LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

RATION & PROPORTION - INTRODUCTION OF PROPORTION

**PROPORTION –
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**An equality of two ratios is called a proportion. Four non-zero quantities a, b, c, & d are said to be in proportion if a : b = c : d and we write a : b : : c : d (we write it as ‘a’ is to ‘b’ as ‘c’ is to ‘d’)
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**If, a : b : : c : d, then;
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**(i) a, b, c, d are known as first, second, third, and fourth term respectively.
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**(ii) d is called the fourth proportional to a, b, c.
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**(iii) a & d are called extremes, while b & c are called means.
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** Extremes Means
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** ------------ = -----------**

** Means Extremes
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** a c
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** ------- = -------**

** b d
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**An important property –
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**If a : b : : c : d, then the product of extremes is equal to the product of means.
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**Proof- a : b : : c : d
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** a c
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**=> ------ = ------**

** b d
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**=> ad = bc
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**So, product of extremes = product of means**

**Third Proportional -**

**If, a : b = b : c, then c is called the third proportional to a & b
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**Clearly, it is the fourth proportional to a, b, c.
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**Example) If, x : 10 : : 8 : 5, find the value of x
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**Ans.) Given, x : 6 : : 8 : 5
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**So, as per the rules –
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**=> x : 10 = 8 : 5
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** x 8
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**=> ------- = ------**

** 10 5
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** 8 X 10
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**=> x = ---------- = 16
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** 5
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**So, the desired value of ‘x’ is 16. (Ans.)**

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