Proportion Calculator
Solve proportions using cross multiplication and find missing values in ratios
Calculate Proportions
Solution
Example Calculation
Recipe Scaling Example
Problem: A recipe for 4 people needs 2 cups of flour. How much flour for 6 people?
Set up proportion: 4 : 2 = 6 : x
Cross multiply: 4 × x = 2 × 6
Solve: 4x = 12, so x = 3
Answer: You need 3 cups of flour for 6 people
Map Scale Example
Problem: On a map, 2 cm represents 5 km. What distance does 7 cm represent?
Proportion: 2 : 5 = 7 : x
Solution: x = (5 × 7) ÷ 2 = 17.5 km
Types of Proportions
Direct Proportion
As one value increases, the other increases proportionally
Example: Speed and distance
Inverse Proportion
As one value increases, the other decreases proportionally
Example: Speed and time
Cross Proportion
Used to solve for unknown values in ratios
Example: Recipe scaling
Proportion Tips
Cross multiplication: a/b = c/d means a×d = b×c
Always check units are consistent
Set up ratios in the same order
Verify answers make logical sense
Understanding Proportions
What is a Proportion?
A proportion is a mathematical relationship between two ratios that are equal. It states that two ratios are equivalent, often written as a : b = c : d or a/b = c/d.
Cross Multiplication Method
To solve proportions, we use cross multiplication. If a/b = c/d, then a × d = b × c. This allows us to find any missing value when we know the other three values.
Real-World Applications
- •Recipe scaling and cooking
- •Map scales and distances
- •Currency conversion
- •Unit conversions
Solving Proportions
a : b = c : d
a × d = b × c
Step-by-Step Process:
- 1. Identify the known and unknown values
- 2. Set up the proportion equation
- 3. Cross multiply to eliminate fractions
- 4. Solve for the unknown variable
- 5. Check your answer by substitution
Remember: The units in corresponding positions must be the same for proportions to be valid.