Money - Unitary Method

The Unitary Method is a technique where we first find the value of a single unit (one item) and then use that value to calculate the value of the required number of units. The word 'unitary' is derived from 'unit', which means 'one'. Visualise this as taking a large pack of 10 chocolates and breaking it down to see the price of 1 chocolate before deciding how many you want to buy.

The method involves two primary arithmetic operations: Division and Multiplication. First, we use division to go from 'many' to 'one', and then we use multiplication to go from 'one' to 'many'. Picture a funnel: many items enter the wide top, we narrow it down to one unit in the middle, and then it widens back out to the specific quantity you need.

Finding the Cost of One (The 'Many to One' step): To find the value of one item, divide the total cost by the total number of items. For example, if a bunch of 5 bananas costs ₹25, the cost of one banana is $\frac{25}{5} = ₹5$. This is like sharing a bill equally among a group of friends.

Finding the Total Cost (The 'One to Many' step): Once the cost of a single unit is known, multiply that unit price by the number of units required. If 1 banana costs $₹5$, then 3 bananas will cost $5 \times 3 = ₹15$. You can visualize this as a repeated addition or a staircase where each step up represents adding the price of one more item.

Direct Variation: In these problems, as the quantity of items increases, the cost also increases at a constant rate. Imagine a straight line on a graph starting from zero; as you move right (more items), the line goes up (more cost) at a steady angle. If you buy zero items, you pay $₹0$.

Handling Currency Units: Before performing calculations, ensure all money values are in the same unit. If a problem gives some values in Rupees ($₹$) and others in Paise ($p$), convert them using the relation $1 \text{ Rupee} = 100 \text{ Paise}$. Visualise this as exchanging a large ₹1 coin for 100 smaller 1p coins to keep the math consistent.

Finding Quantity from a Given Amount: Sometimes, the unitary method is used to find 'how many' items can be bought with a specific amount of money. In this case, find the cost of one item first, then divide the total money available by the cost of one unit. Visualize having a stack of ₹10 notes and checking how many ₹2 candies you can 'match' against them.