This document provides an overview of ratios, rates, proportions, unit rates, average rates, and converting units. It includes definitions and examples of each concept. Students are guided through step-by-step worked examples and then prompted to try similar problems on their own. The document concludes by announcing an in-class practice session for students to apply the concepts.

1. Topic 2.
Ratios, Rates
and
Proportions
WEEK 4

2. Homework Review

3. Answer

4. Homework Review

5. Answer

6. Homework Review

7. Homework Review

8. Ratio and Proportions Review
Ratio: A ratio is a comparison between 2 numbers by
division. It can be written in 2 different ways.
Proportion: A equation in which two ratios are set equal to
each other is called a proportion.

9. What is a Rate?
●Rate is a specific type of ratio that compares two
different types of measurement
Examples:
Distance and Time (miles per hour)
Money and Weight (dollars per pound)

10. Unit Rate
A unit rate is a rate that is simplified so that it has a
denominator of 1.
Example – Larry can type 240 words in 4 minutes. Find out how
many words he can type in one minute.
240 words 60 words
_________ = ___________
4 minute 1 minute
Larry can type 60 words in one minute.

11. Unit Rate
Example problem 2: A 12-ounce can of Diet Coke costs 60
cents. Find the cost of 1 ounce.

12. Unit Rate
Answer: A 12-ounce can of Diet Coke costs 60 cents. Find the
cost of 1 ounce.
60 cents 5 cents
_________ = ___________
12 ounces 1 ounce
Each ounce of Diet Coke costs 5 cents ($0.05).

13. Unit Rate
Now you try: Steven drives 280 miles in 4 hours. How far does
Steven drive in one hour?
Answer:

14. Unit Rate
Now you try: Steven drives 280 miles in 4 hours. How far does
Steven drive in one hour?
Answer:
280 miles 70 miles
_________ = ___________
4 hours 1 hour
Steven drives 70 miles in one hour.

15. Using Unit Rates

16. Using Unit Rates
Example: joe’s car goes 25 miles per gallon of gasoline. How
far can it go on 8 gallons of gasoline?

17. Using Unit Rates
Example: joe’s car goes 25 miles per gallon of gasoline. How
far can it go on 8 gallons of gasoline?
Answer:

18. Comparing Unit Prices
Example: Juice is sold in two different sizes. A 48-fluid ounce
bottle costs $2.07. A 32-fluid ounce bottle costs $1.64. Which is
the better buy?
The "Unit Price" (or
"unit cost") tells you
the cost per liter, per
kilogram, per pound,
etc, of what you
want to buy.

19. Comparing Unit Prices
Example: Juice is sold in two different sizes. A 48-fluid ounce
bottle costs $2.07. A 32-fluid ounce bottle costs $1.64. Which is
the better buy?
Answer:

20. Comparing Unit Prices
Now you try: the cost of a 12 ounce box of Cheerios is $3.29.
Lucky Charms cost $4.89 for an 18 ounces box. Which one is
the better buy?
Answer:

21. Comparing Unit Prices
Now you try: the cost of a 12 ounce box of Cheerios is $3.29.
Lucky Charms cost $4.89 for an 18 ounces box. Which one is
the better buy?
Answer:
x = 0.27417 x = 0.2717
Lucky Charms is the better choice.

22. Average Rate
●Average rate is the average speed (how fast
something is happening).
distance
average rate = ___________
time
and vice versa… distance = average rate times time

23. Average Rate
Example: Jean finishes a 4-mile race in 0.5 hour. Find
Jean’s average rate in miles per hour.

24. Average Rate
Example: Jean finishes a 4-mile race in 0.5 hour. Find
Jean’s average rate in miles per hour.
average rate = distance divided by time
= 4/0.5
= 8 miles per hour
Now you try: Helen finished running 6 miles in 2.5
miles. What her average rate in miles per minute?

25. Average Rate
Now you try: Helen finished running 6 miles in 2.5
miles. What her average rate in miles per minute?
Answer: 0.04 miles per minute. This is because the
unit that we are looking for is minutes instead of
miles.

26. Converting Units
Conversion Factors:
●Conversion Factors are relationships
between units that we know are true. Some
examples:
12 inches = 1 foot 1 minute = 60 seconds
24 hours = 1 day 16 ounces = 1 lb

27. Converting Units
Steps to converting units:
Example: How many inches are there in 4.3 feet?

28. Converting Units
Example: How many inches are there in 4.3 feet?
1) Write the number that you want to convert
1) Multiply it by the conversion factor, written as a
fraction. Make sure this fraction has the unit you
want to convert from on the bottom and the unit
you want to convert to on the top

29. Converting Units
Example: How many inches are there in 4.3 feet?
3) Make sure the old units cancel
4) Multiply all the numbers on the top and divide by
the number on the bottom to find your answer

30. Converting Units
Now you try:
1) How many minutes are in 5 hours?
1) Convert 52.8 hours to days

31. Converting Units
Answer:
1) How many minutes are in 5 hours?
1) Convert 52.8 hours to days

32. Converting Units
Challenge Problem: How many seconds are in 1.5
weeks?
Try this problem on your own first. If you can't get the
answer, that’s ok. We’ll go over this problem once
everyone gives it a try.

33. Converting Units
Challenge Problem: How many seconds are in 1.5
weeks?

34. NLMC Word Problems

35. Answer

36. NLMC Word Problems

37. Answer

38. NLMC Word Problems

39. Answer

40. Time for in-class practice!
Take out the in-class practice that you printed out at home and using
the concepts that we learned today, start working on them. If you
don’t finish that’s okay, you can finish it at home.