Proportion Calculator

Solve proportions a/b = c/d using cross multiplication. Leave one field empty to solve for the missing value.

Enter Proportion Values

Leave exactly one field empty to solve for the unknown value.

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Result

Missing Value (c)
15
Proportion 3/4 = 15/20
Left Ratio (a/b) 3/4 = 0.75
Right Ratio (c/d) 15/20 = 0.75
Cross Products a x d = b x c => 60 = 60
Verification Both ratios equal 0.75

Step-by-Step Solution

a/b = c/d => a x d = b x c

Understanding Proportions

A proportion is an equation stating that two ratios are equal. Written as a/b = c/d, it means that the relationship between a and b is the same as the relationship between c and d. Proportions are fundamental in mathematics and have wide-ranging applications in science, engineering, cooking, map reading, and everyday problem-solving.

Cross Multiplication Method

The most common method for solving proportions is cross multiplication. Given a/b = c/d, we multiply diagonally: a x d = b x c. This gives us a simple equation that can be solved for any one unknown variable when the other three are known.

Solving for a

When a is unknown, multiply b and c, then divide by d.

a = (b x c) / d

Solving for b

When b is unknown, multiply a and d, then divide by c.

b = (a x d) / c

Solving for c

When c is unknown, multiply a and d, then divide by b.

c = (a x d) / b

Solving for d

When d is unknown, multiply b and c, then divide by a.

d = (b x c) / a

Types of Proportions

Direct Proportion

Two quantities are directly proportional if they increase or decrease together at the same rate. If y = kx (where k is a constant), then y is directly proportional to x. Example: distance traveled is directly proportional to time when speed is constant.

Inverse Proportion

Two quantities are inversely proportional if one increases as the other decreases. If y = k/x, then y is inversely proportional to x. Example: the time to complete a task is inversely proportional to the number of workers.

Real-World Applications

  • Cooking: Scaling recipes up or down while maintaining the same ratios of ingredients.
  • Maps and models: Scale factors relate distances on a map to actual distances.
  • Medicine: Calculating drug dosages based on body weight.
  • Finance: Exchange rates, interest calculations, and unit pricing.
  • Science: Concentration dilutions, chemical stoichiometry, and unit conversions.
  • Photography: Maintaining aspect ratios when resizing images.

Tips for Solving Proportions

  • Make sure the units on each side match (e.g., miles/hour = miles/hour).
  • Cross multiplication only works when neither denominator is zero.
  • Always verify your answer by substituting back into the original proportion.
  • Simplify ratios before solving when possible to make calculations easier.