Ratio
The ratio of two quantities in the same unit is the fraction a/b and is written as a:b
In the ratio a : b, we call a as the first term or antecedent and b, the second term or consequent.
Important : If you multiply or divide each term of a ratio with the same non zero number then the ratio does not change.
Proportion
The equality of two ratios is called proportion.
If a:b = c:d then a:b::c:d and we say that a, b, c, d are in proportion.
In this case a and d are called the extremes and b and c are called mean terms
Important : Product of Extremes = Product of Means i.e. (a x d) = (b x c)
Fourth Proportional
In a:b::c:d, d is called fourth proportional to a, b, c.
Third Proportional
In a:b::c:d, c is called third proportional to a and b.
Mean Proportional
Mean Proportional between a and b is √ab
Compounded Ratios
The compounded ratio of the ratios (a:b), (c:d), (e:f) is (ace:bdf)
Duplicate Ratios
Duplicate ratio of (a : b) is (a2 : b2).
Sub-duplicate ratio of (a : b) is (√a : √b).
Triplicate ratio of (a : b) is (a3 : b3).
Sub-triplicate ratio of (a : b) is (a1/3 : b1/3).
If a/b = c/d then (a + b)/(a - b) = (c + d)/(c - d) [By componendo and dividendo]
Variations
We say that x is directly proportional to y, if x = ky for some constant k and then x
y
We say that x is inversely proportional to y, if xy = k for some constant k and then x 1/y
Click here for Online Test on Ratio and Proportion
The ratio of two quantities in the same unit is the fraction a/b and is written as a:b
In the ratio a : b, we call a as the first term or antecedent and b, the second term or consequent.
Important : If you multiply or divide each term of a ratio with the same non zero number then the ratio does not change.
Proportion
The equality of two ratios is called proportion.
If a:b = c:d then a:b::c:d and we say that a, b, c, d are in proportion.
In this case a and d are called the extremes and b and c are called mean terms
Important : Product of Extremes = Product of Means i.e. (a x d) = (b x c)
Fourth Proportional
In a:b::c:d, d is called fourth proportional to a, b, c.
Third Proportional
In a:b::c:d, c is called third proportional to a and b.
Mean Proportional
Mean Proportional between a and b is √ab
Compounded Ratios
The compounded ratio of the ratios (a:b), (c:d), (e:f) is (ace:bdf)
Duplicate Ratios
Duplicate ratio of (a : b) is (a2 : b2).
Sub-duplicate ratio of (a : b) is (√a : √b).
Triplicate ratio of (a : b) is (a3 : b3).
Sub-triplicate ratio of (a : b) is (a1/3 : b1/3).
If a/b = c/d then (a + b)/(a - b) = (c + d)/(c - d) [By componendo and dividendo]
Variations
We say that x is directly proportional to y, if x = ky for some constant k and then x
yWe say that x is inversely proportional to y, if xy = k for some constant k and then x
1/yClick here for Online Test on Ratio and Proportion
