Ratio|proportion

# Proportion

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An equality of two ratios is called proportion.

If four numbers a,b,c and d are in propor-tion, then we write

a : b : : c : d

Which is read as
a is to b as c is to d. Here a, b ,c and d are the 1st,
2nd ,3rd and 4th terms of the propor-tion.

1st and 4th terms ------------> Extremes

2nd and 3rd terms ------------> Means.

Thus, we observe that if four numbers are in propor-tion, then the

Product of extremes = Product of means

In other words, a : b = c : d if and only if

a x d = b x c

If ad ≠ bc , then a, b, c and d are not in propor-tion.

Examples :
1) Find which of the following are in propor-tion?
a) 33, 44, 66, 88
Solution :
The four numbers are 33,44,66,88.
If Product of extremes = product of means then the numbers are in propor-tion.
∴ Product of extremes = 33 x 88 = 2904
And Product of means = 44 x 66 = 2904
So, from the above its clear that Product of extremes = product of means
∴ 33,44,66 and 88 are in propor-tion.
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b) 36, 49, 6, 7
Solution :
The four numbers are 36, 49, 6, 7.
If Product of extremes = product of means then the numbers are in propor-tion.
∴ Product of extremes = 36 x 7 = 252
And Product of means = 49 x 6 = 294
So, from the above its clear that Product of extremes ≠ product of means
∴ 33,44,66 and 88 are not in propor-tion.
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2) If 3,a, 12 and 20 are in propor-tion then find the value of a.
Solution :
As 3, a , 12 and 20 are in propor-tion,
⇒ Product of extremes = product of means
⇒ 3 x 20 = a x 12
⇒ 60 = 12a
⇒ a = 60/12
∴ a = 5.

Ratio and Propor-tions
Ratio in the simplest form
Comparison of ratios
Equivalent ratios
Proportion
Continued-Propor-tions

To number system

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