Rate — Grade 7 Accelerated, what it means and where it is taught
A ratio of two different units, like miles per hour or dollars per pound.
Taught in Grade 7 Accelerated.
Where it is taught
What it rests on
Work through these first if this one does not settle.
- Ratio — A comparison of two quantities, like 3 cups flour to 2 cups water.
What uses it later
This idea is needed for:
- Unit rate — A rate with denominator 1 — how much for exactly one.
- Accumulation — The total built up by a rate acting over an interval.
- Constant speed — A rate that does not change, so distance and time stay proportional.
- Conversion factor — A rate used to change units, like 12 inches per foot.
Practise this idea
17 questions in the course bank use Rate, in Sampling, Inferences & Comparing Populations, Representing Other Algebraic Relationships, Reading Graphs & Estimation, Slope & Unit Rate, Lines of Best Fit, Operations with Scientific Notation. The first 8 are below; the rest are in those units.
Problem 1
A factory samples 80 items and finds 24 defective. Estimate the number of defective items in a batch of 1,500.
Worked answer
450
2480 = 0.30
0.30 × 1500 = 450
Problem 2
Six workers finish a job in 10 days. At the same rate, how many days would 15 workers take?
Worked answer
4
Total work: 6 × 10 = 60 worker-days
60 ÷ 15 = 4 days
Notice the product stays constant: xy = 60.
Problem 3
A line graph shows temperature rising from 12° to 20° over 4 hours. What is the rate of increase per hour?
Worked answer
2
20 - 12 = 8 degrees
8 ÷ 4 = 2 degrees per hour
Problem 4
A printer prints 1,260 pages in 18 minutes. Find the rate in pages per minute.
Worked answer
70
1260 ÷ 18 = 70
70 pages per minute
Problem 5
Runner A covers 9 km in 45 minutes; runner B covers 14 km in 80 minutes. Who is faster, in km per minute?
Worked answer
A
A: 9 ÷ 45 = 0.2 km/min
B: 14 ÷ 80 = 0.175 km/min
A is faster
Problem 6
For y = 2.5x + 8 where x is hours and y is dollars, what does 2.5 mean?
Worked answer
2.50 per hour
Dollars per hour
$2.50 for each extra hour
Problem 7
Light travels 3 × 108 m/s. How far does it travel in 2 × 103 seconds?
Worked answer
6 x 10^11
3 × 2 = 6
8 + 3 = 11
6 × 1011 metres
Problem 8
A recipe needs 34 cup per serving. How many cups for 14 servings?
Worked answer
10.5
34 × 14 = 424
= 10.5 cups