# Decomposing Money

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## Decomposition of Money

When we were trying to understand the denominations of money, we discussed the example of how a shopkeeper would repay you the change after you bought something from him. That is just one example of how we can break down a sum of money into its smaller denominations.

## What is the decomposition of money?

Let us take the example of a ₹2000 currency note. It represents a value of ₹2000, and it has a declaration from the central bank that it promises to pay that amount to the bearer of that currency note. We know that below ₹2000, there are other denominations such as 500, 200, 100, 50, 20, 10, 5 and 1. There are different combinations in which a ₹2000 note can be exchanged.

2000 = 4×500

2000 = 10×200

2000 = 20×100

If we use combinations of 500, 200 and 100, then ₹2000 can be decomposed  into

2000=(3×500)+(2×200)+(1×100)

2000=(2×500)+(4×200)+(2×100)

….and so on.

## Purpose of decomposition of money

Understanding the decomposition of money helps in getting a grip on the basic mathematics involved in the handling of money. This equips us with the tools to handle money better. Money is something that sees the principles of mathematics being applied in daily life.

When you wish to find out a fraction, you need to know how to decompose money. So, if your grandfather has ₹1000 and he wants to give equal parts of it to each of his five grandchildren, then how much would you and your four cousins get? You would get 1/5×1000=₹200. If there were 4 grandchildren instead of 5, then each child would get ₹250.

How about when you wish to understand how to get back change when you buy something. Suppose you buy a board game for ₹165, then these are the amounts you would depending on the cash you pay.:

When you give ₹200 note:

You can get back ₹35=20+10+5

When you give ₹500 note:

You can get back ₹335=200+100+10+10+10+5

When you give ₹2000 note:

You can get back ₹1835=500+500+500+200+100+20+10+5

There are multiple iterations on how much change you would get depending on the denominations available.

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