Quantitative Comparison Using Basic Operations

Why Do We Compare Quantities?

We compare quantities every day—who scored more, which bottle has more milk, or who ran more laps. To find these differences or relationships, we use subtraction and division.

In this method, we compare how much one quantity is more or less than another.

Example: 1
If Mohit is 15 years old and Saran is 10 years old, how many years older is Mohit than Saran? 

• Mohit's age = 15 years, Saran's age = 10 years
• Mohit's age is 5 years more than Saran's.
  15 - 10 = 5 years older than Saran. 

Example 2:
If the weight of object A is 40 kg and that of object B is 60 kg, which of these two objects has more weight, and by how much? 

• Weight of object A = 40 kg, Weight of object B = 60 kg
• Object B weighs 20 kg more than object A.
  (60 kg - 40 kg = 20 kg)

In this method, we compare how many times one quantity is of the other. This is done by dividing one quantity by the other.

Example 1:

• Age of a boy = 7 years, Age of his father = 35 years
  
  
• `"Father's age"/ "Son's age"` = `"35 years" / "7 years"` = 5
  
  
•  The father's age is 5 times the son's age. 

Example 2:

• Weight of object A = 40 kg, Weight of object B = 60 kg

• `"A's weight"/ "B's weight "` = `"40 kg" / "60 kg"` = `2 / 3`
  
  i.e., A's weight is `2 / 3` times that of B

• `"B's weight"/ "A's weight "` = `"60 kg" / "40 kg"` = `3 / 2`
  
  i.e., B's weight is `3 / 2` times that of A

• Use subtraction to find “how much more or less”.

• Use division to find “how many times”.

• Always state your answer in a sentence that explains the relationship.