TEAS: Rates, Proportions & Ratios

Express 30 minutes to 4 hours as a ratio of minutes in fraction form

1. First, change the 4 hours to minutes: 4 hours × 60 minutes = 240 minutes 2. Then, write the ratio in fraction form keeping the order of the ratio indicated in the problem - the number after the word "to" is the denominator of the fraction: 30/240 = 1/8 3. The ratio of 30 minutes to 4 hours is 1/8

Student A reads 10 pages an hour. Student B reads 18 pages per hour. Each has a 288 page book to complete this weekend. At this rate, how much sooner will Student B complete the book compared to Student A?

1. Set-up proportions 2. 12.8 hours

A club has 9 male and 21 female members. What is the ratio of male to female members in the club?

1. Set-up proportions 2. 3 to 7

The following amounts of beverages are needed to serve 72 people: 4 gallons of punch, 3 gallons of lemonade, and 2 gallons of tea. How many total gallons of these beverages are needed to serve 240 people?

1. Set-up proportions 2. 30 gallons

If John can travel 130 miles in 2 hours, how far can he travel in 5 hours if he travels at the same rate of speed?

1. Set-up proportions 2. 325 miles

If Jake can ride his bike to a town that is 21 miles away in 45 minutes, how far can he ride in 1 hour?

21 miles/45 minutes = 7 miles/15 minutes = 28 miles/60 minutes 1. However, it is not easy to go directly from 45 minutes to 60 minutes (1 hour). So, let's first figure the rate for 15 minutes, which is easy. 2. Why? Because to get from 45 minutes to 15 minutes you simply divide both terms of the rate by 3. 3. Then from 15 minutes, we can easily get to 60 minutes: Just multiply both terms by 4. We find that he can ride 28 miles in one hour.

Proportion

States that two ratios are equal When setting up a proportion, the numerators of both ratios must be in the same units and the denominators of both ratios must be in the same units units of a item/units of a different items = units of a item/units of a different items Use the method called finding cross products to solve the equation.

In a certain class, the ratio of passing grades to failing grades is 7 to 5. How many of the 36 students failed the course?

The ratio, "7 to 5" (or 7 : 5 or 7/5), tells me that, of every 7 + 5 = 12 students, five failed. That is, 5/12 of the class flunked. Then (5/12 )(36) = 15 students failed.

Last year...1,250 students were enrolled in 50 sections of beginning algebra. This year 1,550 students will enroll in beginning algebra. If the number of students per section is the same for each section and does not change from year to year, how many sections will need to be offered?

a. 1250 students/50 sections = 1500 students/ x sections b. criss cross c. 62 sections of beginning algebra need to be offered

Rate of change problems

problems use proportions to determine the difference in completion times for a given task

Rate

used to express a relationship between two quantities