Math -Exam Chap. 6 and 7

26(d). In order to get the right octane of gasoline for his car, Will always mixes premium gas and regular gas in a ratio of 3 to 2. Use reasoning on a double number line to answer each of these questions. How many gallons of premium gas should Will add if he just added 5 gallons of regular gas?

7 1/2 gallon

7(a). Each story problem is solved by finding 23/5 Determine whether the answer is best expressed as a whole number with remainder, the whole number part only, the remainder part only, a mixed number, a decimal, or some other whole number not in the quotient. Give the most appropriate answer. Parker owns The Glass Store. He received a shipment of 23 glass animals. He put the same number of animals on each of 5 display shelves. How many glass animals are on one shelf?

4 animals(whole number only)

3(B). Write a simple story problem for using each interpretation of division. 56/8 how many groups

-Jerry made 56 sandwiches for a picnic. He boxed 8 sandwiches in each container. How many containers did Jerry use?

3(a). Write a simple story problem for using each interpretation of division. 56/8 how many units in one group

-Jerry made 56 sandwiches for a picnic. He boxed them in 8 plastic containers so each container holds an equal number of sandwiches. How many sandwiches did Jerry put in each container?

13. Bert only knows the multiplication facts below. Show how he could use the scaffold methodflexibly to find 844 ÷ 32: 10x32=3205x32=1602x32=641x32=32

26 remainder 10

7(b). Each story problem is solved by finding 23/5 Determine whether the answer is best expressed as a whole number with remainder, the whole number part only, the remainder part only, a mixed number, a decimal, or some other whole number not in the quotient. Give the most appropriate answer. jug holds 5 gallons of water. If Mark uses 23 gallons of water, how many jugs of water is this?

4 3/5 jugs(mixed number)

12. Use both the scaffold method and the common long division algorithm to calculate 3,458 ÷ 6.

Both methods result in 576, remainder 2

1(c). Identify the interpretation of division used in each story problem as how many groups or how many units in one group. Then, write a division equation that gives the answer. Four pencils cost 36 cents. How much does one pencil cost?

How many units in one group; 36/4=9 cents

5. Use a mathematical sketch and the Common Core definition of fraction to explain why the operation 3/5= gives the result 3/5(fraction)

Using the how many units in one group interpretation of division, 3/5 means that 3 wholes are equally divided among 5 groups. Each whole can be split into 5 parts, each 1/5 of the whole. As shown in the sketch, each group gets 3 of these parts. Therefore, 3/5 = 3/5 .

1(e).Identify the interpretation of division used in each story problem as how many groups or how many units in one group. Then, write a division equation that gives the answer. It takes a battery powered toy train 5 seconds to go 20 inches. How far does the train go in 1 second?

how many units in one group; 20/5 = 4 inches

17(e). Darnisha repackages a 7-pound box of peanuts into small bags so she can sell them in her store. Each bag will contain 2/3 pounds of peanuts. Draw a mathematical sketch for 7/ 2/3 and use the sketch to answer the questions e. What interpretation of division does this problem use?

e. how many groups

1(d). Identify the interpretation of division used in each story problem as how many groups or how many units in one group. Then, write a division equation that gives the answer. There are 4 quarts in a gallon. How many gallons can be made with 40 quarts?

how many groups; 40/4 = 10 gallons

4(c). Give the result of each division problem involving 0. Justify your answer using a multiplication equation. 0/0=

indeterminate; The division problem 0/0=? corresponds to the multiplication problem ?x0=0. Every number will multiply by 0 to give a product of 0.

4(a). Give the result of each division problem involving 0. Justify your answer using a multiplication equation. 12/0=

not defined; The division problem 12/0 = ? corresponds to the multiplication problem ?x0 = 12 . There is no number that multiplies by 0 to give a product of 12.

