Unit Rate
Find the unit rate: 12 miles in 3 hours. State your answer as miles per hour.
What is
4 miles per hour?
Write the ratio of 8 pencils to 2 students in simplest form.
4:1 pencils to students
Are the ratios 2:3 and 4:6 equivalent? Explain briefly
Yes — 4:6 simplifies to 2:3.
True or False: If two quantities are proportional, their graph is a straight line that passes through the origin. Explain your answer in one sentence.
True — proportional relationships are linear through origin.
Sarah buys 3 notebooks for $6. How much does one notebook cost?
$2.00 each notebook
A recipe uses 4 cups of flour for 6 batches. What is the amount of flour per batch (unit rate) in cups per batch?
4:6 = 2/3 cups of flour per batch
If a class has 14 girls and 7 boys, write the ratio of girls to total students in simplest form.
14:21 girls to total students
reduces to
2:3 girls to total students
Fill in the blank to make an equivalent ratio: 5:8 = ___ : 32
20:32
A taxi charges a flat $3 fee plus $2 per mile. Is the total cost proportional to miles driven? Explain why or why not.
No — because of the flat fee, it is not proportional (does not pass through origin).
A store sells 5 cans of soup for $8. If you buy 15 cans, how much will it cost assuming the same rate?
8/5 = 1.60 each
1.60 x 15 = $24
A car travels 150 miles on 5 gallons of gas. What is the unit rate in miles per gallon?
What is 30 mile per gallon?
Express the ratio 5:12 as a fraction and as a decimal (rounded to the thousandths place).
5/12 = 0.417
List two pairs of equivalent ratios to 3:5
6:10, 9:15, 12:20, 15:25, 18:30, 21:35, 24:40, 27:45, 30:50
Identify the constant of proportionality (unit rate) for y when y = 4x. Then explain what the point (1, 4) means in context.
k = 4. Point (1,4) means when x=1, y=4 (one unit of x gives 4 units of y).
A scale drawing uses a scale where 4 cm represents 10 m. A model has a length of 14 cm. What is the actual length in meters?
14 x 10 =140/4 = 35
35 meters
A painter covers 3/4 of a wall in 1/2 hour. What is the painting rate in walls per hour?
What is 1.5 walls per hour?
A map scale shows 1 inch represents 30 miles. What is the ratio of map inches to actual miles?
BONUS - Double Jeopardy!!!!
How many miles are represented by 2.5 inches?
1:30 inches to miles
75 miles
Use a table to determine whether (x, y) pairs (2, 6), (4, 12), and (5, 15) show equivalent ratios. Explain your reasoning.
Yes — each y/x = 3, so equivalent.
Given the table: x: 1, 2, 3, 4 and y: 2, 4, 6, 8 — write an equation that represents this relationship and state whether it is proportional. If it is, give the constant of proportionality.
Equation y = 2x; proportional with k = 2.
A currency exchange converts $50 to 42 euros. At this rate, how many euros will you get for $275? Show your calculation using a proportion or unit rate.
275 x 42/50 = 231 euros
A cyclist covers 7 kilometers in 3/8 of an hour. Compute the unit rate in kilometers per hour as a mixed number.
What is 18 2/3 kilometer per hour?
A mixture has sugar: water = 7:11. If the mixture has 126 grams of sugar, how many grams of water are in the mixture?
198 grams of water
Solve for x to make ratios equivalent: 7:x = 21:45. Show work and simplify the result if possible.
7/x = 21/45 →
x = 7×45/21 = 15
x = 15
A graph shows a line through the origin and the point (3, 7.5). Determine whether the relationship is proportional; if so, find the unit rate.
DAILY DOUBLE!!
Write the equation in the form y = kx.
k = 7.5/3 = 2.5
y = 2.5x
A tank fills at a rate proportional to time. After 2/3 hour it is 3/5 full. How long will it take to fill the tank completely?
1 1/9 hour or about 1 hour and 6.6 repeating minutes.