Different units
A rate links two measured quantities, like distance and time, or cost and weight.
Why it works
miles per hour, price per kilo.
Ratios · Rates & unit rates · 2.1
What is a rate?
A rate is a ratio that compares two quantities with different units — miles per hour, dollars per pound. 120 miles in 3 hours is the rate 120 miles : 3 hours.
See it work.
Double number line
The two quantities move together.
40 for every 1 — and it stays in step as you scale up.
Watch the method
What is a rate?
120 miles in 3 hours is a rate.
1
Divide to get “per 1”
Divide the first quantity by the second to find the amount per 1.
2
The unit rate
This is the rate for a single unit.
Practice until it feels automatic.
Your turn
Work it out.
Type a number, e.g. 40.
streak 0
best 0
… =
The idea underneath.
From easy to tricky.
24 units in 3 — what is the unit rate (per 1)?
1
Divide to get “per 1”
Divide the first quantity by the second to find the amount per 1. 24 ÷ 3
2
The unit rate
This is the rate for a single unit. = 8
24 units in 4 — what is the unit rate (per 1)?
1
Divide to get “per 1”
Divide the first quantity by the second to find the amount per 1. 24 ÷ 4
2
The unit rate
This is the rate for a single unit. = 6
40 units in 8 — what is the unit rate (per 1)?
1
Divide to get “per 1”
Divide the first quantity by the second to find the amount per 1. 40 ÷ 8
2
The unit rate
This is the rate for a single unit. = 5
Where students slip.
Trap
Dropping the units.
Fix
A rate keeps track of both units.
Trap
Confusing the order.
Fix
Miles per hour is miles ÷ hours.
Test yourself.
The Test
12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.
0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so
t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).Core
Core (4)
C1
24 units in 6 — what is the unit rate (per 1)?
Need a hint?
- Identify the two quantities and units.
- Set them up as a ratio.
C2
8 units in 4 — what is the unit rate (per 1)?
Need a hint?
- Identify the two quantities and units.
- Set them up as a ratio.
C3
49 units in 7 — what is the unit rate (per 1)?
Need a hint?
- Identify the two quantities and units.
- Set them up as a ratio.
C4
72 units in 8 — what is the unit rate (per 1)?
Need a hint?
- Identify the two quantities and units.
- Set them up as a ratio.
Apply
Apply (4)
A1
10 units in 5 — what is the unit rate (per 1)?
Need a hint?
- Identify the two quantities and units.
- Set them up as a ratio.
A2
72 units in 8 — what is the unit rate (per 1)?
Need a hint?
- Identify the two quantities and units.
- Set them up as a ratio.
A3
40 units in 8 — what is the unit rate (per 1)?
Need a hint?
- Identify the two quantities and units.
- Set them up as a ratio.
A4
56 units in 8 — what is the unit rate (per 1)?
Need a hint?
- Identify the two quantities and units.
- Set them up as a ratio.
Extension
Extension (4)
E1
6 units in 2 — what is the unit rate (per 1)?
Need a hint?
- Identify the two quantities and units.
- Set them up as a ratio.
E2
55 units in 5 — what is the unit rate (per 1)?
Need a hint?
- Identify the two quantities and units.
- Set them up as a ratio.
E3
45 units in 5 — what is the unit rate (per 1)?
Need a hint?
- Identify the two quantities and units.
- Set them up as a ratio.
E4
20 units in 4 — what is the unit rate (per 1)?
Need a hint?
- Identify the two quantities and units.
- Set them up as a ratio.