25. Punch is made by mixing grape juice and bubbly water in a ratio of 5 to 2. Draw a double number line and use it to give at least three other pairs of quantities of grape juice and bubbly water that you could use to make the punch mixture in that ratio. At least one of your pairs should include numbers that are not whole.

see study guide

27(a). Susie mixed 5 cups of yellow paint with 4 cups of red paint to make an orange paint. She liked the color and decided to mix a larger batch. Use strip diagrams to answer these questions. what fraction of the mixed paint comes from the yellow paint?

there are a total of 9 parts and 5 parts are yellow. The fraction of the mix comes from yellow paint is 5/9

2(a). Write a multiplication equation that corresponds to each division equation using the given interpretation 10/2=x how many groups

x*2=10

7(e).Each story problem is solved by finding 23/5 Determine whether the answer is best expressed as a whole number with remainder, the whole number part only, the remainder part only, a mixed number, a decimal, or some other whole number not in the quotient. Give the most appropriate answer. Jessa has 23 one-dollar bills and no way to make change. If Jessa gives her 5 children as much as possible while dividing the money fairly, how much will her children and Jessa each have?

$4 for each child and $3 for Jessica(whole number and remainder)

7(d). Each story problem is solved by finding 23/5 Determine whether the answer is best expressed as a whole number with remainder, the whole number part only, the remainder part only, a mixed number, a decimal, or some other whole number not in the quotient. Give the most appropriate answer. Jessa has $23 that she wants to divide fairly between her 5 children. How much will each child get?

$4.60(decimal)

4(b). Give the result of each division problem involving 0. Justify your answer using a multiplication equation. 0/12=

0; The division problem 0/12=? corresponds to the multiplication problem ?x12=0. The only number that multiplies by 12 to give a product of 0 is 0.

17. Darnisha repackages a 7-pound box of peanuts into small bags so she can sell them in her store. Each bag will contain 2/3 pounds of peanuts. Draw a mathematical sketch for 7/ 2/3 and use the sketch to answer the questions c. After she makes as many bags as possible, what fraction of another bag can Darnisha make?

1/2 bag

17. Darnisha repackages a 7-pound box of peanuts into small bags so she can sell them in her store. Each bag will contain 2/3 pounds of peanuts. Draw a mathematical sketch for 7/ 2/3 and use the sketch to answer the questions b. how many pounds of peanuts will be left after Darnisha fills as many bags as she can?

1/3 pounds

11(a). Tamara is working on the following problem: There are 350 stickers to be put in packages of 16. How many packages of stickers can we make, and how many stickers will be left over? Here is Taylor's solution: Ten packages will use up 160 stickers. After another 10 packages, 320 stickers will be used up. After 1 more package, 336 stickers are used. Then there are only 14 stickers left and that's not enough for another package. So the answer is 21 packages of stickers with 14 stickers left over. Write a single equation that uses Taylor's reasoning.

11(a). (10x16)+(10x16)+(1x16)+14=350 (10+10+1)x16+14=350 or 350-(10x16)-(10x16)-(1x16)=14

11(a). Tamara is working on the following problem: There are 350 stickers to be put in packages of 16. How many packages of stickers can we make, and how many stickers will be left over? Here is Taylor's solution: Ten packages will use up 160 stickers. After another 10 packages, 320 stickers will be used up. After 1 more package, 336 stickers are used. Then there are only 14 stickers left and that's not enough for another package. So the answer is 21 packages of stickers with 14 stickers left over. Use your equation from part a and the distributive property to obtain another equation which shows that 10/16 has a whole number quotient 21, remainder 14

11(b). 21x16+14=250 21x16+14=350 q=21, r=14 or 350-(10+10+1)x16=14 350-21x16=14 q=21; r =14

26(f). In order to get the right octane of gasoline for his car, Will always mixes premium gas and regular gas in a ratio of 3 to 2. Use reasoning on a double number line to answer each of these questions. Will just added 20 gallons of gas. What fraction of it was premium?

12/20=3/5

17. Darnisha repackages a 7-pound box of peanuts into small bags so she can sell them in her store. Each bag will contain 2/3 pounds of peanuts. Draw a mathematical sketch for 7/ 2/3 and use the sketch to answer the questions a. how many full bags can Darnisha make from the box of peanuts?

17(a). 10 bags

26(b). In order to get the right octane of gasoline for his car, Will always mixes premium gas and regular gas in a ratio of 3 to 2. Use reasoning on a double number line to answer each of these questions. How many gallons of premium gas should Will add if he just added 12 gallons of regular gas?

18 gallons

26(c). In order to get the right octane of gasoline for his car, Will always mixes premium gas and regular gas in a ratio of 3 to 2. Use reasoning on a double number line to answer each of these questions. How many gallons of regular gas should Will add if he just added 1 gallon of premium gas?

