RATIOS - RUSD Mathrusdmath.weebly.com/uploads/1/1/1/5/11156667/g6_u3_-_answer_key.pdf · determine...

Copyright © 2015 Pearson Education, Inc. 59

EXERCISES

MATH GRADE 6 UNIT 3

RATIOS

ANSWERS FOR EXERCISES


Grade 6 Unit 3: Ratio

ANSWERSLESSON 2: WHAT IS A RATIO?

ANSWERS

6.RP.1 1. B 2 : 1

6.RP.1 2. The ratio of squares to circles is 4 : 11.

6.RP.1 3. The difference between the number of circles and the number of squares is 7.

6.RP.1 4. The ratio of squares to circles is 11 : 4.

6.RP.1 5. The value of the ratio of circles to squares, expressed as a decimal is 2.75.

6.RP.1 6. The ratio of cars to empty parking spaces is 7 : 2.

6.RP.1 7. Here are two examples.

No, you can’t tell. It is possible to have any number of empty parking spaces that is a multiple of 7 and still have a car to empty parking space ratio of 7 : 2.

OR

No, you can’t tell how many empty spaces there are just from the ratio. You can determine other things based on the ratio: for example, for every 9 spaces in the parking lot, 2 of them are empty and 7 have cars. So, there might be 2 empty spaces. If there were 18 total spaces, 4 would be empty and 14 would have cars. If there were 27 spaces, 6 would be empty and 21 would have cars. However, the ratio alone isn’t enough to tell you the actual number of empty spaces.

6.RP.1 8. If there are 28 spaces and 24 of them have cars, I can find the number of empty parking spaces by subtracting.

28 – 24 = 4

There are 4 empty parking spaces.

6.RP.1 9. The ratio of cars to empty parking spaces is 24 : 4 or 6 : 1.

6.RP.1 10. The number of cars is 24 and the number of empty parking spaces is 4, so the difference is 20.

6.RP.1 11. The ratio of cars to all the spaces in the lot is 24 : 28 or 6 : 7.



ANSWERS

Challenge Problem

6.RP.1 12. a. The ratio of dogs to cats is 27 : 12, or 9 : 4.b. For each group of 4 cats, there are 9 dogs. This is because if the cats are

divided into groups of 4, there are 3 groups; 3 groups of 27 dogs means 9 dogs in each group.

c. There are 24 dogs and 12 cats. If some dogs are adopted, the ratio of dogs to cats will decrease from 2 : 1 and become closer to a 1 : 1 ratio. If some cats are adopted, the ratio of dogs to cats will increase. The question asks how to increase the ratio from 2 : 1 to 3 : 1, so that means the number of cats needs to go down.

To find how many cats need to be adopted, I set up equivalent fractions. 24 31x

=

Since 248

31

= , I know that the number of cats remaining needs to be 8. 12 – 8 = 4

So, 4 cats need to be adopted to change the ratio of dogs to cats to 3 : 1.

LESSON 2: WHAT IS A RATIO?



ANSWERSLESSON 3: REPRESENTING RATIOS

ANSWERS

6.RP.1 1. B 0.5

6.RP.1 2. D 3 : 1.5 E 6 : 3

6.RP.1 3. A Martin uses 12 ounces of chocolate chips for every 2.5 cups of flour.

C The ratio of number of cookies to ounces of chocolate chips is 2 : 1.

6.RP.1 4. 2024

1012

56

= =

6.RP.1 5. 1.4

6.RP.1 6. Any ratios equivalent to 0.2, such as 1 : 5, 2 : 10, 4: 20, 5 : 25, 10 : 50, and so on.

6.RP.1 7. a. 1.6

b. 2415

85

=

6.RP.1 8. Mia should enter the decimal 0.625 or .625 as the scaling ratio.

