# Proportion

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

• Ratio in the simplest form

• Comparison of ratios

• Equivalent ratios

• Proportion

• Continued-Propor-tions

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