Rates and Ratios
Billy ran 24 laps at the track in 3 days.

Rates and Ratios

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A rate is a special ratio because it is a comparison of measurements that have different units such as dollars and cents or pounds and ounces. A unit rate is a rate with a denominator of 1.

Let’s look at the following example:

Betty is buying jellybeans for her sister’s birthday party. She buys a bag of 10 lbs. of jellybeans that costs $45.00. Betty is wondering how much 1 lb. of jellybeans cost.

First, we convert $45.00 to cents by moving the decimal point two spaces to the right. $45.00 = 4500 cents.

We now create a fraction using the cents with the pounds of jellybeans. In this case we have 10 lbs. of jellybeans so our fraction will be 4500/10 lbs. We now need to divide the denominator with the numerator so 4500 ÷ 10 = 450. Since we divided the numerator by10 we must do the same with the denominator so 10 ÷ 10 = 1. Now our fraction is 450/1 which is a unit rate. 450/1 = 450. Now we convert back to dollars by adding our decimal back in by placing it two spaces to the left or 4.50. This tells us that 1 lb. of jellybeans cost $4.50. $4.50 is the rate.

1.
Candice bought movie tickets for herself and six friends. The total cost of the tickets was $47.25. What was the rate of each ticket?
$7.88
$6.85
$6.75
$0.75
We first convert $47.25 to cents by moving the decimal point two spaces to the right giving us 4725. We then know that there were a total of 7 tickets bought (Candice (1) + (6) friends) so we now have the fraction 4725/7. We now need to divide the numerator by the denominator so 4725 ÷ 7 = 675. We also must divide the denominator by the same number so 7 ÷ 7 =1 giving us the new fraction of 675/1 which becomes 675. Now we convert that back into dollars by adding our decimal point back in two spaces to the left giving us $6.75. $6.75 is the rate of each ticket. Answer (c) is the correct answer
2.
Savannah completed 80 problems in 34 minutes. What is the rate of the number of problems she did per minute?
2
2.25
2.35
2.4
Since Savannah completed 80 problems in 34 minutes, we convert these numbers to a fraction to read 80/34. We then divide the numerator by the denominator so 80 ÷ 34 = 2.35. Next we must divide the denominator by the same number so 34 ÷ 34 = 1 giving us the fraction 2.35/1. 2.35/1 becomes 2.35. The rate of the problems Savannah completed per minute was 2.35. Answer (c) is the correct answer
3.
The Hershey’s machine produced 450,000 Kisses every 60 minutes. What is the rate of the number of Kisses produced every minute?
750
7,500
75,000
75
Since the Hershey’s machine produced 450,000 Kisses every 60 minutes, we convert these numbers to a fraction to read 450000/60. We then divide the numerator by the denominator so 450000 ÷ 60 = 7500. Next we must divide the denominator by the same number so 60 ÷ 60 = 1 giving us the fraction 7500/1. 7500/1 becomes 7500. The rate of the number of Kisses produced every minute is 7,500. Answer (b) is the correct answer
4.
Jason has to deliver 289 newspapers every Sunday morning on his paper route. It takes him 3 hours to deliver the newspapers. What is the rate of the number of newspapers he delivers each hour?
83
89
96
96.33
Since Jason delivers 289 newspapers in 3 hours we convert these numbers to a fraction to read 289/3. We then divide the numerator by the denominator so 289 ÷ 3 = 96.33. We must also divide the denominator by the same number so 3 ÷ 3 = 1 giving us the fraction 96.33/1. (Remember, a unit rate is a rate with a denominator of 1.) 96.33/1 becomes 96.33. The rate of the number of newspaper Jason delivers each hour is 96.33. Answer (d) is the correct answer
5.
Billy ran 24 laps at the track in 3 days. What is the rate of laps that he ran per day?
9
7
6
8
Since Billy ran 24 laps in 3 day, we convert these numbers to a fraction to read 24/3. We then divide the numerator by the denominator so 24 ÷ 3 = 8. Next we must divide the denominator by the same number so 3 ÷ 3 = 1 giving us the fraction 8/1. 8/1 becomes 8. The rate of the laps ran each day is 8. Answer (d) is the correct answer
