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Proportion Calculator

Solve a:b = c:d with cross-multiplication, find missing values, simplify ratios, set precision, and check proportionality.

Solve a : b = c : d

Enter values (leave one blank for the unknown)
Settings

Your Results

Solved Values
a = 3, b = 4, c = 6, d = 8
Proportional? (direct)
Yes
Simplified Ratios
Left: 3 : 4
Right: 3 : 4

Categories

Direct Proportion

a increases → b increases (a/b = constant)

Inverse Proportion

a increases → b decreases (a·b = constant)

How to Calculate Proportion

Cross Multiplication

a : b = c : d ⇔ a/b = c/d
Cross multiply: a · d = b · c
If d unknown: d = (b · c) / a

Sources: Wikipedia — Proportion; Britannica — Ratio and Proportion.

Calculation Steps:

  1. 1
    Write as a/b = c/d
    Check denominators are non‑zero
  2. 2
    Cross multiply
    a·d = b·c
  3. 3
    Solve and simplify
    Isolate the unknown; reduce ratios by gcd

Important Considerations

⚠️ Domain Note

Keep denominators non‑zero, maintain consistent units, and reduce ratios to compare correctly.

🧮 Reduce Ratios

Use gcd to simplify before comparing

📐 Unit Consistency

Convert to consistent units before forming ratios

➗ Non‑zero Denominators

b and d must be non‑zero in a/b and c/d

🎯 Rounding

Set precision appropriately; heavy rounding may break equality

Example Cases

Case 1

3 : 4 = 6 : d → d = (4·6)/3 = 8

Case 2

a : 5 = 12 : 20 → a = (5·12)/20 = 3

Frequently Asked Questions

What is a proportion?
A proportion states that two ratios are equal, e.g., a:b = c:d or a/b = c/d. You can solve the unknown by cross-multiplication.
How do you solve for x in a proportion?
Use cross-multiplication: a:b = c:d implies a·d = b·c. If x is missing, rearrange accordingly (e.g., x = b·c/d).
How to use proportions in percent word problems?
Set up part/whole = percent/100. For example, 30 is what percent of 120? 30/120 = p/100 → p = 25%.
Map scale conversion with proportions (long-tail: map scale 1:50,000)?
Use distance_on_map : distance_in_real = 1 : scale. For 3 cm on map at 1:50,000, real = 3 × 50,000 cm = 1.5 km.
Similar triangles — find a missing side using proportions?
Corresponding sides are proportional: a1/a2 = b1/b2 = c1/c2. Cross multiply to solve the unknown side length.

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