Two equal ratios — the foundation of proportional reasoning
A Proportion Is Two Equal Ratios
A proportion is a statement that two ratios are equal.
It can be written as: a:b = c:d or a/b = c/d
Example
1:2 = 3:6 is a proportion because both ratios simplify to the same thing.
1/2 = 3/6 ✓ — both equal 0.5.
How to Check If It's a Proportion
Cross multiply. If the cross products are equal, the two ratios form a proportion.
Do 3:4 and 9:12 form a proportion?
Cross multiply: 3 × 12 = 36
Cross multiply: 4 × 9 = 36
36 = 36 ✓ → Yes, it's a proportion
Do 2:5 and 4:9 form a proportion?
Cross multiply: 2 × 9 = 18
Cross multiply: 5 × 4 = 20
18 ≠ 20 → No, not a proportion
Why Proportions Matter
Proportions let you solve for unknown values. If you know three of the four numbers, you can find the fourth. This is the basis for scaling recipes, converting units, reading maps, and solving countless real-world problems.
💡 Proportions vs equivalent ratios: They're the same concept. Equivalent ratios are pairs that share the same relationship. A proportion is the equation that says they're equal.
🎯 Practice Problems
1. Do 2:3 and 8:12 form a proportion?
A) Yes
B) No
2. Do 5:6 and 10:11 form a proportion?
A) Yes
B) No
3. Which of these is a proportion?
A) 1:3 = 2:5
B) 4:5 = 8:10
C) 3:7 = 6:15
D) 2:9 = 4:16
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🎯 Bonus Practice
1. If 3/5 = x/15, what is x?
A) 5
B) 3
C) 9
D) 45
2. Do 7:2 and 21:6 form a proportion?
A) Yes
B) No
3. What is a proportion?
A) Two ratios added together
B) A ratio greater than 1
C) Two equal ratios
D) A ratio with fractions
4. Do 1:4 and 3:12 form a proportion?
A) Yes
B) No
5. If a/b = c/d is a proportion, what must be true?