Ratios and Proportions are fundamental concepts in mathematics and have various real-world applications.
- Ratios compare two quantities of the same kind
- Proportions compare two ratios or fractions
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Ratios
Ratio a:b is a fraction a/b.
A Ratio has no unit.
In order to find the ratio between two quantities of the same kind, you must first convert both the quantities (for example Kg and g) in the same unit (convert to Kg or g)
- When you multiply or divide each term of the ratio by the same non-zero number, the ratio remains the same.
The ratio a:b is said to be in the simplest form if H.C.F of ‘a’ and ‘b’ is 1.
Since ratios are fractions, ratios can be compared similar to fractions.
Proportions
A Proportion is a equation that states if two ratios (or fractions) are equal or not.
If a, b, c, d are in proportion then:
- a:b = c:d (we can also write this as a:b::c:d where the symbol “::” stands for ‘is as’)
- a/b = c/d
- ad = bc
In a proportion, the first and the fourth terms are called the extremes. The second and third terms are known as the means.
Product of means = Product of extremes