6.RP.1 9.True False

The ratio of boys to girls is 1 : 1. 4 �Two out of every 3 students are boys. � 4There are 3 girls for each car. � 4There are 4 students for each car. 4 �The ratio of all students to boys is 2. 4 �The ratio of all students to girls is 1

2. � 4

Challenge Problem

6.RP.1 10. a. Any ratio can be written in its simplest form, a : b. If there were more than one decimal for any given ratio, then a

b would have multiple values, which is false.

So, the statement is false.

b. Any decimal can be written as some ratio a : b. The ratio ac : bc has the same decimal representation as a : b for any value of c, so there are many different ratios for a given decimal.

So, the statement is true.



ANSWERS

ANSWERS

6.RP.3 1. A Mia

Emma

6.RP.1 2. The ratio of Mia’s postcards to the total number of postcards is 2 : 5.

6.RP.1 3. There are 8 units of students; there are 3 units of men. The ratio of men to all students is 3 : 8.

6.RP.1 4. There are 8 units of students; there are 5 units of women. The ratio of women to all students is 5 : 8.

6.RP.3 5. a.

5women

3men

b. There are 8 total squares in the tape diagram, so each square represents 32 ÷ 8 = 4 students. Then there are 5 × 4 = 20 women and 3 × 4 = 12 men. So, there are 20 women and 12 men.

6.RP.1 6.RP.3

6. The ratio of cars to trucks that passed through the intersection is 7 : 2.

6.RP.1 6.RP.3

7. The ratio of trucks to all vehicles (cars and trucks) that passed through the intersection is 2 : 9.

6.RP.3 8. Two squares in the tape diagram represent trucks, so if there were 34 trucks, each of those squares represents 34 ÷ 2 = 17 trucks. Since each square represents an equal number of vehicles, then each square represents 17 vehicles.

Seven squares are used to represent the number of cars, so there were 7 × 17 = 119 cars.

6.RP.3 9. 9. If there were 84 cars, each square in the tape diagram represents 84 ÷ 7 = 12 vehicles. So, there were 12 × 2 = 24 trucks. Therefore, there were 84 + 24 = 108 total vehicles.

LESSON 4: RATIOS AND TAPE DIAGRAMS



ANSWERSLESSON 4: RATIOS AND TAPE DIAGRAMS

Challenge Problem

6.RP.1 6.RP.3

10. a. First, I subtracted 8 from 24 to find the total number of containers of blue paint and yellow paint. 24 – 8 = 16 containers of blue paint and yellow paint

The ratio of blue paint to yellow paint is 3 to 5. Together that’s 8, so each square represents 2 containers of paint.

blue = 3 yellow = 5

2 • 3 = 6 containers of blue paint

2 • 5 = 10 containers of yellow paint

There were 6 containers of blue paint and 10 containers of yellow paint yesterday.

b. If Ms. Siboyani doubles the blue paint from yesterday, the blue paint goes from 6 containers to 12 containers.

The ratio of blue paint to yellow paint becomes 12 : 10, or 6 : 5.

blue = 3 • 2 = 6 yellow = 5

The value of yesterday’s ratio of blue paint to yellow paint (3 : 5) is 0.6.

The value of today’s ratio of blue paint to yellow paint (6 : 5) is 1.2.

0.6 • 2 = 1.2

So, doubling the amount of blue paint doubles the value of the ratio of blue paint to yellow paint.



ANSWERS

ANSWERS

6.RP.3 1. D Minutes

8 16 24 32 40

0.5 1 1.5 2 2.5Miles

6.RP.3 2.Price

$20 $40 $60 $80 $100

6 12 18 24 30Fillets

6.RP.3 3.Meters

1 2 3 4 5

100 200 300 400 500Centimeters

6.RP.3 4. Martin uses 25 cups of water.

6.RP.3 5. The cook decides how much he wants to make based on the number of people he is cooking for or the amount of some ingredient. Then, he uses the listed amounts that are vertically in line with that quantity. So, for example, if he were cooking for 8 people, he would need 2 lb of crabmeat, 24 oz of cream cheese, 16 oz of sour cream, and 1 tsp of lemon juice.

