6 th Grade Fractions Chapter Questions. 1. Explain how to add, subtract, multiply and divide fractions.
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1 6 th Grade Fractions Chapter Questions. Explain how to add, subtract, multiply and divide fractions.. Explain why you multiply by the inverse when dividing.. What is the GCF and how do you determine it?. What is the LCM and how do you determine it? NJ Center for Teaching and Learning ~ ~
2 Chapter Problems Greatest Common Factor Classwork Find the Greatest Common Factor of each set of numbers. ) and 6 ) and 6 ) and 9 ) and ) 66 and 6) 8 and ) and 8 8) 98 and 66 9) and 0) 8 and Homework Find the Greatest Common Factor of each set of numbers. ) 0 and ) 0 and 0 ) 98 and 0 ) and 66 ) and 6) 6 and ) 6 and 6 8) and 0 9) 6 and 0) 6 and 99 Least Common Multiple Classwork Find the Least Common Multiple of each set of numbers. ) 9 and ) and 80 ) 6 and 0 ) and ) and 6 6) 8 and 0 ) 9 and 6 8) and 0 9) 8 and 0) and Homework Find the Least Common Multiple of each set of numbers. ) 9 and ) and ) and ) 0 and 9 ) 8 and 6) and ) and 8) and 6 9) and 6 0) and 8 GCF/LCM Applications Classwork ) Kiara baked 0 oatmeal cookies and 8 chocolate chip cookies to package in plastic containers for her friends at school. She wants to divide the cookies into identical containers so that each container has the same number of each kind of cookie. a. If she wants each container to have the greatest number of cookies possible, how many plastic containers does she need? b. How many of each cookie will she put in each container? ) Beginning at 8:0 A.M., tours of the National Capitol and the White House begin at a tour agency. Tours for the National Capitol leave every 8 minutes. Tours for the White House leave every 0 minutes. How often do the tours leave at the same time? NJ Center for Teaching and Learning ~ ~
3 ) Joe is making key chains with beads. He wants each key chain to have the same number of beads. He has 90 blue beads and yellow beads. a. What is the greatest number of key chains he can make that are exactly the same? b. How many of each color bead will be on each key chain? ) A florist has 6 roses, tulips, and 8 carnations she must use to create bouquets. a. What is the largest number of bouquets she can make without having any flowers left over? b. How many of each flower will she put in each bouquet? ) A radio station is giving away prizes to its callers. Depending on what number caller you are, you receive a different prize. Prizes Hat T-shirt Backpack Caller Every rd caller Every th caller Every 6 th caller What number caller will be the first to receive all prizes? Homework 6) Two neon lights are turned on at the same time. One blinks every seconds and the other blinks every 6 seconds. In 60 seconds, how many times will they blink at the same time? ) Shannon is making identical balloon arrangements for a party. She has maroon balloons, white balloons, and 6 orange balloons. She wants each arrangement to have the same number of each color. a. What is the greatest number of arrangements that she can make if every balloon is used? b. How many balloons of each color will be in each arrangement? 8) At a display booth at an amusement park, every visitor gets a gift bag. Some of the bags have items in them as shown in this table. Items Hat T-shirt Backpack Bags Every nd visitor Every th visitor Every 0 th visitor What number visitor will be the first to receive all items in the gift bag? 9) There are 8 girls and 6 boys in the school choir. The choir teacher plans to arrange the students in equal rows. The same number of boys and the same number of girls will be in each row. What is the greatest number of rows the teacher can arrange? 0) Mike can buy red push pins in packages of 0 and yellow push pins in packages of. What is the least amount of packages of each color he must buy in order to have the same number of pins? NJ Center for Teaching and Learning ~ ~
