# Types of Proportions –Properties of Proportional

Based on the type of relationship between two or more quantities. The **proportion** can be Divided or classified into different types. There are 2 types of proportions.

**Types of proportions**

Based on the type of relationship between two or more quantities. The proportion can be Divided or classified into different types. There are 2 types of proportions.

- Inverse Proportion
- Direct Proportion

**Inverse proportion**

This type explains the indirect relationship between two quantities. In simple words, if one quantity decreases, the other quantity increases and vice-versa. In notation, an inverse proportion is written as

** y ****∝**** 1/x.**

**For example:**

If 15 workers can build a wall in 48 hours how many workers will be required to do the same work in 30 hours?

**Solution:**

In 48 hours wall was built by 15 workers

in 30 hours wall was built by x workers

if the time decrease, the number of workers m be an increase

number of workers and time have taken are inversely proportional

x_{1 }y_{1}=x y2

15×48=x X 30

15×48/30=x

24=x

in 30 hours wall was built by 24 workers.

**Direct Proportion**

This type explains the direct relationship between two quantities. In simple words, if one quantity decrease, or increases the other quantity also decreases or increases and vice-versa. The direct proportion is written as

**y ****∝**** x**

** For example:**

A motorist travels 275 km in 5 hours. how far can he travel in 9 hours at the same speed?

**solution:**

in 5 hours motorist travels 275 km

in 9 hours motorist travels x km

if time increases distance covered must be an increase

time and distance taken are directly proportional

km/h=km/h

275/5=x/9

275/5×9=x

55×9=x

495=x

Motorists can travel 495km in 9 hours.

**Properties of proportional**

Proportion equivalent relation between two **ratios**. The properties of proportion that is allowed by this relation:

- Addendo – If

a : b = c : d,

then

a + c : b + d

- Subtrahendo – If

a : b = c : d,

then value of each ratio is

a – c : b – d

**.**Dividendo – If

a : b = c : d, then

a – b : b = c – d : d

- Componendo – If a : b = c : d,

then

a + b : b = c + d : d

- Alternendo – If

a : b = c : d,

then

a : c = b: d

- Invertendo – If

a : b = c : d, then

b : a = d : c

- Componendo and dividendo – If

a : b = c : d, then

a + b : a – b = c + d : c – d

*Summary*

*Proportion is a mathematical comparison between two numbers.*

**Basic proportions are of two types: inverse proportions. And direct proportions.**

*We can apply the concepts of proportions to dietetics geography, comparing**quantities in physics, cooking, etc.*

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