6.RP.3 6. The casserole serve 20 people.

6.RP.3 7. The cook needs 1.5 lb crabmeat, 18 oz cream cheese, 12 oz sour cream, and 34

tsp lemon juice.

6.RP.3 8. The amount for 1 person is 14

the amount for 4 people. To find the amounts for 1

person, multiply the amount of each ingredient for 4 people by 14

(or divide by 4).

The recipe for 1 person is 0.25 lb crabmeat, 3 oz cream cheese, 2 oz sour cream,

and 18

tsp lemon juice.

LESSON 5: DOUBLE NUMBER LINES



ANSWERSLESSON 5: DOUBLE NUMBER LINES

6.RP.3 9. People

lb

oz

tsp

oz

Crabmeat

Cream Cheese

Sour Cream

Lemon Juice

1 2 3tsp

tsp

cup

Dry Mustard

Old Bay Seasoning

Mozzerella Cheese1 2 3

1 2 3

2 4 6 8 10

1 2 3

12

8 16 24

12 24 36

112

112



ANSWERSLESSON 5: DOUBLE NUMBER LINES

Challenge Problem

6.RP.1 6.RP.3

10. a. The ratio of centimeters to kilometers in Map A is 1 : 10. So, a measurement of 5 cm represents 50 km.

b. Emma’s statement is incorrect. The measurements on the two maps are the same, but the actual distances are not.

She made a mistake in thinking that she could compare the distances on the two maps directly with one another. However, since the maps have different scales, she can’t directly compare the distances.

According to the scale for Map B, the ratio of kilometers to centimeters is 9 : 2. The distance in kilometers between Valpovo and Osijek is:

92 5

5 92 5

452

22 5

=

=

=

=

x

x

x

x

• • 5

.

The distance from Valpovo to Osijek is 22.5 km. It is a little less than half the actual distance between San Isidro de El General and Palmar Norte.



ANSWERS

ANSWERS

6.RP.1 1.C

79

6.RP.3 2. a.

1 2 4 5 73 6

5 10 15 20 25 30 35

b. 1 : 5, 2 : 10, 3 : 15

6.RP.3 3. The missing value is 15.



6.RP.3 6. 134 is equal to 7

4.

74

4 7• = , so you multiply the denominator by 4.

Thus, you also have to multiply the numerator by 4.

What number multiplied by 4 is 5? Use 1 4 514 • = to find the missing term.

So, you have 1 1 5 714

34: := .

6.RP.3 7. The ratio of people to pancakes is 5 : 15 or 1 : 3. Each person got 3 pancakes. To find how many pancakes Denzel made, fill in the tick marks on the top part of his sheet.

Pancakes

People

30 60

10 205 15 25

15 45 75

Denzel made 60 pancakes for 20 people.

LESSON 6: EQUIVALENT RATIOS



ANSWERSLESSON 6: EQUIVALENT RATIOS

6.RP.3 8. a. Pancakes

People5 15 25

2 6 10

2 6 10

cups

cups

tsp

tsp

tsp

15 22.5

7.5

3

3

3

3

3

45 75

tsp

12

34

Flour

Sugar

Baking Powder

Salt

Milk

4 12 6 3

4

1 12 2 1

2

13 12 22 1

2

2 6 10

2 6 10

2 6 10

Vanilla

Eggs

b. With 3 eggs, Denzel can make 22.5 pancakes, but it doesn’t make sense to make 22.5 pancakes. He can make the 22nd pancake bigger than the others to use all the batter. Or, his 23rd pancake can be half as big as the other pancakes but you would still say you have 23 pancakes.



ANSWERSLESSON 6: EQUIVALENT RATIOS

Challenge Problem

6.RP.3 9. a. If everyone eats more than 3 pancakes each, the numbers along the People number line go down.