4 Distribution Classwork Use the Distributive Property to rewrite each expression: ) + ) 8 + ) + 9 ) + ) ) + ) ) ) ) + Homework Use the Distributive Property to rewrite each expression: 6) 0 + 6) ) 6 + 6) 9 + 6) + ) + 8) + 9) ) + 8) + 8) + 8) 0 + 8) 6 + 8) ) + 8) + 88) ) ) 6 + 6) + 66) + 6) ) ) ) 6 + Adding Fractions Classwork Simplify to lowest terms: ) + Homework Simplify to lowest terms: 9) + 9) ) ) + 9) ) ) + ) + ) + ) ) ) + 00) + 9) NJ Center for Teaching and Learning ~ ~
5 0) 0) 0) 0) ) + 06) ) + 08) ) + 6 Subtracting Fractions Classwork 0) ) ) ) ) ) 6) 6 6 ) 8) ) 0) ) ) ) ) ) 0 9) Homework 0) ) ) ) ) ) 6) 6 ) 6 8) 6 9) ) ) ) ) ) ) 6) 6 6 ) 9 6 8) ) 6 0) ) 6) ) 6 NJ Center for Teaching and Learning ~ ~
6 Multiplying Fractions Classwork ) ) ) ) ) ) ) 8 8) 6 9 9) 6 60) 6) 6) 6) 8 6) 9 Homework 66) 6) 68) 69) 0) ) 6 ) 8 ) 8 ) 0 0 ) 6) 6 ) 8 8) 9) 6 80) 0 6) 0 Dividing Fractions Classwork 8) Use the model below to demonstrate: 8) Use the model below to demonstrate: 6 NJ Center for Teaching and Learning ~ 6 ~
7 8) Use the model below to demonstrate: 8) 8) 86) 8) ) ) 6 90) 9) 8 9) 8 9) 9) 6 9 9) Homework 96) Use the model below to demonstrate: 6 9) Use the model below to demonstrate: 6 98) Use the model below to demonstrate: NJ Center for Teaching and Learning ~ ~
8 99) 00) 0) 0) ) 8 0) 8 0) ) 0) 08) 8 09) 0 8 0) 9 6 Fraction Operations Application Classwork ) How much candy will each person get if people share 6 ½ pounds of Swedish Fish? ) How many cup servings are in ½ cups of cheese? ) How long is a rectangle if its width is feet and its area is 0 8 square feet? 0 ) A recipe calls for cup of brown sugar. If you want to make of the recipe, how many cups of brown sugar do you need? ) For a party, you buy salt water taffy does each person get? 8 lbs of salt water taffy. If 0 people are attending, how much 6) A cook has ounce of pepper. A recipe for a steak marinade requires ounce of pepper. How many batches of marinade can the cook produce from ounce of pepper? ) Max wants to run miles to train for track season. If the total length around the track is mile, how many laps does Max need to run around the track? 8) You are making hamburgers for a barbeque with your family and bought pounds of ground beef. If you want to make pound hamburgers, how many can you make from pounds of ground beef? NJ Center for Teaching and Learning ~ 8 ~
9 9) Annie is baking cupcakes. The recipe calls for cup of butter, cup of sugar, and cup of milk. How many cups of ingredients is that altogether? 0) Ben has baseball cards. He will give of his cards to his younger brother, Phil. How many cards will Phil get? ) Kelly has cookies. She plans on bringing of the cookies to school to share with her class. How many cookies is she not bringing to school? ) Jim needs cups of bleach for every ten gallons of water for cleaning. How many cups of bleach should he use if he is making gallons? ) If x = is true, is x = also true? Why or why not? ) Evaluate the expression + if d =. d ) Sue has a picture that is inches across and 8 inches long. She wants to put a border that is inches around the picture. What is the new perimeter of the picture, including the border? Homework 6) How many nuts will each person get if 9 people share ) How many cup servings are in cups of salsa? 8) How long is a rectangle if its width is 9) A recipe calls for cups of flour do you need? 0) For the first day of school, you buy cups of flour. If you want to make 8 pounds of nuts? feet and its area is square feet? 8 of the recipe, how many lbs of cookies. If you share with the people in homeroom, how many pounds of cookies do you give each person? NJ Center for Teaching and Learning ~ 9 ~
