Proportion Proportion is a comparison of two or more quantities that are related in some way. It is expressed as a fraction, where the numerator represents...
Proportion
Proportion is a comparison of two or more quantities that are related in some way. It is expressed as a fraction, where the numerator represents the part of the whole, and the denominator represents the whole.
Properties of Proportion
Equality: If a/b = c/d, then a = b and c = d. This means that the two parts are equal in value.
Multiplication: If a/b = c/d, then a * c = b * d. This means that the product of the parts is equal in value.
Division: If a/b = c/d, then a/b = d/c. This means that the quotient of the parts is equal in value.
Addition and subtraction: Adding or subtracting the same amount from both numerator and denominator will result in the same value.
Composition: If a/b = c/d, and b/c = e/d, then a/b = (c + e)/d. This means that the product of the parts is equal when the two parts are added together.
Inverse proportion: If a/b = c/d, then b/a = d/c. This means that if we swap the roles of a and b, we get a reciprocal proportion.
Examples
If a farmer has 6 acres of land, and he plants 2 crops that cover 3 and 4 acres each, then the total area planted is 6 acres.
If a shirt costs 15, then the ratio of the shirt to pants is 2:1.
If a train travels 200 miles in 4 hours, then its speed is 50 miles per hour