For example, if each person has 5 pancakes, the sheet looks like this:

Pancakes

People6

3 9 15125 15 25

15 45 75

Nothing else would change on the conversion sheet.

b. If the ratio of pancakes to people increases or decreases, the ratio of eggs to people increases or decreases in the same way.

For example, if the number of pancakes per person decreases from 3 pancakes per person to 11

2 pancakes per person, then the ratio of pancakes to people goes

down by 12

. The ratio of eggs to people also goes down by 12

.

Ratio of pancakes to people before is 15 : 5 = 3 : 1. The value of the ratio is 3 ÷ 1 = 3.

Ratio of pancakes to people after is 15 : 10 = 3 : 2. The value of the ratio is 3 ÷ 2 = 1.5.

Ratio of eggs to people before is 2 : 5. The value of the ratio is 2 ÷ 5 = 0.4.

Ratio of eggs to people after is 2 : 10 = 1 : 5. The value of the ratio is 1 ÷ 5 = 0.2.

1.5 is half of 3 and 0.2 is half of 0.4. The value of the pancakes to people and eggs to people ratios both decrease by half.



ANSWERS

ANSWERS

6.RP.3 1. A 6 : 8 D 18 : 24

6.RP.3 2. Cost per ounce ratio is 0.15 or .15

6.RP.3 3. Cost per ounce ratio is 0.14 or .14

6.RP.3 4. The ratio of cost to ounces for the 18 oz bottle in simplest form is $0.15 : 1 oz. The ratio of cost to ounces for the 12 oz bottle in simplest form is $0.14 : 1 oz.

The 12 oz bottle has the lower cost per ounce.

6.RP.3 5. The ratio of people per square kilometer for Australia in 2005 is 2.604

6.RP.3 6. The ratio of people per square kilometer for the United States in 2005 is 30.68

6.RP.3 7. Australia had about 2.604 people/km2. The U.S. had about 30.68 people/km2. The United States was far more densely populated in 2005.

6.RP.1 8. The ratio is 1 : 3

6.RP.1 9.Carlos needs to use

212

or 16

cup of chopped onions.

6.RP.3 10. Both ratios simplify to 9 : 7 : 11. So, the two shades have the same hue.

6.RP.3 11. 250 : 175 : 25 simplifies to 10 : 7 : 1, while 120 : 80 : 12 simplifies to 30 : 20 : 3. Because the ratios are different, the two shades do not have the same hue.

Challenge Problem

6.RP.3 12. 22530

7.5=

Green units: 457.5

6= Blue units: 2407.5

32=

The darker shade of pink will have 6 units of green and 32 units of blue.

LESSON 7: COMPARING RATIOS



ANSWERS

ANSWERS

6.RP.3.a 1. B 80

6.RP.3.a 2. 9 18 22.5 36 99 270 405 351

34 68 85 136 374 1,020 1,530 1,326

Here is one possible method.

I compared each column with the first column, working from left to right.

18 ÷ 2 = 9 So, 68 ÷ 2 = 34

85 ÷ 34 = 2.5 So, 9 • 2.5 = 22.5

36 ÷ 9 = 4 So, 34 • 4 = 136

374 ÷ 34 = 11 So, 9 • 11 = 99

270 ÷ 9 = 30 So, 34 • 30 = 1,020

405 ÷ 9 = 45 So, 34 • 45 = 1,530

351 ÷ 9 = 39 So, 34 • 39 = 1,326

6.RP.3.a 3. 10 20 30 50 100 80 220 400

5.5 11 16.5 27.5 55 44 121 220

Here is one possible method.

I found the ratio between 55 and 100 and used that ratio (by multiplying or dividing) to complete the other columns.

55 ÷ 100 = 0.55

For example, 11 ÷ 0.55 = 20 and 50 • 0.55 = 27.5.