10 ) A cook has ounce of baking powder. A recipe for chocolate chip cookies requires 8 ounce of baking powder. How many batches of cookies can the cook produce from ounce of baking powder? ) Anthony wants to run 8 miles to train for track season. If the total length around the track is mile, how many laps does Anthony need to run around the track? ) You are making a cake for a friend s birthday and bought pounds of butter. If each layer of the cake requires pound of butter, how many layers can you make from pounds of butter? ) Pamela is baking muffins. She will put cup of dried cranberries, cup of sliced almonds, cup of raisins, and cup of milk. How many cups of ingredients is that 8 altogether? ) Brenda has 0 stickers. She will use of them to decorate her folder. How many stickers will she put on her folder? 6) Melanie works with people. of her coworkers are male. How many are female? ) Krista uses tablespoons of drink mix for every liter of fruit punch. How many tablespoons does she need if she is making liters for her class party? 8) If = is true, is t = also true? Why or why not? t 9) Evaluate the expression + v if v =. 6 0) Karla has a painting that is 0 inches across and inches tall. She wants to put a inch border around the painting. What is the area of the painting, including the border? NJ Center for Teaching and Learning ~ 0 ~
11 Fractions Multiple Choice Questions ) Find the Greatest Common Factor of and. a. b. c. 6 d. ) What is the Least Common Multiple of and 8? a. 6 b. 6 c. d. 8 ) A cookie recipe calls for cups of chocolate chips. If you want to make of the recipe, how many cups of chocolate chips should you use? a. cups b. 6 cup c. cups d. 8 cups ) Use the distributive property to rewrite a. 6( + ) b. 8( + 8) c. ( + 6) d. (8 + ) ) is the GCF of which two numbers? a. 8 and 6 b. 6 and c. 8 and d. and 6 6) 8 is the LCM of which two numbers? a. 6 and 8 b. and c. 6 and 8 d. and ) How many ounce servings are in ounces? a. servings b. servings c. 8 servings d. 8 servings 8) Use the distributive property to rewrite + a. 6( + ) b. ( + 9) c. (6 + ) d. ( + 6) NJ Center for Teaching and Learning ~ ~
12 9) a. b. 8 c. d ) 8 9 a. 8 0 b. c. d. 8 ) 8 a. b. c. 0 d. 9 0 ) 9 a. 0 b. 0 c. d. Fractions Short Constructed Response Questions ) + = ) 6 0 = ) 9 6 = 8) 6 8 = ) 6 8 = 9) 9 = 6) = 0) Use the distributive property to rewrite 6 + ) What is the GCF of and? ) What is the LCM of 6 and 6? NJ Center for Teaching and Learning ~ ~
13 Extended Constructed Response Questions ) In order to buy wall paper, Abby needed to find the perimeter (total distance around the outside) of her bedroom. She measured each of the following lengths of her walls East wall: 0 8 ft North Wall: 6 ft West Wall: 0 8 ft South Wall: 8 6 ft What is the perimeter of Abbey s room? Her sister Anna s room is a square (four equal sides) of walls that are 0 ft. Will Anna need to 8 buy more or less wallpaper than Abbey? Show all of your work to support your answers. ) Nick wants to order enough food for his party. He knows medium pizzas come in slices of 6, and large pizzas come in slices of 8. He wants enough pizza for each of his friends to have slices. Write a fraction to show how many slices per large pizza each of his friends will eat. If Nick wants to invite 0 friends over, how many large pizzas should he order? If he wants to order medium pizzas instead, how many will he need? A large pizza costs $ and a medium pizza costs $9. Which type of pizza should Nick buy for his party? Show all of your work to support your answers. ) To find the volume of a swimming pool, you must multiply the length, width, and depth of the pool together. Michelle wants to find out how much water she needs to fill her pool. She measured a length of 0 ft, a width of ft, and a depth of 6 ft. What is the volume of Michelle s pool in cubic feet? If she needs to buy 6 gallons of water for each cubic foot of space, how many gallons of water will it take to fill her pool? Show all of your work to support your answers. 6) For a science project, Ms. States asked each of her students to measure how much gas they used driving to school each week. The students measured the amount of gas in fractions of a tank. Mike used of a tank, Jamie used of a tank, Josh used of a tank, 6 9 Adam used of a tank, and Kate used of a tank. Rank the amount of gas used by each student, from least to greatest If a tank of gas costs dollars, how much money did Josh and Kate spend on gas combined? Show all of your work to support your answers. NJ Center for Teaching and Learning ~ ~
