Ratios
Write the ratio of water to flour in simplest fractional form for a recipe that uses 3/2 cup of water and 33 cups of flour. Then give its numeric value.
Ratio = water : flour = 32:323:3 As a fraction (water divided by flour): 323=32⋅13=12323=23⋅31=21 Numeric value = 1221 (or 0.5). So the simplified ratio is 1221 (water per flour).
Compute the unit rate: If someone walks 1/2 mile in 1/4 hour, how many miles per hour do they walk?
4=2 miles per hour.
Are the quantities proportional? For pairs (x, y) = (0.5, 7), (1, 14)
Yes
Find the slope of the line that passes through (0, 0) and (1, 3).
3
Express the ratio "Miles:Hours" for 20 miles in 4 hours as a fraction in simplest form and as a unit rate (miles per hour).
Ratio as fraction: 20/4=5 (so 20:4 simplifies to 5:1) Unit rate = 5 miles per hour.
A runner completes 6 kilometers in 24 minutes. What is the runner’s pace in minutes per kilometer?
4 minutes
If 4 pencils cost $1.20, how much do 10 pencils cost?
$3
Find the slope of the line through (−3, −6) and (3, 6)
2
A ratio table shows these pairs: Miles — 3, 6, 9; Hours — 1, ___, 3. Fill in the missing hours so each pair is equivalent ratios to 3 miles in 1 hour. Then write the equivalent ratios as fractions.
Base rate: 3 miles in 1 hour (unit rate 3 mph). For 6 miles: hours = 6/3=2 hours. For 9 miles: hours = 9/3=3 hours (given). Equivalent ratios as fractions: 3 miles : 1 hour = 3/1 6 miles : 2 hours = 6/2=3 (equivalently 6/2) 9 miles : 3 hours = 9/3=3
If a cyclist travels 9 miles in 0.5 hour, what is the speed in miles per hour?
18 miles
A map shows 2 inches = 50 miles. How many miles does 7 inches represent?
175 miles
Determine the slope of the line passing through (−2, 1) and (4, −11).
-2
A person jogs 2 1/2 miles in 10 1/2 hours. Find the person's speed in miles per hour as a fraction in simplest form and as a decimal rounded to two decimal places.
Convert to improper fractions: 2 1/2=5/2 miles 10 1/2=21/2 hours Speed = miles / hours = 5/2 / 21/2=5/2⋅2/21= 5/21 miles per hour. Decimal: 5/21≈0.238095...≈0.24 miles per hour (rounded to two decimals).
A 5-pound bag of apples costs $6.25. What is the cost per pound in dollars (rounded to cents)?
$1.25
A machine packages 15 toys in 3 minutes. How many toys in 8 minutes?
40 toys
Delivery driver: when he drives 30 miles uses 2 gallons; when 75 miles uses 5 gallons. Treat gallons as y and miles as x. Find slope (gallons per mile) and interpret.
Answer: 1/15. Each mile uses 1/15 gallon (about 0.0667 gal/mile).
You mix paint by combining 1 1/2 quarts of blue paint with 2 quarts of red paint to make 2 1/2 quarts of purple paint. (Assume the intended ratio in the prompt is consistent.) If the recipe scales proportionally, how much blue and how much red paint are used to make 14 quarts in total? Show your reasoning.
Blue - 6 qt
red - 8qt
Two cars travel at the same speed to different destinations. Car A's trip takes 15 minutes; Car B's trip takes 35 minutes. Car B travels 15 miles farther than Car A. How fast are the cars traveling? Give the answer as a fraction in simplest form (miles per minute) and convert to miles per hour.
45 miles per hour.
A car travels 150 miles on 5 gallons. At that same rate, how many gallons for 420 miles?
14 gallons
Calculate the slope between the points (2, 5) and (2, 9). Describe the type of line
Undefined, vertical line.