6.RP.3.a 4. Eggs 1

1 2

2 4 8

Flour (cups)14

12

LESSON 9: RATIO TABLES



ANSWERSLESSON 9: RATIO TABLES

6.RP.3 5. She can make 8 brownies with 1 egg. She can make 32 brownies with 4 eggs.

6.RP.3.a 6.

6.RP.3 7. The ratio of the cups of liquid coffee to ounces of grounds is 8 : 3

6.RP.3.a 8. Jason multiplied both 4 and 17 by 2. Then he doubled the results two more times.

6.RP.3.a 9. Jan multiplied both 4 and 17 by 16. Then she divided the results by 2.

6.RP.3.a 10. a. Mia divided both 17 and 4 by 4. Then she multiplied both 4.25 and 1 by 10. Then she multiplied 42.50 and 10 by 3. Then she added 127.50 and 2 to get 129.50 and added 30 and 2 to get 32.

This last step is where Mia made a mistake. She fell into the trap of blindly performing the same operation to both quantities. When you use addition or subtraction, you must add or subtract the values in the corresponding columns.

b. Mia should have first calculated the price of 2 paintbrushes (by doubling the price of 1 paintbrush) and then added the prices for 30 brushes and for 2 brushes, getting $136.

4 1 10

Price ($) 17 4.25 8.5042.50 127.50 136

30 322Number ofBrushes

Challenge Problem

6.RP.3.a 11. a. This table is not a ratio table, because the ratio of the number of brushes to price is not constant for each pair of values.

4 : 12 = 1 : 3 8 : 30 = 1 : 3.75 16 : 58 = 1 : 3.625

b. This table is a ratio table, because the three ratios are equal.

a : b = 4a : 4b = 16a : 16b

Fraction12

14

2740

38

720

25

4750

425

53100

1100

Decimal 0.5 0.25 0.675 0.375 0.35 0.4 0.94 0.16 0.53 0.01

Percent 50% 25% 67.5% 37.5% 35% 40% 94% 16% 53% 1%

Ratio 1 :2 1 :4 27 :40 3 :8 7 :20 2 :5 47 :50 4 :25 53 :100 1 :100



ANSWERS

ANSWERS

6.RP.3.a 1. The ratio in the first column is 1 : 9

6.RP.3 2. B 5 20 15 40 75 135

2 8 6 16 30 54

C

E 2.5 7.5 12.5 17.5 22.5

1 3 5 7 9

6.RP.3 3. 30 students

6.RP.3.a 4.

105

10

15

25

5

20

30

40

35

45

2015 x

50

y

LESSON 10: RATIO TABLES AND GRAPHS



ANSWERSLESSON 10: RATIO TABLES AND GRAPHS

6.RP.3.a 5. a. Quantity(no. of crates) 1 2 3 4 5

Cost $5.00 $10.00 $15.00 $20.00 $25.00

1

5

10

15

20

Number of Crates

Cos

t ($

)Cost of Apples

25

y

2 3 4 5 6 x

I plotted quantity on the x-axis and cost on the y-axis.

b. The table and graph show that 1 crate of apples costs $5. Therefore, the cost of 5 crates of apples is: 5 • $5 = $25 The cost of 5 crates of apples is $25.




6.RP.3.a 6. a. Quantity(no. of boxes) 1 2 5 10 29

Cost $2.40 $4.80 $12.00 $24.00 $69.60

10

20

30

40

50

2010 30 x

60

70

y

Number of Boxes

Cos

t ($

)Cost of Oatmeal


b. The table and graph show that 1 box of oatmeal costs $2.40. Therefore, the cost of 29 boxes of oatmeal is: 29 • $2.40 = $69.60 The cost of 29 boxes of oatmeal is $69.60.




