Ratios/Rates/Proportions/Percents Study Guide
Student Name: _________________________________
Write each decimal as a fraction or mixed number in simplest form.
6 ÷2
3
25
25 ÷25
1
Ex1: 0.6 =
=
Ex2: .25 =
=
=
10 ÷ 2
1.
2.
5
100
100 ÷ 25
4
.75
1.25
3.
4.
0.06
2.125
Write each fraction or mixed number as a decimal and a percent
Ex:
3
4
3 x 25
=
5.
6.
4 x 25
=
75
100
= 75%
or
3÷4=
1
5
2
1
0.75
4 3. 00
28
20
20
00
.75 =
75
100
= 75%
4
7.
8.
5
8
15
30
Write each percent as a decimal and a fraction in simplest form.
Ex: 20% =
20
100
1
=
5
9. 525%
10. 1.5%
11. .6%
12. 22.8%
Order the numbers from least to greatest.
6
13. 0.32, , 30%
25
2
14. , 39%, 0.41
5
15.
15
20
,
3
5
,
1
2
,
14
16
6RP A1 Ratio
16. Use the shapes pictured to write the following ratios
a.
b.
c.
d.
e.
Squares to Circles __________
Circles to Squares __________
Triangles to Squares ___________
Triangles to the total group __________
Write 3 equivalent ratios to compare the number of circles with the number of triangles.
17. A package containing 3 T-shirts costs $9.99. A package containing 6 T-Shirts costs $17.99. Which is a better deal? Explaining
your reasoning.
18. Daniel has 15 pomegranates for every 45 bananas. Write the ratio of pomegranates to bananas as a simplified fraction.
19. In math class, the girl to boy ratio is 8 to 5.If there are 25 boys, how many girls are there?
6 RP A2 Rate
20. The scale on a map is 8cm: 5km. If two cities are 72cm apart on the map, what is the actual distance in km between the two
cities?
21. Esteban is running in a 5-kilometer race this weekend. How many miles will he run? Round your answer to the nearest
tenth of a mile. (1 kilometer = 0.621 miles)
6 RP A2 Unit Rate
22. Matt can jog 12 miles in 3 hours. How many miles can Matt jog per hour?
23. James can wash 133 cars in 7 days. How many cars can James wash per day?
24. How many centimeters are in 7 feet, given that 1 inch = 2.54 cm?
6 RP B
25. Using the information in the table, find the number of yards in 24 feet. (Identify the pattern)
Feet
3
6
9
15
Yards
1
2
3
5
24
26. Compare the number of black to white circles. If the ratio remains the same, how many black circles will you have if you
have 60 white circles? (Identify the pattern)
Black
4
40
20
60
White
3
30
14
45
60
27. The two tables below show equivalent ratios to 322:22 and 333:33. Fill in the tables to answer the following question:
Which ratio is greater, 322:22 or 333:33?
Numerator
Denominator
Numerator
Denominator
161
322
11
22
333
33
44
66
1288
999
Refer to the graph on the right for problems 28-33.
U.S. Recorded Music
Sales, 2000
28. What is the fraction of the total 2000 music sales in the
United States were rock recordings?
29. On this grid, model the percent of total United States
music sales that were rap recordings. Then write that
percent as a decimal.
Oldies
1% 3% 3%
Classical
5%
10%
18%
Jazz
Religious
25%
11%
13%
11%
R&B
Country
Pop
Rap
Rock
30. What kind of music made up
1
20
of the total U.S. Music recording sales?
31. What fraction of the United States music sales were country recordings?
32. What fraction of all the United States recording sales did jazz and classical music make together?
33. What kind of music made up
1
10
of the total music recording sales in the United States in 2000?
6. RP.A.3 –
Formula - Amount = rate x base
Find the unknown amount in a percent problem
34. What is 18% of 300?
35. Find 65% of 200.
Find the unknown percent of a problem
38. 30 is what percent of 150?
39. 75 is what percent of 300?
Equation -
𝑨𝒎𝒐𝒖𝒏𝒕
𝑩𝒂𝒔𝒆
=
𝒓𝒂𝒕𝒆
𝟏𝟎𝟎
? = rate x base
36. What is 150% of 50?
37. What is 125% of 300?
Amount =? x base
Find the unknown base of a percent problem.
42. 28 is 40% of what number?
43. 70 is 35% of what number?
40. 5 is what percent of 2?
41. What percent of 200 is 340?
Amount = rate x?
44. 34 is 8.5% of what number?
45. 58.5 is 13% of what number?
46. It is customary when eating in a restaurant to leave a 15% tip.
a. Outline a method to do a quick approximation for the amount of tip to leave.
b. Use this method to figure a 15% tip on a bill of $47.76.
c. Calculate the total bill with a 20% tip.
47. Is this the proper way to set up an equation for this word problem: Movies are on sale for 15% of their original price? If a
movie cost $22.10, what was the original price? My equation is: 15% of what is $22.10 or 15/100 = 22.1/x.
48. 15% of taxi's go to airport, 15% is 30 taxi's. How many cabs all together?
49. Gordon buys a soccer ball for $14.00. Sales tax is 8%. What is the total cost for the soccer ball?
a. Determine the total price if Gordon used a coupon for 25%.
50. Emily just hired a new employee to work in your bakeshop. In one hour the employee burned 55 chocolate chip cookies. If
this represented 15% of the day’s production, how many cookies did you plan on producing that day?
51. A scale model of a building is constructed using the scale of 1 inch: 20 feet. The actual height of the building is 280 ft. Find
the height of the scale model.
52. A 8-foot tall fence posts casts a shadow 10 feet long. How long would the shadow be for a 5-foot tall mailbox?
Proportions
Find the missing value
53.
4
𝑦
54.
5
20
55.
5
8
+
+
+
6
15
𝑥
6
𝑤
12
56. The length of a football field is 100 yards. Convert this measurement of feet.
57. A dump truck can haul 34 tons of stone in one day. Convert this measurement to pounds.