Basics of Ratio and Proportions

1. RATIO &
PROPORTION
GRADE 7

2. What is Ratio
Definition :
The relation between two quantities which shows how
much bigger or smaller one quantity is than another.

3. Lets take an example….
A boy asked his father , how much time do you spent on your work
Father replied – “ I spent ONE THIRD of my whole day on work”
Total Time Spent On Work : 8 hours
Hours in a day : 24hours
Ratio = 8/24
= 1/3 or 1:3
in its lowest form or simplified form.

4. Points to remember
◦Ratio is a PURE NUMBER
As in the example
8hours to 24 hours = 8/24 = 1/3
Or 1:3 (pronounced as 1 is to 3)
The quantities in comparison have units,
But ratio does not have a unit as it is a pure number.

5. POINTS TO REMEMBER
Ratio should always be in its LOWEST FORM.
For example
There are 15kg of apples and 20 kg of Oranges in a Basket.
Find the ratio of apples to oranges.
15/20 = ¾ or 3 : 4
(Lowest or simplified form)
The Ratio of Apples to Oranges in the Basket is 3:4.

6. POINTS TO REMEMBER
1:3
The first term is called antecedent
and the second term is called consequent
Here 1 is the antecedent and 3 is the consequent

7. POINTS TO REMEMBER
◦Quantities into consideration must be of SAME KIND
In the example discussed
The two quantities are in terms of hours
(both represent time)

8. POINTS TO REMEMBER
The quantities in consideration must have same UNITS.
8 hours to 24 hours (Both are in Hours)
Note : One quantity cannot be having different units
for example : 5hours to 360minutes.

9. ◦5 Hours to 360 Min
60min = 1 hours
360mins = 6 hours
5hours to 6hours
5/6 or 5:6 (5 is to 6)
(Simplified Form)

10. PERCENTAGE
PERCENT is also a ratio
It is a RATIO with denominator 100.
“Per” = / and “centum” = 100
So percent means “ /100”

11. Another example
Father asked his son - “ what is your result”
Son – I have scored in total 415 marks out of a total of 500.
Father – so what is your score in percentage?
Son - (415/500) x 100 = 83 %
Here 83% means 83/100 or 83:100 (ratio with denominator 100)
If the maximum marks would be 100, his son would score 83.

12. SUMMARY
◦ Ratio is a COMPARISON Of 2 Quantities
◦ Ratio is a PURE NUMBER , it does not have any units
◦ It should always be expressed in the LOWEST FORM
◦ The first term is called antecedent
and the second term is called consequent.
◦ Quantities in Comparison must be of the SAME KIND.
◦ Quantities in Comparison must have SAME UNITS.
◦ PERCENT is also a comparison quantity with a denominator 100
(ratio).