Ratio
Introduction
In our surroundings, many times we compare two things of the same type.
Example :
Nishika and Mihir collected some fruits from the big basket.
- From the information given in the above table, we can find how many more apples Nishika has collected than Mihir.
Method 1: can use subtraction.
22 – 11 = 11
Nishika has collected 11 apples more than Mihir.
Method 2: We can use division.
So, Nishika has collected twice as many apples as Mihir.
Here we have actually found a ratio of the apples collected by Nishika to the apples collected by Mihir.
- So,
Number of oranges collected by Nishika / Number of oranges collected by Mihir=17 / 34=1 / 2
So, Nishika has collected half as many apples as Mihir.
What is the ratio?
- Comparing two things by division is called a Ratio.
- Ratio is a comparison of two values or quantities of the same type in the terms of ‘how many times’.
- So, to find the ratio between two objects, both the objects should have the same unit.
How to read and write the ratio?
- Ratio of the two quantities is written by using the symbol':'.
- Ratio can be read as follows:
Example :
The ratio of pens to the books is written as 7:10
It is read as: ‘7 is to 10’
The fraction can be written in the form of division as 7:10 =
Here, pens are mentioned first. So,
The ratio of books to the pens is written as 10:7
It is read as: ‘10 is to 7’
The fraction can be written in the form of division as 10:7 =
Here, pens are mentioned first. So,
‘Part to part ratio’ and ‘part to whole ratio’
Example :
Number of black and white cows = 5
Number of brown cows = 2
Total cows = 7
How to find the ratio from part to part?
The ratio of black and white cows to brown cows =
The ratio of brown cows to black and white cows =
How to find the ratio from part to whole?
The ratio of black and white cows to all cows =
The ratio of brown cows to all cows =
Note: To write the ratio keep the following points in mind.
- Write the terms in the given manner. There should be significant order of terms.
- Both of the objects or quantities should have the same units.
- Write the correct numbers.
What are the equal ratios?
- Equivalent fractions of the given ratio have an equal ratio.
- When we multiply or divide the first term and second term /numerator and denominator of the ratio by the same number, we get equal ratios.
- To find an equal ratio, we can simplify the fraction of the given ratio.
Example :
- Above two ratios represent the same colour parts.
- If we multiply the numerator and denominator of the first ratio by 4, we get
1 × 4 / 4 × 4=4 / 16→ fraction of the second ratio - If we find the simple form of the second ratio, we get the first ratio.
- So,
1 / 4=4 / 16
- 1 : 4 = 4 : 16 → Equal ratios
Some real life examples where the concept of ratio is used.
- Cooking - To decide the quantities of the ingredients.
- Architecture – To decide the strong structure of the buildings.
- Health – To decide the quantity of the medicine according to the age of the patient.
- In Share market, Electronics and many more industries.
Did you know?