1.5 Ratios and Rates as Percentages:

​Ratios and Rates as Percentages
Tutorial

​Objective
In this lesson, you will find a percentage of a quantity as a rate per 100 and solve problems that involve finding the whole, given a part and the percentage.

​Introduction
Tabitha is running for class president. The election is over, and the results of the vote have just been counted. The student who gets the highest number of votes will become the class president, and the student who gets the next highest number of votes will become the vice president. The teacher announces that 200 students voted in the election and that Tabitha has received 32% of the votes. To understand what this tells her about the number of students who voted for her, Tabitha needs to understand percentages. In this lesson, you'll learn how the number of votes is related to the percentage of votes.

​Each small square is 1 part out of 100 parts, or 1%.

In the class election, the student who gets the highest number of votes will become the class president and the one who gets the second highest number of votes will become the class vice president. Tabitha and four other students were candidates. Tabitha’s teacher announces the election results as percentages of the total number of votes. Two hundred votes were cast in the election. In this activity, you will relate the percentages of the votes received to the actual numbers.

​

​Activity

​Question 1
The table gives the percentage of votes each candidate received. Use the information in the table to understand the results of the election.

Multiple Choice

Part A: Two hundred votes were cast in the election. How many votes did Tabitha receive?

• 60 votes

• 100 votes
• 150 votes
• 200 votes

Multiple Choice

Part B: Two hundred votes were cast in the election. What was the highest number of votes received by a single candidate?

• 64 votes

• 60 votes

• 62 votes

• 66 votes

Multiple Choice

Part C: Two hundred votes were cast in the election. What was the second highest number of votes?

• 64 votes

• 60 votes

• 62 votes

• 66 votes

Open Ended

Part D: Did Tabitha win the election? If she did not, will she still get one of the posts?

​Activity

​Question 2
Tabitha’s brother, Toby, is in a runoff for president in his grade, which means that there is only one other student in the election. To win, Toby has to get more than 50% of the total votes cast.

Multiple Choice

Part A: Toby gets 78 votes, which is 52% of the total votes cast. How many students voted in Toby’s grade?

• 150 students
• 200 students
• 100 students
• 50 students

Multiple Choice

Part B: From the previous question, we know that 150 students in Toby’s grade voted. We also know that 75% of the students in Toby’s grade voted. If 75% of the students in Toby’s grade voted, how many students are in Toby’s grade?

• 200 students
• 225 students
• 250 students
• 300 students

Open Ended

Part B: If 75% of the students in Toby’s grade voted, how many students are in Toby’s grade?

Open Ended

Self-Evaluation

How did you do? Rate your work on a scale of 1 to 5, with 5 as the highest score. Then write a brief evaluation of your work below. Note what you learned and what challenged you.

Multiple Choice

The original price of a shirt is $20. The shirt is on sale for a 20% discount. How much money does a buyer save because of the discount?

• $4

• $16

• $2

• $1

Open Ended

Alex buys 24 apples from the supermarket. When he gets home, he finds that 6 apples are bad. What percentage of the apples are bad? Round your answer to the nearest number.

A decimal number can be converted to a percentage.

Match

Match each percentage to the fraction or decimal expression that it equals. Drag the items on the left to the correct location on the right.

• 25%

• 75%

• 100%

• 80%

0.25

3/4

1

4/5

• 0.25

• 3/4

• 1

• 4/5

​Calculating Rate

We've seen how to calculate the amount of discount from the base price and discount rate. We can also use the formula