 7.10) 4. Ursula and Yi share a submarine sandwich. Ursula eats _28 of the sandwich. Yi eats 3_ of the sandwich. How much 8 of the sandwich do the two friends eat? (Lesson 7.5) 1 A __ 8 __ B 4 8 __ C 5 8 __ D 6 8 6. Jeff drinks _23 of a glass of juice. Which fraction is equivalent to 2_ ? (Lesson 6.2) A A 2 1_6 feet B B 2 5_6 feet C C 3 1_6 feet D D 3 5_6 feet P182 1 __ 3 3 __ 2 3 __ 6 8 ___ 12 3 © Houghton Mifflin Harcourt Publishing Company 3. Phillip saves $8 each month. How Lesson 9.7 Name COMMON CORE STANDARDS MACC.4.NF.3.7 Compare Decimals Understand decimal notation for fractions, and compare decimal fractions. Compare. Write ,, ., or 5. 1. 0.35 , 0.53 2. 0.6 0.60 3. 0.24 0.31 Think: 3 tenths is less than 5 tenths. So, 0.35 , 0.53 4. 0.94 0.9 5. 0.3 0.32 6. 0.45 0.28 7. 0.39 0.93 Use the number line to compare. Write true or false. 8. 0.8 . 0.78 9. 0.4 . 0.84 10. 0.7 , 0.70 11. 0.4 . 0.04 14. 0.17 , 0.32 15. 0.85 . 0.82 Compare. Write true or false. © Houghton Mifflin Harcourt Publishing Company 12. 0.09 . 0.1 13. 0.24 5 0.42 16. Kelly walks 0.7 mile to school. Mary walks 0.49 mile to school. Write an inequality using ,, ., or 5 to compare the distances they walk to school. 17. Tyrone shades two decimal grids. He shades 0.03 of the squares on one grid blue. He shades 0.3 of another grid red. Which grid has the greater part shaded? Chapter 9 P183 Lesson Check (MACC.4.NF.3.7) 1. Bob, Cal, and Pete each made a stack of baseball cards. Bob’s stack was 0.2 meter high. Cal’s stack was 0.24 meter high. Pete’s stack was 0.18 meter high. Which statement is true? 2. Three classmates spent money at the school supplies store. Mark spent 0.5 dollar, Andre spent 0.45 dollar, and Raquel spent 0.52 dollar. Which statement is true? A 0.2 . 0.24 A 0.45 . 0.5 B 0.24 . 0.18 B 0.52 , 0.45 C 0.18 . 0.2 C 0.5 5 0.52 D 0.24 5 0.2 D 0.45 , 0.5 Spiral Review (MACC.4.NF.2.3c, MACC.4.NF.2.4c, MACC4.NF.3.5) $0.40 in her pocket. How much money do Pedro and Alice have in their pockets altogether? (Lesson 9.6) A $0.05 B $0.39 C $0.75 D $0.79 5. Joel has 24 sports trophies. Of the trophies, _1 are soccer trophies. How 8 many soccer trophies does Joel have? (Lesson 8.4) A 2 B 3 C 4 D 6 P184 4. The measure 62 centimeters is equivalent 62 to ___ meter. What is this measure written 100 as a decimal? (Lesson 9.3) A 62.0 meters B 6.2 meters C 0.62 meter D 0.6 meter 6. Molly’s jump rope is 6 _13 feet long. Gail’s jump rope is 4 _2 feet long. How much 3 longer is Molly’s jump rope? (Lesson 7.8) A 1 1_3 feet B 1 2_3 feet C 2 1_3 feet D 2 2_3 feet © Houghton Mifflin Harcourt Publishing Company 3. Pedro has $0.35 in his pocket. Alice has COMMON CORE STANDARDS MACC.4.NF.3.5, MACC.4.NF.3.6, MACC.4.NF.3.7, MACC.4.MD.1.2 Name Chapter 9 Extra Practice Lessons 9.1–9.2 Write the fraction or mixed number and the decimal shown by the model. 1. 2. 3. ' '%, (%' (%, )%' Lesson 9.3 Write the number as hundredths in fraction form and decimal form. 8 1. ___ 10 2. 0.1 3 3. ___ 10 Write the number as tenths in fraction form and decimal form. 60 4. ____ 100 70 5. ____ 100 6. 0.20 Lesson 9.4 © Houghton Mifflin Harcourt Publishing Company Write as a money amount and as a decimal in terms of dollars. 30 1. ____ 100 91 2. ____ 100 5 3. ____ 100 Write the total money amount. Then write the amount as a fraction and as a decimal in terms of dollars. 4. 4 dimes, 9 pennies 5. 3 quarters, 1 dime 6. 7 nickels, 2 pennies Chapter 9 P185 Lesson 9.5 1. Camila, Jocelyn, and Audrey each earned 2. Elijah, Xavier, and Adrian earned a total 3. Anthony saves $7 each week. In how many 4. Brianna has $2 less than Victoria. Victoria $2.55. How much did the three girls earn altogether? weeks will he have saved at least $40? of $8.34. The boys shared the earnings equally. How much did each boy get? has $11 more than Damian. Damian has $6. How much money do they have in all? Lesson 9.6 Find the sum. 6 39 1. ___ 1 ____ 10 100 14 8 2. ____ 1 ___ 100 10 4 18 3. ___ 1 ____ 10 100 5 16 4. ___ 1 ____ 10 100 5. $0.43 1 $0.20 6. $0.07 1 $0.35 7. $0.80 1 $0.15 8. $0.52 1 $0.28 3. 0.54 4. 0.04 0.06 8. 0.63 0.48 Lesson 9.7 1. 0.3 0.39 2. 0.9 5. 0.7 0.70 6. 0.36 0.90 0.51 7. 0.8 0.45 0.67 Compare. Write true or false. 9. 0.32 . 0.23 P186 10. 0.86 5 0.9 11. 0.68 , 0.83 12. 0.97 . 0.94 © Houghton Mifflin Harcourt Publishing Company Compare. Write ,, ., or 5.