Equivalent Ratios
What are equivalent ratios?
Ratios that equal the same.
What is the definition of unit price?
The price for one.
What is the definition of unit rate in terms of speed?
The distance per one unit of time.
What is the definition of a conversion factor?
A comparison of two units of measurement
What is the definition of a percent?
A part out of 100.
Write one equivalent ratio for the following:
a) 8:12
b) 9:21
Sample answers -
a) 2:3, 16:24, 24:36
b) 3:7, 18:42, 27:63
How do you find unit price? (What's the formula?)
Price / # of units = unit price
How do you find unit rate in terms of speed?
Distance / Time = Speed
How many numbers do you need in a conversion factor?
Two
What are the factors of 100?
25, 4, 2, 50, 20, 5, 10
Are these ratios equivalent?
20 pies for every 44 cakes
14 pies for every 26 cakes
No.
A grocery store is selling a dozen oranges for $15.12. What is the unit price?
Each orange costs $1.26.
$15.12 /12 = $1.26
An airplane pilot is mapping a trip and wants to know the distance the airplane will travel over certain time intervals. Assuming that the airplane travels at a constant speed, what is its speed?
Time (hours) Distance (Miles)
0.5 225
1 450
1.5 670
450 miles per hour
How do you convert between units of measurement?
1) Multiply the given by the conversion factor with the same units in the denominator.
2) The like units cancel eachother out.
3) Do cross simplification.
4) Multiply straight across.
There are 12 pieces of fruit in a bowl and 9 of them are apples. What percentage of the pieces of fruit in the bowl are apples?
75% are apples
9 / 12 = 0.75
0.75 x 100 = 75%
Complete the chart with equivalent ratios.
Number of Items 1 5 10 ?
Cost ($) ? 25 ? 250
Number of Items 1 5 10 50
Cost ($) 5 25 50 250
Which is a better deal, 5 tickets for $12.56 or 9 tickets for $22.50?
They are the same.
$12.56 / 5 = $2.50
$22.50 / 9 = $2.50
Bob runs 4 laps around a track in 10 minutes.
A. How many minutes per lap is that?
B. How many laps per minute is that?
C. If Bob runs 17 laps at the same rate, how long does it take him?
A. 2.5 minutes per lap
B. 0.4 laps per minute
C. 6.8 minutes
Work:
A. 10 / 4 = 2.5
B. 4 / 10 = 0.4
C. 0.4 x 17 = 6.8
A recipe for chocolate chip cookies calls for 9 ounces of chocolate chips for 3.5 cups of flour. Complete the table provided.
Choc. Chips (ounces) Flour (cups)
8 ?
? 10.5
28 ?
Choc. Chips (ounces) Flour (cups)
8 3.5
24 10.5
28 12.25
Joe’s family has completed 60% of a trip. They have traveled 30 miles. How far is the trip?
50 miles
30 / 6 = 5
5 x 10 = 50
The ratio of boys to girls in Mrs. Townsend's class is 3:4. If there are 15 boys in her class, how many students does Mrs. Townsend have in her class altogether?
35 students altogether.
3:4 = 15:20
15 + 20 = 35
Here are the prices for cans of juice that are the same brand and the same size at different stores. Which store offers the best deal?
Store A: 4 cans for $4.56
Store B: 6 cans for $6.36
Store C: 8 cans for $9.04
Store D: 10 cans for $11.00
Store B
$6.36 / 6 = $1.06
Select all of the trips that would take 4 hours.
A. Drive 50 miles per hour between two cities which are 200 miles apart.
B. Walk 4 miles per hour to school, which is 8 miles away.
C. Take a train going 90 miles per hour between two cities which are 22.5 miles apart.
D. Bicycle 30 miles at 7.5 miles per hour
A. Drive 50 miles per hour between two cities which are 200 miles apart.
D. Bicycle 30 miles at 7.5 miles per hour
Work:
A. 200 / 50 = 4 hours
B. 8 / 4 = 2 hours
C. 22.5 / 90 = 0.25 hours
D. 30 / 7.5 = 4 hours
Which weighs more: a puppy that weighs 8.5 kilograms or a baby that weighs 11 pounds? (Note: 1 pound is about 0.45 kilograms)
The puppy.
11 pounds x 0.45 kilograms = 4.95 kilograms
Jenna and Richie go shopping at the mall to buy their mom a present. They buy a scarf for $12 and a necklace for $36. Their state charges 8% sales tax. How much does sales tax do Jenna and Richie pay on their gifts they bought?
They pay $3.84 in sales tax.
$12 / 100 = $0.12 x 8 = $0.96
$36 / 100 = $0.36 x 8 = $2.88
$2.88 + $0.96 = $3.84