Unit Rates
A car travels 120 miles in 3 hours. What is the unit rate in miles per hour?
40 miles per hour
What is the ratio of 12 apples to 8 oranges in simplest form?
3:2
If y = 3x, what is the constant of proportionality?
3
You buy 3 notebooks for $6. What’s the cost of 1 notebook?
$2 per notebook
Evaluate: 5 + (–8)
–3
A smoothie uses 6 cups of fruit for 8 servings. How many cups of fruit are used per serving?
0.75 cups per serving
There are 18 boys and 12 girls in a class. What is the ratio of girls to total students in simplest form?
2:5
A babysitter earns $45 for 3 hours of work and $60 for 4 hours of work. Is the relationship between hours worked and money earned proportional?
Yes; both have a rate of $15 per hour
A recipe uses 4 cups of flour for every 2 cups of sugar. What is the ratio of flour to sugar in simplest form?
2:1
Simplify: (–6) × (–3)
18
A factory makes 225 toys in 5 hours. How many toys does it make per hour?
45 toys per hour
If the ratio of cats to dogs is 5:3 and there are 12 dogs, how many cats are there?
20 cats
A taxi company charges $4 per mile, plus a $2 flat fee to start the ride. Is the cost proportional to the miles traveled?
No; the $2 starting fee makes it non-proportional (does not start at 0,0)
If y = 5x represents a proportional relationship, what is the constant of proportionality?
k = 5
Simplify: (–12) ÷ 3
–4
If 4 notebooks cost $6.80, what’s the cost per notebook?
$1.70
The ratio of red to blue marbles is 2:7. If there are 36 marbles in total, how many are red?
8 marbles
At a bakery, 5 muffins cost $10 and 8 muffins cost $16. Is the relationship between muffins and cost proportional? If so, what is the constant of proportionality?
Yes; k = $2 per muffin
Evaluate:
(−3.5)+(7.25)−(2)
1.75
Simplify: (–3/4) + (1/2)
–1/4
A runner completes 7/8 of a mile in 1/10 of an hour. What is the unit rate in miles per hour?
8.75 miles per hour
A recipe calls for 3/4 cup of sugar for every 2 cups of flour. What is the ratio of sugar to flour?
3:8
You earn $20 for mowing 2 lawns and $35 for mowing 4 lawns. Is your pay proportional to the number of lawns mowed?
No; the rates are different ($10 per lawn vs. $8.75 per lawn)
A runner travels 4.8 kilometers in 0.4 hours.
a) Find the unit rate in kilometers per hour.
b) State whether the relationship between distance and time is proportional.
a) 12 km/h
b) Yes, proportional
Simplify: (–2.5) × (4/5) ÷ (–0.5)
4