6.RP.3.a 7. a. Quantity(gal) 1 5 10 17 20

Cost $4.20 $21.00 $42.00 $71.40 $84.00

10

20

30

40

50

255 15

60

70

80

90

Gallons of Milk

Cos

t ($

)y

x

Cost of Milk


b. The table and graph show that 1 gal of milk costs $4.20. Therefore, the cost of 17 gal of milk is:

17 • $4.20 = $71.40

The cost of 17 gal of milk is $71.40.

6.RP.3 8. The total cost of the new order is 166.00 or 166.




6.RP.3.a 9.

6.RP.3.a 10. Based on the graphs, Brand A is the best buy. It has the lowest price per ounce of peanut butter.

Challenge Problem

6.RP.3 6.RP.3.a

11. a. b. The graph of Emma’s wages goes up more quickly than the graph of Carlos’s wages. Therefore, she has the greatest y-value (wage) for any given x-value (hours).

I can make the conclusion that Emma makes more money per hour than Carlos does.

I can also find how much money each makes per hour by finding 1 on the x-axis and going up the grid line. I find that Carlos makes $5 per hour dog walking and Emma makes $7.50 per hour babysitting.

Brand A B C D E

oz 40 20 28 20 40

$ 3.10 1.98 3.50 2.15 3.75

oz per $ (written as 1 : ) 1 : 0.0775 1 : 0.099 1 : 0.125 1 : 0.1075 1 : 0.09375

0.5

$1.00

$2.00

$3.00

$4.00

$5.00

$6.00

$7.00

$8.00

$9.00

$10.00

$11.00

$12.00

$13.00

$14.00

$15.00

$16.00

$17.00

$18.00

y

1 1.5 2.0 2.5 3.0 3.5 4.0 xTime (hr)

Wa

ges

($)

Emma’s and Carlos’sWages Per Hour

Emma’s wages

Carlos’s wages



ANSWERS

ANSWERS

6.RP.3.a 1. Boeing 767-200

HorizontalDistance (ft) 12 300 498

VerticalHeight (ft) 0.5 2 12 1,200

6 24 144 14,400

1 25 41.5

6.RP.3.a 2. Paraglider

HorizontalDistance (ft) 55

21

1,100

VerticalHeight (ft) 1

11

5 7 12

231

100

12,10077 132

1,100

6.RP.3 3.

LeastGreatest

A Boeing 767-200(engines off) has aglide ratio of 12 : 1.

A Grunau Baby gliderhas a glide ratio

of 34 : 2.

A paraglider has a glide ratio of 77 : 7.

A hang glider has aglide ratio of 56 : 4.

6.RP.3 4. First, I simplified all the glide ratios.

The hang glider has a glide ratio of 56 : 4, or 14 : 1.

The Grunau Baby glider has a glide ratio of 34 : 2, or 17 : 1.

The paraglider has a glide ratio of 77 : 7, or 11 : 1.

The Boeing 767-200 with engines off has a glide ratio of 12 : 1.

The Grunau Baby glider is the best glider, since it can glide the farthest horizontal distance (17 units) for each vertical unit.

The paraglider is the worst glider, since it can glide the shortest horizontal distance (11 units) for each vertical unit.

LESSON 11: SOLVING RATIO PROBLEMS



ANSWERSLESSON 11: SOLVING RATIO PROBLEMS

6.RP.3 5. Horizontal Distance (m)

Vertical Height (m)

0

0

2.5

1

5

2

7.5

3

10

4

6.RP.3 6. Horizontal Distance (m)

Vertical Height (m)

0

0

4.4

1

8.8

2

13.2

3

17.6

4

Horizontal Distance (m)

Vertical Height (m)

0

0

5.5

1

11

2

16.5

3

22

4

6.RP.3 7. The car can travel 182 or 182.0 or 182.00 mi.

6.RP.3 8. The cost of 3 cans is $0.48 or .48

6.RP.3 9. 20 goals8 soccer game

2.5 goals1 soccer game

=

Jason scored 2.5 goals per game.

6.RP.3 10. 1,680 words30 min

56 words1 min

=

Denzel types 56 words per minute.