6.
Mrs. Milner bought 62 new math books for her school. She spent $2,092.50 in total. What was the rate of each new math book?
$92.50
$34.25
$33.75
$31.75
We first convert $2092.50 to cents by moving the decimal point two spaces to the right giving us 209250. We then know that there were a total of 62 new math books purchased. This gives us the fraction of 209250/62. Next we need to divide the numerator by the denominator so 209250 ÷ 62 = 3375. We also must divide the denominator by the same number so 62 ÷ 62 =1 giving us the new fraction of 3375/1 which becomes 3375. Now we convert that back into dollars by adding our decimal point back in two spaces to the left giving us $33.75. $33.75 is the rate of each new math book. Answer (c) is the correct answer
7.
The Walton family went to the county fair and each person was given $35.00 to ride 14 rides. What was the rate of each ride?
$2.25
$2.50
$3.00
$3.25
We first convert $35.00 to cents by moving the decimal point two spaces to the right giving us 3500. We then know that this was for a total of 14 rides. This gives us the fraction of 3500/14. Next we need to divide the numerator by the denominator so 3500 ÷ 14 = 250. Next we must divide the denominator by the same number so 14 ÷ 14 =1 giving us the new fraction of 250/1 which becomes 250. Now we convert that back into dollars by adding our decimal point back in two spaces to the left giving us $2.50. $2.50 is the rate of each ride. Answer (b) is the correct answer
8.
The Smith family went to Disney World for their summer vacation. They traveled 885 miles and it took them 13 hours to get there. What is the rate of miles they drove per hour?
68.1 mph
88.5 mph
67 mph
66.5 mph
Since they drove 885 miles in 13 hours, we convert these numbers to a fraction to read 885/13. We then divide the numerator by the denominator so 885 ÷ 13 = 68.076. As the last number to the right of the decimal is a “6” we can round the preceding number up giving us 68.08. As the last number to the right of the decimal is an 8 we can round up the preceding number giving us the number 68.1. Next we must divide the denominator by the same number so 13 ÷ 13 = 1 giving us the fraction 68.1/1. (Remember, a unit rate is a rate with a denominator of 1.) 68.1/1 becomes 68.1. The rate of the miles driven per hour is 68.1 mph. Answer (a) is the correct answer
9.
The theater owner determined he could make $1,565.00 dollars if he sold 150 seats for the coming concert. What would be the rate of each seat?
$15.65
$10.43
$104.30
$104.33
We first convert $1,565.00 to cents by moving the decimal point two spaces to the right giving us 156500. We then know that there were a total of 150 seats so we now have the fraction 156500/150. We now need to divide the numerator by the denominator so 156500 ÷ 150 = 1043.33. (As the last numbers to the right of the decimal is “33” we can round this number down to 1043.) Next we must also divide the denominator by the same number so 150 ÷ 150 =1 giving us the new fraction of 1043/1 which becomes 1043. Now we convert that back into dollars by adding our decimal point back in two spaces to the left giving us $10.43. $10.43 is the rate of each seat. Answer (b) is the correct answer
10.
Rachel bought four new bangle bracelets for $98.00. What was the rate for each bracelet?
$24.50
$32.00
$36.00
$37.50
We first convert $98.00 to cents by moving the decimal point two spaces to the right giving us 9800. We then know that there were a total of 4 bangle bracelets so we now have the fraction 9800/4. Next we need to divide the numerator by the denominator so 9800 ÷ 4 = 2450. We also must divide the denominator by the same number so 4 ÷ 4 =1 giving us the new fraction of 2450/1 which becomes 2450. Now we convert that back into dollars by adding our decimal point back in two spaces to the left giving us $24.50. $24.50 is the rate of each bangle bracelet. Answer (a) is the correct answer
Author:  Christine G. Broome

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