Ratios · Rates & unit rates · 2.4

Speed & rate.

Constant-rate problems use the unit rate. Speed = distance ÷ time; price = cost ÷ amount. Once you have the unit rate, you can scale it to any amount. 240 km in 4 h = 60 km/h.

01 / THE IDEA

See it work.

Watch the method

Speed & rate problems

240 km ÷ 4 h = 60 km/h.

1 / 2
240:4240 : 4
1

Divide to get “per 1”

Divide the first quantity by the second to find the amount per 1.

240÷4240 \div 4
2

The unit rate

This is the rate for a single unit.

=60= 60
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type a number, e.g. 40.

streak 0
best 0
… =
— / WHY IT WORKS

The idea underneath.

Rate as a tool

The unit rate lets you predict any amount: multiply the rate by the quantity.

Why it works

60 km/h → 180 km in 3 h.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

24 units in 2 — 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 ÷ 2

2

The unit rate

This is the rate for a single unit. = 12

EX 2medium

16 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. 16 ÷ 8

2

The unit rate

This is the rate for a single unit. = 2

EX 3hard

22 units in 2 — 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. 22 ÷ 2

2

The unit rate

This is the rate for a single unit. = 11

04 / COMMON TRAPS

Where students slip.

Trap

Not finding the unit rate first.

Fix

Get the per-1 rate, then scale.

Trap

Mixing up the quantities.

Fix

Speed is distance ÷ time.

05 / QUIZ

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

32 units in 8 — what is the unit rate (per 1)?

Need a hint?
  • Compute the unit rate.
  • Scale it to the amount you need.
C2

8 units in 4 — what is the unit rate (per 1)?

Need a hint?
  • Compute the unit rate.
  • Scale it to the amount you need.
C3

9 units in 3 — what is the unit rate (per 1)?

Need a hint?
  • Compute the unit rate.
  • Scale it to the amount you need.
C4

42 units in 7 — what is the unit rate (per 1)?

Need a hint?
  • Compute the unit rate.
  • Scale it to the amount you need.
Apply

Apply (4)

A1

60 units in 6 — what is the unit rate (per 1)?

Need a hint?
  • Compute the unit rate.
  • Scale it to the amount you need.
A2

80 units in 8 — what is the unit rate (per 1)?

Need a hint?
  • Compute the unit rate.
  • Scale it to the amount you need.
A3

10 units in 2 — what is the unit rate (per 1)?

Need a hint?
  • Compute the unit rate.
  • Scale it to the amount you need.
A4

8 units in 4 — what is the unit rate (per 1)?

Need a hint?
  • Compute the unit rate.
  • Scale it to the amount you need.
Extension

Extension (4)

E1

42 units in 7 — what is the unit rate (per 1)?

Need a hint?
  • Compute the unit rate.
  • Scale it to the amount you need.
E2

35 units in 5 — what is the unit rate (per 1)?

Need a hint?
  • Compute the unit rate.
  • Scale it to the amount you need.
E3

24 units in 2 — what is the unit rate (per 1)?

Need a hint?
  • Compute the unit rate.
  • Scale it to the amount you need.
E4

12 units in 3 — what is the unit rate (per 1)?

Need a hint?
  • Compute the unit rate.
  • Scale it to the amount you need.