2/3 gallon

14(a). Alecia used base-ten materials for division as shown If Alecia used the how many groups interpretation, what division fact is shown? Give the dividend, divisor, whole number quotient, and remainder.

434/144=3 R 2

14(b). Alecia used base-ten materials for division as shown Suppose Alecia used the how many units in one group interpretation. What division fact is shown? Give the dividend, divisor, whole number quotient, and remainder.

434/3=144 R 2

7(c). Each story problem is solved by finding 23/5 Determine whether the answer is best expressed as a whole number with remainder, the whole number part only, the remainder part only, a mixed number, a decimal, or some other whole number not in the quotient. Give the most appropriate answer. class of 23 children will take a field trip. Each car can take 5 children. How many cars are needed to take all the children on the field trip?

5 cars (whole number different from the quotient)

2(b). Write a multiplication equation that corresponds to each division equation using the given interpretation. 14/7=x how many units in one group

7*x=14

26(a). In order to get the right octane of gasoline for his car, Will always mixes premium gas and regular gas in a ratio of 3 to 2. Use reasoning on a double number line to answer each of these questions. How many gallons of regular gas should Will add if he just added 12 gallons of premium gas?

8 gallons

8. Write a story problem for 33/12 where the answer is best given as a. whole number with remainder

8(a). Rachel collected 33 eggs this morning from the chicken coop and put them in egg cartons. If each carton holds a dozen eggs, how many full cartons can she make and how eggs are left?

26(e). In order to get the right octane of gasoline for his car, Will always mixes premium gas and regular gas in a ratio of 3 to 2. Use reasoning on a double number line to answer each of these questions. How many gallons of each type should Will add if he wants to put a total of 15 gallons of gas in his car?

9 gallons premium; 6 gallons regular

8(b). write a story problem for 33/12 where the answer is best given as b. mixed number

A school club has adopted a 33-mile stretch of highway to keep clean of litter. If 12 teams are fairly assigned to clean up the highway, how many miles of highway must each team clean?

18. Use the how many groups interpretations and a math drawing find the quotient of 5/6 / 1/4 as a mixed number. Explain in detail how you used your sketch to find the quotient.

Determine how many 1/4 's there are in 5/6 . The pieces are different sizes, so rewrite each fraction using a common denominator: 5/6 = 10/12 and 1/4 = 3/12. In the math sketch, we count that there are three 3/12's in 10/12. The one part left over is one part of the three needed for another group. The quotient is 3 1/3 .

6. Use the how many units in each group interpretation of division and a sketch to show the result of 11/4= a. a whole number with remainder b. a mixed number

Distribute the 11 circles into 4 equal sized groups of 2 whole circles. Then partition each of the 3 left over circles into 4 parts and distribute each of the 1/4s into the 4 groups. There will be 2 whole circles and 3 parts, each 1/4 of a whole circle in each of the 4 groups.

6(b). 6. Use the how many units in each group interpretation of division and a sketch to show the result of 11/4= b. a mixed number

Distribute the 11 circles into.4 equal sized groups of 2 circles. Then partition each of the 3 left over circles into 4 parts and distribute each of the 1/4s into the 4 groups. there will be 2 whole circles and 3 parts each 1/4 of a whole circle in each of the 4 groups

1(b). Identify the interpretation of division used in each story problem as how many groups or how many units in one group. Then, write a division equation that gives the answer. Maria has 12 feet of ribbon and wants to wrap some gifts. Each gift needs 3 feet of ribbon. How many gifts can she wrap using the ribbon?

How many groups 12/3=4 gifts

1(a). Identify the interpretation of division used in each story problem as how many groups or how many units in one group. Then, write a division equation that gives the answer. June has 24 cookies. She puts them on 4 plates with the same number of cookies on each plate. How many cookies are on each plate?

How many units in one group; 24/4=6 cookies

28. To make jewelry, jewelers often mix gold and copper in a 7 to 5 ratio. How much gold and how much copper should a jeweler mix to get 60 grams of the metal mixture? Use your favorite strategy (strip diagram, table, double number line, proportion, or reasoning with quantities to solve.

If the metal mixture is formed by a ratio of 7 parts gold and 5 parts copper, there are a total of 12 parts in the mixture. To make 60 grams of the mixture, each part must contain 60/12=5 grams. Therefore, use 7 x 5 =35 grams of gold and 5 x 5 = 25 grams of copper.