14 ) Miriam s uncle donated 0 cans of juice and 90 packs of cheese crackers for the school field trip. Each student is to receive the same number of cans of juice and the same number of packs of crackers. What is the greatest number of students that can go on the field trip and share the food equally with no food left over? How many cans of juice and how many packs of crackers will each student receive? Explain. 8) Jeremy and his little sister, Deborah, are at a carnival. There are both a large and a small Ferris wheel. Jeremy gets on the large Ferris wheel at the same time his sister gets on the small Ferris wheel. The rides begin at the same time. The large wheel makes one revolution in 0 seconds and the small wheel makes one revolution in seconds. How many seconds will pass before Jeremy and Deborah are at the bottom at the same time again? How many times will each Ferris wheel go around before Jeremy and his sister are both on the ground again? NJ Center for Teaching and Learning ~ ~
15 ) 8 ) ) ) ) 6) 6 ) 8) 9) 9 0) ) ) 0 ) ) ) 6) 9 ) 9 8) 9) 0) 9 ) 6 ) 0 ) 0 ) 8 ) 80 6) 0 ) 8 8) 0 9) 6 0) 0 ) ) 8 ) 60 ) 90 ) 6 6) ) 8) 9) 6 0) 88 ) Answer Key a. 6 containers b. oatmeal and 8 chocolate chip ) Every 0 minutes ) ) a. 8 key chains b. blue, yellow a. 9 bouquets b. roses, tulips, carnations ) 0 th caller 6) times ) a. 8 arrangements b. maroon, white, orange 8) 0 th visitor 9) 6 rows 0) 6 packages of red, packages of yellow ) ( + ) ) 9( + ) ) ( + ) ) (8 + ) ) ( + ) 6) ( + ) ) 6( + ) 8) 9( + ) 9) ( + 9) 60) ( + ) 6) ( + ) 6) 0( + 0) 6) 9( + 8) NJ Center for Teaching and Learning ~ ~
16 6) ( + ) 8) 9 8 0) 6) ( + ) 88) ) 66) ( + ) 6) ( + ) 68) 6( + ) 69) 6( + ) 0) ( + ) ) ) ) 89) ) 8 9) 9) 6 9) 9) 6 9) 8 96) ) ½ ) 0 ) ½ ) ½ 6) ) 0 8) 9) ) 9) 0) 0 ) 8 98) 9 ) 6) ) ½ 99) 6 00) 8 ) ) 6 6 8) 6 9) 0 9 0) 6 ) 80) 9 6 8) 6 8) 8) 60 8) 8) 86) 6 0) 0) 9 0) 0) 0 06) 6 0) 8 08) ) 8 8 ) 6) 9 ) 0 8) ) 9 0) ) ) NJ Center for Teaching and Learning ~ 6 ~
17 ) ) 60 ) 6) ) 8 8) 9 9) 0) ) ) ) ) 6 ) 0 6) ) 8 6) ) 8) 9) 8 60) 6) 6) 6) 6) 6) 66) 6) 68) 69) 0) ) 80) 9 8) 8) 8) 9 8) 8) 86) 8) 88) 89) 6 90) 6 9) 9) 9) 6 9) 9 8) ) 9) 8 0) 00 ) ) 6 ) 9) 0 6 ) 8 ) ) 96) 9) 98) 99) 9 ) 8 6) 00) ) ) 8 ) 8 8) 0 0) 0) 9 NJ Center for Teaching and Learning ~ ~
18 0) 0) 6 0) 06) 6 0) ) laps 8) burgers 9) cups 0) cards ) cookies 0) lbs ) 6 batches ) laps ) layers ) 9 cups 08) 09) 0 ) cups ) Yes, because ) 0 stickers 6) workers 0) ) 0 lbs ) servings ) feet ) ) 6 cups 0 lbs 6) 9 batches x = = 0 ) ) inches 6) lbs ) 0 0 servings 8) 8 feet 9) 6 8 cups ) tablespoons 8) It is false because t = or 9) 0) 6 9 Multiple Choice Questions ) b ) d 6) a ) d 8) c ) d Short Constructed Response Questions ) 0 ) b 9) b ) 8 ) a ) c 0) a ) c ) 0 6) 6 NJ Center for Teaching and Learning ~ 8 ~
19 ) 60 8) 9) 0) 8( + 9) ) ) Extended Constructed Response Questions ) = = 0 6 = feet Anna's Room: (0 ) = 8 x = ft She needs to buy the same amount. 8 8 ) 0 x 8 = 0 = so he should buy large pizzas 8 0 x 6 = 0 6 = so he should buy medium pizzas x = $8 and 9 x = $ so he should buy medium pizzas ) 0 x x 6 = = 0 = 68 6 ft 6 x 68 6 = 9 x 0 6 x 8 x = gallons 6) =, =, = 8, =, = Least to greatest:, 6,,, 9 + = = x = 9 x = = = $ ) 0 students can go on the field trip Each student will get cans of juice and packs of crackers. 0 is the GCF, so x 0 = 0 (juice) and x 0 = 90 (crackers) 8) It will be 0 seconds before they are both on the bottom again. The large Ferris Wheel will go around times, small will go 0 times. NJ Center for Teaching and Learning ~ 9 ~
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