Ratio and proportion handwritten notes

Ratio and proportion 

Ratio and proportion handwritten notes ⬇️

 RATIO

In our day-to-day life, we compare one quantity with another quantity of the same kind by using the ‘method of subtraction’ and ‘method of division’.
Example: The height of Seema is 1 m 67 cm and that of Reema is 1 m 62 cm. The difference in their heights is:
167 cm – 162 cm = 5 cm
Thus, we say Seema is 5 cm taller than Reema.
Similarly, suppose the weight of Seema is 60 kg and the weight of Reema is 50 kg. We can compare their weights by division, i.e.,
Weight of SeemaWeight of Reema=50 kg60 kg
=65
So, the weight of Seema is 65 times the weight of Reema.
When we compare two similar quantities by division, the comparison is called the ‘ratio’. It is denoted by ‘:’ and read as ‘is to’.
Example: 58 = 5 : 8 (read as 5 is to 8).
As shown in the above example a ratio is like a fraction or comparison of two numbers, where a numerator and a denominator is separated by a colon (:). The first term or the quantity (5), called antecedent means ‘that precedes’ and the second term, called consequent means ‘that follows’.

Properties of Ratio

When we compare two quantities, the following points must be taken care of:

1. A ratio is usually expressed in its simplest form.
   Example: 
   1236=13=1:3
2. Both the quantities should be in the same unit. So, ratio is a number with no unit involved in it.
   Example: 200 g : 2 kg
   = 200 g : 2000 g
   2002000=110=1:10
3. The order of the quantities of a ratio is very important.
   Example: 5 : 6 is different from 6 : 5.
   They are not equal.
   5 : 6 ≠ 6 : 5

PROPORTION
A proportion is an equation with a ratio on each side. It is a statement that two ratios are equal. When two ratios are equal then such type of equality of ratios is called proportion and their terms are said to be in proportion.

Example: If the cost of 3 pens is Rs. 21, and that of 6 pens is Rs. 42, then the ratio of pens is 3 : 6, and the ratio of their costs is 21 : 42. Thus, 3 : 6 = 21 : 42. Therefore, the terms 3, 6, 21, and 42 are in proportion.
Generally, the four terms, a, b, c, and d are in proportion if a : b = c : d.
Thus, a : b : : c : d means  a/b = c/d or ad = ad = bc
Conversely, if ad = be, then a/b = c/d  or a : b : : c : d
Here, a is the first term, b is the second term, c is the third term, and d is the fourth term. The first and the fourth terms are called extreme terms or extremes and the second and third terms are called middle terms or means.

Continued proportion
In a proportion, if the second and third terms are equal then the proportion is called continued proportion.
Example: If 2 : 4 : : 4 : 8, then we say that 2, 4, 8 are in continued proportion.