Ratios, Rates, Unit Rates
Proportions
Partitive Proportions and Scale Drawings/Models
Direct and Inverse Proportions
Indirect Measurement and Similarity
100
1. Find the unit rate:
Spencer can type 420 words in 7 minutes
2. Find 2 ratios equivalent to the unit rate.
1. 60 words per minute
2. 120/2 , 180/3 , ...
100
h / (1/3) = 4 / 2
h = 2/3
100
Noah has 400 acres of land. He wants to divide the land into three parts (barn, garden, pasture) using the ratio 2 : 5 : 9. How many acres will go to each part?
The barn will use 50 acres, the garden will use 125 acres, and the pasture will use 225 acres.
100
Gabriella makes greeting cards. She can make 5 cards in 1 hour. How long would it take to make 17 cards?
It will take Gabriella 3.4 hours to make 17 cards.
100
Fill in the blanks:
Similar figures have the same shape and same or different size. Two figures are similar polygons if their corresponding angles are _________________ and the lengths of their corresponding _________ are proportional
1. congruent/same/equal
2. sides
200
Find the unit rate
$25 for 20 tickets
The unit price is $1.25 per ticket.
200
3 / (x+5) = 12 / 36
x=4
200
Find the scale factor: 5 inch model of 75 foot RV.
(hint: must have the same units of measure to find the scale factor)
5 / 900 = 1 / 180
200
Charlie makes bookmarks. He can make 8 bookmarks in 1 hour. How long would it take him to make 20 bookmarks?
Is this an example of a direct proportion or inverse proportion? Explain.
This is an example of direct proportion because as time increases, the number of bookmarks she can make increases.
200
What is the angle measure of angle F?
22 degrees
300
Which is the better deal, a dozen roses for $19.99 or 18 roses for $25?
The better buy is 18 roses for $25.
300
1.2 / 73.2 = n / 91.5
n=1.5
300
The width of Christina's living room is 25 feet. If the blueprint has a scale of 1.5 in.:3 feet, how wide is the living room on the blueprint?
12.5 inches
300
It takes 6 workers 8 hours to build a fence. If 2 workers leave, how long will it take to build the fence?
*Think: If there are LESS workers, will it take MORE or LESS time to build the fence?
It will take 12 hours to build the fence.
300
What is the angle measure of angle B?
45 degrees
400
There are 24 dogs, 19 cats, and 4 rabbits at the local shelter.
a) What is the ratio of dogs to rabbits?
b) What is the ratio of cats to total number of animals at the shelter?
a) The ratio of dogs to rabbits is 24/4 = 6/1.
b) The ratio of cats to total animals is 19/47.
400
If 5 apples cost $2.50, how much will 12 apples cost?
Twelve apples will cost $6.00.
400
The perimeter of a polygon is 800 m. If the sides are in a ratio of 4 : 7 : 9, find the length of each side.
The side lengths are 160 m, 280 m, and 360 m.
400
It takes 6 workers 8 hours to build a fence. If 2 workers leave, how long will it take to build the fence?
Is this an example of a direct proportion or inverse proportion? Explain.
It is an example of inverse proportion because if there are LESS workers, will it take MORE time to build the fence.
400
What is the length of side AC?
6
500
Shannon says that 7/8 and 4/5 form a proportion because you can subtract 3 from the numerator and denominator of 7/8 to get 4/5. Is she correct? Explain your reasoning.
Shannon is incorrect. Proportions can only be formed by multiplying or dividing the numerator and denominator by the same number.
500
There are 8 pints in a gallon. How many pints are in 7 gallons? (1 quart = 2 pints, 4 quarts = 1 gallon)
There are 56 pints in 7 gallons.
500
Hot Wheels are created on a scale factor of 1 : 64. If a Dodge Ram is 204 inches long, how many inches will the toy car be? Round your answer to the nearest tenth.
The toy car will be 3.2 inches long.
500
If Matthew makes $24 babysitting for 3 hours, how much will he make if he babysits 10 hours at the same rate?
Matthew will earn $80.
500
Find side DE.
x=1.5 in