Proportion Calculator

Solve proportions by finding the missing value in a:b = c:d relationships. Perfect for cross multiplication, recipe scaling, unit conversion, and real-world ratio problems.

Solve Proportion

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Enter 3 values and leave 1 blank to solve for the unknown

Understanding Proportions

What is a Proportion?

A proportion states that two ratios are equal. Written as a:b = c:d or a/b = c/d, it means the relationship between a and b is the same as between c and d. Cross multiplication (a×d = b×c) is the key to solving proportions.

Real-World Applications

Recipe Scaling
Adjust ingredients proportionally
Maps & Models
Scale conversions
Chemistry
Solution concentrations
Business
Price comparisons

Cross Multiplication Method

If a/b = c/d, then a×d = b×c

This fundamental property allows us to solve for any unknown value by rearranging the equation. It works because multiplying both sides by b×d maintains equality.

Common Proportion Types

  • Direct: As one increases, the other increases (speed vs distance)
  • Inverse: As one increases, the other decreases (workers vs time)
  • Compound: Multiple ratios combined (currency exchange chains)
  • Continued: a:b:c = x:y:z (multi-part comparisons)

Pro Tip: When setting up word problems, identify what stays constant (the ratio) and what changes. Write known values in the same positions: if comparing “part to whole”, keep parts in numerators and wholes in denominators consistently.

Quick Reference

Cross Multiply
a×d = b×c
Solve for a
a = (b×c)÷d
Solve for d
d = (b×c)÷a

Example Problems

Recipe Scaling
2 cups : 4 servings = ? : 10 servings
Answer: 5 cups
Map Scale
1 inch : 50 miles = 3.5 inches : ?
Answer: 175 miles
Currency
$100 : €85 = $250 : ?
Answer: €212.50

Problem Solving Tips

  • 1.Identify what's being compared
  • 2.Keep units consistent
  • 3.Set up ratios in same order
  • 4.Cross multiply to solve
  • 5.Check answer makes sense