Part-to-part, part-to-whole
A ratio can compare one part to another part, or a part to the whole. Keep the quantities in the order stated.
Why it works
3 cats : 2 dogs, or 3 cats out of 5 pets.
Ratios · Ratios · 1.1
What is a ratio?
A ratio compares two quantities. 3 cats to 2 dogs is the ratio 3:2 (part-to-part). 3 cats out of 5 pets is 3:5 (part-to-whole). Order matters — 3:2 is not 2:3.
See it work.
Equivalent ratios
Scale both parts together.
Every column is the same ratio as 2:3.
| first | 2 | 4 | 6 | 8 | 10 |
| second | 3 | 6 | 9 | 12 | 15 |
| base | ×2 | ×3 | ×4 | ×5 |
Watch the method
What is a ratio?
3 cats to 2 dogs is the ratio 3:2.
1
Find the common factor
3 divides both 6 and 9.
2
Divide both parts
Divide each part by the common factor.
Practice until it feels automatic.
Your turn
Work it out.
Type lowest terms, e.g. 3:4.
streak 0
best 0
… →
The idea underneath.
From easy to tricky.
Simplify the ratio 8:24 to lowest terms.
1
Find the common factor
8 divides both 8 and 24. gcd(8,24) = 8
2
Divide both parts
Divide each part by the common factor. 8:24 = 1:3
Simplify the ratio 6:18 to lowest terms.
1
Find the common factor
6 divides both 6 and 18. gcd(6,18) = 6
2
Divide both parts
Divide each part by the common factor. 6:18 = 1:3
Simplify the ratio 18:18 to lowest terms.
1
Find the common factor
18 divides both 18 and 18. gcd(18,18) = 18
2
Divide both parts
Divide each part by the common factor. 18:18 = 1:1
Where students slip.
Trap
Reversing the order.
Fix
3:2 means 3 of the first to 2 of the second.
Trap
Mixing part-to-part with part-to-whole.
Fix
Decide whether you compare parts or a part to the whole.
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
Simplify the ratio 20:10 to lowest terms.
Need a hint?
- Compare the two quantities in order.
- Simplify like a fraction.
C2
Simplify the ratio 12:36 to lowest terms.
Need a hint?
- Compare the two quantities in order.
- Simplify like a fraction.
C3
Simplify the ratio 4:8 to lowest terms.
Need a hint?
- Compare the two quantities in order.
- Simplify like a fraction.
C4
Simplify the ratio 4:12 to lowest terms.
Need a hint?
- Compare the two quantities in order.
- Simplify like a fraction.
Apply
Apply (4)
A1
Simplify the ratio 10:10 to lowest terms.
Need a hint?
- Compare the two quantities in order.
- Simplify like a fraction.
A2
Simplify the ratio 8:8 to lowest terms.
Need a hint?
- Compare the two quantities in order.
- Simplify like a fraction.
A3
Simplify the ratio 25:20 to lowest terms.
Need a hint?
- Compare the two quantities in order.
- Simplify like a fraction.
A4
Simplify the ratio 30:30 to lowest terms.
Need a hint?
- Compare the two quantities in order.
- Simplify like a fraction.
Extension
Extension (4)
E1
Simplify the ratio 10:25 to lowest terms.
Need a hint?
- Compare the two quantities in order.
- Simplify like a fraction.
E2
Simplify the ratio 25:25 to lowest terms.
Need a hint?
- Compare the two quantities in order.
- Simplify like a fraction.
E3
Simplify the ratio 25:30 to lowest terms.
Need a hint?
- Compare the two quantities in order.
- Simplify like a fraction.
E4
Simplify the ratio 4:20 to lowest terms.
Need a hint?
- Compare the two quantities in order.
- Simplify like a fraction.