Ways to Multiply and Divide - Unitary Method

The Unitary Method is a mathematical technique where we first find the value of one unit (a single item) to then calculate the value of any number of units. Imagine having a large box of $10$ identical pencils; finding the price of just $1$ pencil is the essential first step of this method.

To find the value of a single unit when the total value for multiple items is known, we use the operation of division. For instance, if a stack of $5$ identical textbooks has a total thickness of $15$ cm, you divide the total thickness by the number of books ($15 \div 5$) to visualize the thickness of a single book as $3$ cm.

To find the value of multiple units when the value of one unit is known, we use multiplication. Picture $1$ bicycle having $2$ wheels; to find the total number of wheels on $6$ bicycles, you multiply the unit value by the total number of bicycles ($2 \times 6$).

The method typically involves two main steps: Step 1 is 'Reduction' (dividing to get the value of one) and Step 2 is 'Expansion' (multiplying the unit value to get the value of the required quantity). It is like zooming into a single detail of a map to understand the scale, then using that scale to calculate the distance of the whole journey.

This method relies on the concept of 'direct proportion', meaning as the number of items increases, the total value increases at a constant rate. In a visual representation like a bar graph, each bar for $1, 2, 3...$ items would grow by the exact same height increment each time.

In real-life situations, the unitary method is used for comparing prices at a grocery store or calculating speed. If a car travels a certain distance in $4$ hours, finding the distance covered in $1$ hour (the unit rate) helps us predict how far it will go in any other amount of time.