Name ________________________________________________ Date _________________ Period _________
Ratios, Rates and Proportional Relationships
Unit 5 - Study Guide
Ratios and Rates
1. There are 10 boys and 15 girls in the class.
a) What is the ratio of girls to boys? Write your answer in 3 different ways.
b) What is the ratio of boys to total students? Write your answer in 3 different ways.
2. Write the following ratios in simplest form. Remember, a ratio in simplest form includes no decimals
or fractions.
a)
b)
to
3. Jane is mixing orange paint to paint her bedroom. She creates the perfect shade of orange by mixing
cups of yellow paint with cups of red paint. If Jane needs
cups of paint to cover all of the walls
in her room, how much yellow paint and red paint should she use?
Unit Rates
4. Find the unit rates:
a.
b. $297 : 11 hours
5. What is the unit rate for the graph, (1, r)?
6. A restaurant sells 3 drink sizes. The 9-ounce cup costs $.89. The 12-ounce cup costs $1.29. The 15ounce cup costs $1.59. Which cup costs the least per ounce? Explain your answer.
7. If Megan can run
miles in each hour, what is the unit rate in miles per hour?
Proportions
8. Tell whether the ratios form a proportion. Show your work.
a.
b.
9. Find the value of x that makes the proportion true.
a.
c.
b.
10. Use the table to write and solve a proportion.
11. Daniel watches 1 hour of television for every 3 hours of homework he does each week. If he did 12
hours of homework last week, how many hours of television did he watch?
12. On a given map, the distance between Madison, NJ and Orlando, FL is
cm. If the map scale is
1 cm = 60 miles, write an equation that represents the distance from Madison to Orlando as a
proportional relationship.
Proportional Relationships
13. Is the relationship shown in the table below proportional? Explain how you know.
x
y
2
3
5
6
8
9
14. Is the relationship shown in the table below proportional? Explain how you know.
Similar Figures
15. At 3pm, a given building casts a 45 foot shadow. At the same time a 20 foot tree casts an 8 foot
shadow. To the nearest tenth of a foot, find the height of the building.
16. You have a 3.5 inch tall by 5 inch wide photograph that you want to enlarge as a gift. If the new height
of the photograph is 15 inches, what is its new width?
Write proportions in each of the problems below to find the length of the unknown side.
17.
19.
18.
20.
Direct Variation
Tell whether x and y show direct variation. If so, determine the constant of proportionality.
21.
22.
23.
24.
25.
26.
Slope
Find the slope of the lines below.
27.
28.
29. The line that passes through (-1, -4) and (1, 4)
31.
30. The line that passes through (1, 2) and (-3, 2)
32.
33. The graph shows the cost of a long distance phone call.
a. Find the slope of the line.
b. Explain the meaning of the slope as a rate of change.
c. How much money is added to the phone bill if you talk for
5 extra minutes?
d. How many minutes did you talk if the phone call costs $3?
Answer Key
1.
a. 3:2
3 to 2
b. 2:5
2 to 5
2.
a. 3:2
b. 9 to 7
3. 12 ½ cups of yellow paint and 8 cups of red paint
4.
c.
d. $27/1 hour
5.
:1
6. Small: $0.09888 per ounce
Medium: $0.1075 per ounce
Large: $0.106 per ounce
The small cup costs the least per ounce.
7.
miles per hour
8.
e. No, cross products are not equal
f. No, cross products are not equal
g. Yes, cross products are equal
9.
h. x =
i.
10.
x = 12.5
; h=3
11. 4 hours of television
12. x = 60 • 15 ½
13. No, cross products are not equal, the fractions do not simplify to the same number, the graph of these
numbers would not pass through the origin.
14. Yes, the graph passes through the origin.
15. 112.5 feet
16. About 21.4 inches
17. x = 15
18. x = 6
19. x = 14.4
20. x = 14
21. yes; k = 3
22. no
23. no
24. yes; k = -4
25. yes; k =
26. no
27. m =
28. m = -1
29. m = 4
30. m = 0
31. m =
32. m = -1
33. a. m =
b. The cost increases by $1 for every 10 minutes talked
c. $0.50
d. 30 minutes