22. For the division problem 6/ 3/10 b. Write a simple story problem showing the how many units in one group interpretation.

In Ms. Martin's class, 3/10 of the students play a musical instrument. If 6 students play a musical instrument, how many students are in Ms. Martin's class?

22. For the division problem 6/ 3/10 a. Write a simple story problem showing the how many groups interpretation.

John is making sandwiches. He has 6 pounds of cheese and uses 3/10 of a pound of cheese on each sandwich. If he uses all the cheese, how many sandwiches can he make?

27(c). Susie mixed 5 cups of yellow paint with 4 cups of red paint to make an orange paint. She liked the color and decided to mix a larger batch. Use strip diagrams to answer these questions. How many cups of yellow paint should be mixed with 10 cups of red paint?

The 10 cups of red paint is divided into 4 parts each containing 2 1⁄2 cups. Therefore, there are 5 x 2 1⁄2 = 12 1⁄2 cups of yellow paint.

27(b). Susie mixed 5 cups of yellow paint with 4 cups of red paint to make an orange paint. She liked the color and decided to mix a larger batch. Use strip diagrams to answer these questions How many cups of red paint should be mixed with 10 cups of yellow paint?

The 10 cups of yellow paint are divided into 5 parts, each containing 2 cups. Therefore, there are 4 x 2 = 8 cups of red paint.

27(d). Susie mixed 5 cups of yellow paint with 4 cups of red paint to make an orange paint. She liked the color and decided to mix a larger batch. Use strip diagrams to answer these questions. How many cups of yellow paint and how many cups of red paint will Suzy need to make 36 cups of the same shade of orange paint?

The 36 cups of orange is divided into 9 total parts. Each part contains 4 cups. Therefore, there are 5 x 4 = 20 cups of yellow and 4 x 4 = 16 cups of red.

9(c). A bottle holds 32 mL of cough syrup. Each adult dose is 5 ounces. Consider the division equation: 32/5=6 R2= 6 2/5 Interpret the meaning of each value below. Make sure you use the labels "ounces" and "doses" in your answers. b. 2/5

The left over cough syrup is 2/5 of a another dose.

24. Construct and explain how you can use a ratio table to determine which of these two mixtures will be more salty: Mixture A: 2 tablespoons of salt mixed in 7 cups of water or Mixture B: 3 tablespoons of salt mixed in 8 cups of water

The ratio tables show that when each mixture has the same amount of water - 56 cups - Mixture B has more salt and therefore more salty. (You could also look to see that when both mixtures have 6 tablespoons of salt, Mixture B contains less water and therefore will have a higher concentration of salt.)

10(b). For each equation, give the dividend (a), divisor (b), quotient (q), and remainder (r) for the related division problem The related division problem is 100-(4x15)-(2x15)=10

The related division problem is 100/15: a=100, b =15, q=6, r=10

10(a). For each equation, give the dividend (a), divisor (b), quotient (q), and remainder (r) for the related division problem. 21q+r=340

The related division problem is 340/21: a=340, b=21, q=16, r=4

17(d). Darnisha repackages a 7-pound box of peanuts into small bags so she can sell them in her store. Each bag will contain 2/3 pounds of peanuts. Draw a mathematical sketch for 7/ 2/3 and use the sketch to answer the questions d. Why are the answers to parts b and c different?

The two fractions give different forms of the same answer. Both are fractions but their unit amounts are different. In part b, the fraction 1/3 gives the fraction of a pound of peanuts that is left. In part c, the fraction 1/2 refers to the fraction of another bag that can be made.

9(a). A bottle holds 32 mL of cough syrup. Each adult dose is 5 ounces. Consider the division equation: 32/5=6 R2= 6 2/5 Interpret the meaning of each value below. Make sure you use the labels "ounces" and "doses" in your answers. a. 6

There are 6 complete doses of cough syrup in the bottle.

9(b). A bottle holds 32 mL of cough syrup. Each adult dose is 5 ounces. Consider the division equation: 32/5=6 R2= 6 2/5 Interpret the meaning of each value below. Make sure you use the labels "ounces" and "doses" in your answers. b. 2

There will be 2 ounces of cough syrup left after taking the 6 doses.