**Proportional**

If two ratios are equal then they are
said to be in **proportion** or **proportional**. If a/b = c/d, it is
written as a:b::c:d and read as ‘a’ is to ‘b’ is as ‘c’ is to ‘d’. The first
term ‘a’ and the fourth term ‘d’ are called **extremes** and second term ‘b’ and third term ‘c’ are called **means**.

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If a:b = b:c = c:d i.e. a/b = b/c = c/d then
the terms a, b, c, d are said to be in **continued
proportion**.

If a/b = b/c then b^{2} = ac. Thus
three quantities are said to be in continued proportion if the product of
extremes is equal to the square of mean.

**Properties of proportion**

If a, b, c and d are four numbers then,

**1. ****Invertendo:**

This property is called as **invertendo**.

**2. ****Alternendo:**

This property is called as

**Alternendo**.

**3. ****Componendo:**

This property is called as **componendo**.

**4. ****Dividendo:**

This property is called as **dividendo**.

**5. ****Componendo and dividendo:**

This property is called **componendo and dividendo**.

**6. ****Convertendo or subtendo:**

This property is called **convertendo or subtendo**.

**7. ****Addendo:**

**addendo**.

*Some
problems on proportional and their solutions: *

*Some problems on proportional and their solutions:*

*Example 1: If 5, 10, 15 are in proportion,
find the fourth proportion.*

*Solution:** Let x be the fourth proportion. Then 5, 10, 15 and x are
in proportion.** *

*Example 2: If 2, x, 6 and 12 are in proportion,
find the value of x.*

*Solution:** Here, 2, x, 6 and 12 are in proportion.** *

*Example 3: 4, x and 9 are in continued
proportion, find the value of x.*

*Solution:** Here, 4, x, 9 are in continued proportion.** *

*Example 4: What number should be added to
each of the numbers 2, 4, 8 and 12 to make them proportional?*

*Solution:** Let the required number be a.** *

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*You can comment your
questions or problems regarding the proportional
here.*

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