Ratio and Proportion, Agrawal
Ratio and Proportion, Agrawal
Ratio and Proportion, Agrawal
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RATIO
Ratio:- Ratio is a comparison of two or more quantities of the same kind
by division (they must be in same units too).
i.e. a/b is called ratio of a to b. it can be written as a:b (read as a is to b or a
ratio b). a and b are called the terms of the ratio, a is called first term or
antecedent and b is called second term or consequent.
Remarks:
Both terms of ratio can be multiplied or divided by same (non-zero)
number.
Usually a ratio is expressed in the lowest term (or simplest form).
Ratio exists only between quantities of the same kind.
Quantities to be compared (by division) must be in the same units.
The order of the terms in ratio is important.
To compare to ratios, convert them into equivalent like fractions.
If a quantity is increased in the ratio a:b then new quantity = b/a times of
the original quantity.
o The fraction by which the original quantity is multiplied to get a
new quantity is called the multiplying ratio (factor).
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Some Techniques:
1. If there are three quantities which are expressed into two ratios, e.g. let A,
B & C are three quantities such that A:B = a:b and B:C = c:d then
Combined Ratio of all the three quantities will be ac:bc:bd.
A
:
B
:
C
a
:
b
ac
bc
bd
Note: Common quantity in the given two ratios should be placed between
the other two quantities. For this necessary adjustment should be done in the
ratio/s.
2. Divide the given Quantity / Amount in to given Ratio.
Let A is to be divide in the ratio a:b:c,
Then,
First part
= (a*A)/(a+b+c)
Second part = (b*A)/(a+b+c)
Third part = (c*A)/(a+b+c)
Alternatively, this can also be done in the following manner:
Let the three parts are ax, bx & cx respectively
Then,
ax + bx+ cx = A
x (a + b + c) = A
x = A / (a + b + c)
after finding the value of x calculate each part by multiplying the value of
x with a, b & c respectively.
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PROPORTION
Proportion: An equality of two ratios is called a Proportion.
Four quantities are said to be in proportion if a : b = c : d (also written as
a:b :: c:d).
a / b = c / d ad = bc
a, b, c, d are called the terms of the proportion
First & fourth terms are called extremes.
Second & third terms are called means (or middle terms).
Product of extremes = Product of means. (Cross Product Rule)
b2 = ac
b = (ac)1/2
If a ratio is equal to the reciprocal of the other, then either of them is in
inverse (reciprocal) proportion of the other. e.g. 3/4 is in inverse
proportion of 4/3 and vice versa.
Note: In a ratio both quantities must be of the same kind while in the
proportion all the four quantities need not be of the same type. The first
two quantities should be of the same kind and last two quantities should
be of the same kind.
Properties of proportion:
1.
2.
3.
4.
5.
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