When we talk of ratio
, it represents the relationship between two numbers or quantities.
Proportion is an extension of ratios
. A Proportion is a statement which shows that two ratios are equal. In other words, when the ratio
of two terms is equal to the ratio
of two other terms, then these four terms are said to be in proportion.
are all in proportion.
, then a, b, c, d are in proportion. a, b, c, d, are called the first, second, third and fourth proportionals respectively. The terms ‘a’ and ‘d’ are called the extremes, while ‘b’ and ’c’ are called the means.
Product of Extremes = Product of Means
(This can be seen by cross multiplication also)
If one of the four numbers in a proportion is unknown, we can find the unknown quantity by equating the cross products, i.e. Product of Extremes = Product of Means
Q. If x/90 =2/3, find x.
Using 'Product of Extremes = Product of Means'
x * 3 = 2* 90 = 180
=> x= 60.
Therefore x = 60
, then a, b, c are said to be in continued proportion and b is called the geometric mean or mean proportional between ‘a’ and ‘c’.
, then a, b, c, d, e are said to be in continued proportion. From here we can easily find out the value of a/d = (a/b)* ( b/c) * ( c/d).
Q. If a/b = 2/3; b/c = 4/5; c/d = 7/9, find a/d.
a/d = (a/b)*(b/c)*(c/d)=(2/3)*(4/5)*(7/9) = 56/135
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