ANSWERSLESSON 11: SOLVING RATIO PROBLEMS

Challenge Problem

6.RP.3 6.RP.3.a

11. a. The sugar glider has a glide ratio of 1.82 : 1.

Here are three possible methods.

The sugar glider traveled a horizontal distance of 27.3 m. To find the glide ratio, I need to know the vertical height. It started at 18.6 m and end at 3.6 m.

18.6 – 3.6 = 15 m. Thus the vertical height is 15 m. So, the ratio is 27 315

1 821

. .=

OR

Sugar Glider

HorizontalDistance (m) 1.82 18.2 27.3

VerticalHeight (m) 1 10 15

Horizontal Distance (m)

Vertical Height (m)

0

0

1.82

1

9.1

2

18.2

3

27.3

4 5 6 7 8 9 10 11 12 13 14 15

b. An animal with a better glide ratio than the sugar glider would go the same distance horizontally, but its vertical height would be less than that of the sugar glider. In other words, the animal would land on the second tree at a height greater than 3.6 m.

For example, suppose the animal landed 2 m higher in the tree, landing at 5.6 m.

18.6 – 5.6 = 12 m is the vertical height. 27 312

2 2751

. .=

The glide ratio would be 2.275 : 1, which is better than the glide ratio of the sugar glider.



ANSWERS

ANSWERS

6.RP.3 6.RP.3.c

1. A 0.52

B 52 : 100

E 1325

6.RP.3 2. The ratio of voters to non-voters is 9 : 11

6.RP.3.c 6.RP.3

3. The percent of Fuji apples is 30%

6.RP.3.a 4. There were 18 Fuji apples.

6.RP.3 5. They have eaten 35 Red Delicious apples.

6.RP.3, 6.RP.3c

6. The percents and the numerical data are not consistent with each other.

According to the table, the total number of election votes is: 13,504 + 186,485 = 199,989

Based on these numbers, percent “yes” should be: 13 504199 989

0 0675 6 75,,

. . %≈ ≈

Percent “no” should be: 186 485199 989

0 9325 93 25,,

. . %≈ ≈

These percents do not match the ones in the table.

6.RP.3.c 7.The statement is true. Any percent a% can be written

100a

, and a ac

ca

100 100= = %

for any value of c. Therefore, there are an infinite number of fractions equal to

a given percent.

6.RP.3.c 8. The statement is false. Any fraction can be written only one way with a denominator of 100, so there is just one percent for any given fraction.

6.RP.3.c 6.RP.3

9. 7.4 or 7.40% of the students were born in June.

6.RP.3.c 6.RP.3

10. 7.4% of the students were born in June. 3.7% of the students were born in February. 7.4 ÷ 3.7 = 2

The percent of students born in June is twice the percent born in February.

LESSON 13: PERCENT



ANSWERSLESSON 13: PERCENT

Challenge Problem

6.RP.3.c 6.RP.3

11. There are five unique proportions included in the table (from smallest to largest): 0.037, 0.074, 0.111, 0.148, and 0.185.

These proportions are in the ratio 37 : 74 : 111 : 148 : 185, or 1 : 2 : 3 : 4 : 5.

Therefore, 0.037 represents x students, 0.074 represents 2x students, 0.111 represents 3x, 0.148 represents 4x students, and 0.185 represents 5x students.

If you add the x-values for each month, you get 27x. If x = 1, the class has 27 students. The number of students in the class is a multiple of 27.



ANSWERS

ANSWERS

6.RP.3.c 1. That year in Greensboro, 12.6 inches of rain fell in May.

6.RP.3.c 2. 123.8% of the annual rainfall fell by November.

6.RP.3.c 3. Ties sell for the least amount after the discount.

