Ratio and Proportion Formulas & Notes:

In everyday life, we always compare something of the same type. The ratio is also a mode of such comparisons. In this section, we will read ratio and proportion notes. Just an example you brought a bicycle for Rs 2000 and one of your friend brought the same bicycle in another shop for Rs. 1500. Now you compare the price as you had been thug by the shopkeeper by an amount of Rs.500.

This amount of 500 came by taking the difference between the price of same quantity. This is the one way of comparison, but the method of taking difference is not good in case when we compare a much smaller amount to much higher amount. Such as we compare the price of a Tata Nano car to Lamborghini car. Read further in ratio and proportion notes.

For this, the most accurate system was given as ratio which is comparison by division which is termed as Ratio.

Ratio:

When two quantities of same units are compared by division, this method of comparison is called ratio. It is said in this mode of comparison that one quantity is how many times the other.

• The symbol for expression of ratio is “ : ”
• For comparison by ratio, the two quantities must be in the same unit. If they are not, they should be expressed in the same unit.
• we can get equivalent ratios by multiplying or dividing the numerator and denominator by the same number.
• Ratio and proportion notes will provide you with the complete guide of chapter of class 6.

Examples of ratio:

• Length of a room is 50 m and its breadth is 40 m. So, the ratio of length of the room to the breadth of the room = \(\frac{50}{40}\) = \(\frac{5}{4}\) = 5 : 4.
• There are 32 girls and 20 boys going for a picnic. Ratio of the number of girls to the number of boys = \(\frac{32}{20}\) = \(\frac{8}{5}\) = 8 : 5.
• Whereas that of the breadth of a table to the length of the table is 2 : 3.

Proportion:

If two ratios are equal, we say that they are in proportion and use the symbol ‘::’ or ‘=’ to equate the two ratios. This equation of ratio is said to be proportion.

If two ratios are not equal, then we say that they are not in proportion. Also take a look at examples given in ratio and proportion notes.

For representation of proportion: we can say 2, 5, 14 and 35 are in proportion which is written as 2 : 5:: 14 : 35 and is read as 2 is to 5 as 14 is to 35 or it is written as 2 : 5 = 14 : 35.

Terms related to proportion:

• Extreme terms: In the statement of proportion which contains 4 terms, in that we denote 1^st and 4^th term as extreme terms.
  Example: In proportion 2 : 5:: 14 : 35, 2 and 35 are extreme terms.
• Middle Terms: In the statement of proportion which contains 4 terms, in that we denote 2^nd and 3^rd term as middle terms.
  Example: In proportion 2 : 5 :: 14 : 35, 5 and 14 are middle terms.

Now read the other section of ratio and proportion notes i.e. unitary method.

Unitary method:

The method in which first we find the value of one unit and then the value of required number of units is known as Unitary Method.

• Suppose the cost of 5 cans is Rs. 175. To find the cost of 4 cans, using the unitary method, we first find the cost of 1 can. It is Rs.175/5 or Rs.35. From this, we find the price of 4 cans as 35 × 4 or Rs.140.

Examples from ratio and proportion notes:

1. There are 40 persons working in an office. If the number of females is 15 and the remaining are males, find the ratio of the number of females to number of males and the number of males to number of females.

Solution:
Number of females = 15

Total number of workers = 40

Number of males = 40 – 15 = 25

Therefore, the ratio of number of females to the number of males
= 15 : 25 = 3 : 5

And that of number of males to the number of females
= 25 : 15 = 4 : 5.

2. Give two equivalent ratios of 12 : 4.
   Solution:
   Ratio 12:4 = \(\frac{12x2}{4x2}\) = \(\frac{24}{8}\)
   Therefore, 24 : 8 is an equivalent ratio of 12 : 4
   similarly, \(\frac{12/4}{4/4}\) = \(\frac{3}{1}\) = 3 : 1
   3 : 1 is also an equivalent of 12 : 4.

Learn and revise ratio and proportion notes to score better in examinations.