Finding a Part of a Whole and Finding the Whole from its Part
Two Inverse Problems That Work Together Like Magic!
The Big Idea
In mathematics, we often work with two inverse (opposite) problems:
- Type 1: When we KNOW the whole, we can FIND the part
- Type 2: When we KNOW the part, we can FIND the whole
These operations are opposites of each other — understanding both is essential for solving fraction word problems!
TYPE 1: Finding a Part
Given: The WHOLE (complete amount)
Find: The PART (a fraction of it)
Part = Whole ÷ Denominator × Numerator
TYPE 2: Finding the Whole
Given: The PART (a fraction's value)
Find: The WHOLE (complete amount)
Whole = Part ÷ Numerator × Denominator