6.RP.3 6.RP.3.c

4. Emma paid $77.40.

6.RP.3 6.RP.3.c

5. No, the savings depends on the original price.

For example, imagine a pair of sunglasses costing $12 with a 60% discount and an $80 pair of shoes with a 10% discount. You save more on the sunglasses in terms of percent, but the actual savings on the shoes ($8) is greater than that of the sunglasses ($7.20).

6.RP.3.c 6. Here is one example. Of the 331 people (68 + 221 + 42) who are 18 years or older, approximately 96.7% can read.

320 ÷ 331 ≈ 0.9667

6.RP.3 6.RP.3.c

7. True False Cannot Tell

90% of the people are bilingual. 4 � �Of children under 5, about 27% are too young for preschool. � � 450% of the people have access to safe drinking water. � 4 �About 8% of people are over 59. 4 � �

6.RP.3.c 8. True False Cannot Tell

About 64% of adults 18 and older can read. � 4 �About 34% of the people are 17 or younger. 4 � �10% of the people speak only one language. � � 4Less than 50% of the people are male. � 4 �

LESSON 14: USING PERCENTS



ANSWERSLESSON 14: USING PERCENTS

Challenge Problem

6.RP.3 6.RP.3.c

9. a. The expression gives the percent of all cars sold that are domestic models.b. The expression gives the percent of all cars sold that are imports.c. r

10 4

0 4 1

0 4 0 40 4 0 6

4 646

2

+=

+( ) =+ =

==

=

rr r

r rr

r

.

.

. .. .

•

33= r

r = 23

The ratio of imports to all cars is 40%.

d. 11

0 4

1 0 4 1

1 0 4 0 4

0 6 0 4

6 464

32

+=

= +( )= +==

= =

rr

r

r

r

.

.

. .

.

rr

.

r = 32

The ratio of domestic cars to all cars is 40%



ANSWERS

ANSWERS

6.RP.3.c 1. 160%

6.RP.3c 2. 175%

6.RP.3.c 3. 230%

6.RP.3.c 4. 181.25%

6.RP.3.c 5. 450%

6.RP.3.c 6. 15 000200

75, =

Martin’s grandpa sold his guitar for 7,500% of the original price.

6.RP.3.c 7. The rainfall of 48.4 in. is about 133.7% of the normal rainfall of 36.2 in.

Here are two examples. 48 436 2 100

100 48 436 2 100

100

4,84036 2

.

.

.

.

.

=

=

=

x

x• •

xx

x133 7. ≈

OR

The percent increase is 12 236 2

33 7..

. %≈ . As a percent of average: 33.7% + 100% = 133.7%.

6.RP.3.c 8.$45,000 is what percent of $40,000? 45 000

40 0001 125,

,= . So, $45,000

is 112.5% of $40,000.

The new salary is 112.5% of her original salary.

6.RP.3c 9. The situation could not be true. A bakery can sell no more than 100% of the bread it has in stock.

6.RP.3.c 10. The situation could not be true. Denzel and his friends cannot eat more than 100% of the pizza they buy.

LESSON 15: GREATER THAN 100%



ANSWERSLESSON 15: GREATER THAN 100%

Challenge Problem

6.RP.3.c 11. Have a classmate read your word problems to make sure you have created one word problem that is about a percent less than 100% and one that is about a percent greater than 100%.



ANSWERS

ANSWERS

6.RP.1 6.RP.3

3. Here is one example.

When I go camping with my older siblings, we like to practice orienteering. We use a map and a compass to navigate from our campsite to a treasure. One of my siblings will set up the activity so it’s like a treasure hunt. We use ratios to compare the location of different points on the map with the actual landscape to find our way to the buried treasure.

LESSON 16: PUTTING IT TOGETHER

RATIOS - RUSD Mathrusdmath.weebly.com/uploads/1/1/1/5/11156667/g6_u3_-_answer_key.pdf · determine...

Documents

Transcript of RATIOS - RUSD Mathrusdmath.weebly.com/uploads/1/1/1/5/11156667/g6_u3_-_answer_key.pdf · determine...