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Addition & Subtraction Involving Money

What is Money?

We need money to buy things, watch movies, travelling to different places, pay taxes, buy a house and do a lot of other things we do in our daily lives. We use the money for the smallest of things we buy /own every day. It is quite similar to the barter system that we sued to have in older days when people would exchange one thing for another. For example, they would give a bag of rice to someone and take from him a bag of wheat. Today that same exchange is done in the form of money; where we buy sell anything according to its monetary value. 

What is Currency?

Money is available in different forms at different places. For buying things we use coins and notes which are issued by the respective governments of the country we live in. These are called currency. Every country has its own currency. For instance, in the United States of America, the currency is dollars ( \$ ), in the United Kingdom, it is pounds ( £ ) and in Europe, it is Euro ( € ) and so on. Moreover, the values of the currency are not the same everywhere. There are different conversion rates depending upon the internal value of the concerned currency. These conversion rates are not static and they change with every trading day. So the value of the conversion depends upon the day of the conversion. For example, if today, 1$ = £ 0.73, this means that for every 1 dollar, we will get £ 0.73 in exchange. It is therefore; very important to understand the addition as well as subtraction of money, without which it is not possible to carry out daily transactions. We can, therefore, define currency as – 

A currency is the system of money used in a country or we can say that a currency is a system of money in common use, especially for people in a nation.

But, before that, it is important to understand the form in which form is money available to us. There are different coins and notes that are issued by the governments having different denominations. Let us, for example, take the example of a pound.

The British currency is the pound sterling. The sign for the pound is £

GBP = Great British Pound £

Since decimalisation in 1971, the pound has been divided into 100 pence. This means that the pound ( £ ) is made up of 100 pence (p). The singular of pence is “penny”. The symbol for the penny is “p”; hence an amount such as 50p is often pronounced “fifty p” rather than “fifty pence”. 

Hence, £1 = 100p

Similarly, the dollar is a currency that is used in many western countries and is represented by the ‘\$’ sign. The dollar is the common currency of countries such as Australia, Belize, Canada, Hong Kong, Namibia, New Zealand, Singapore, Taiwan, Zimbabwe, Brunei and the United States. A cent is also a unit of currency that is usually used along with the dollar. Cent is actually one-hundredth of a dollar and is represented by a small case c with a forward slash or a vertical slash through the c. Therefore, $1 = 100 cents

Let us know understand how to add money.

How to do addition and subtraction involving money?

The addition and subtraction of money are similar to the addition and subtraction of numbers. Just like numbers, we place pence and pounds in different columns.  There are two different methods of adding and subtracting values involving money. The two methods are – 

  1. Addition or subtraction of the amounts with conversion into pence
  2. Addition or subtraction of the amounts without conversion into pence

Addition Involving Money

The basic concepts of addition remain the same irrespective of the kind of values we add. Therefore, the rules of addition, such as carrying forward or regrouping shall remain the same in case of the addition of amounts involving money. As discussed above, the addition involving, money can be done in two ways – 

  1. Converting in pence before addition
  2. In addition without converting into pence

Let us understand both of these methods.

Addition of the amounts with conversion into pence

As the name suggests, this method involves the conversion of the given amounts into pence and then proceeding with addition or subtraction as required. The following steps are included in this process – 

  1. First of all, we convert all the given money into pence. 
  2. Then we add the given amounts as required.
  3. Finally, we divide the result obtained in the above step by 1000 to obtain the amounts in pounds and pence.

 Let us understand the above steps through an example.

Example

Suppose we want to add £ 2.05 and £ 4.20

Solution

We have been given the amounts £ 2.05 and £ 4.20

Going by the above steps, first we will convert the given amounts in pence. We know that

£ 1 = 100 p

Therefore, we have,

£ 2.05 = 2.05 x 100 = 205 p

£ 4.20 = 4.20 x 100 = 420 p

Now we have two values 205 p and 420 p. we can add these values, in the same manner, we add two whole numbers. We will get,

205 p + 420 p = 625 p

Now we have obtained our result in pence. To convert it back into pounds, we will have to divide the result by 100. We will now have,

625 p = £ $\frac{625}{100}$  = £ 6.25

Hence, we can say that the sum of £ 2.05 and £ 4.20 = £ 6.25

Addition of the amounts without conversion into pence

If we want to add two or more amounts of money without first converting it into pence, we will have the go through the following steps – 

  1. Arrange the pounds and pence in columns just the way you place decimal numbers for addition.
  2. Add the given amounts as ordinary numbers.

In other words, for performing addition in money by using without conversion method we arrange the amount in columns i.e., pounds under pounds, pence under pence and dot under dot. Now add as usual as ordinary numbers.

Let us understand this by an example.

Example

Suppose we want to add the amounts £ 15.44, £ 7.524 and £ 25

Solution

We have been given the amounts £ 15.44, £ 7.524 and £ 25

It is important to note here that if we ignore the currency sign, the three amounts are just decimal numbers. Therefore, we will add them in the same manner as we do for decimals.

Recall that in addition of decimal numbers we will have to convert these decimals into like decimals. Therefore, 

£ 15.44 = £ 15.440

7.524 is already a like decimal so no conversion is required.

£ 25 = £ 25.000

Now, that all the three decimals are like decimals, we will proceed ahead and write these decimals in column form, as shown below – 

15.444
+07.524
+25.000
———-
———-

Next, we will add these fractions just as we add the whole numbers. We will get,

15.444
+07.524
+25.000
———-
+47.964
———-

Hence, the addition of £ 15.44, £ 7.524 and £ 25 = £ 4 7 . 9 6 4

Subtraction Involving Money

The basic concepts of subtraction such as defining the subtrahend and minuend remain the same irrespective of the kind of values we subtract. Therefore, the rules of subtraction, such as borrowing from or regrouping shall remain the same in the case of subtraction of amounts involving money. As discussed above, the subtraction involving, money can be done in two ways:

  1. Converting in pence before subtraction
  2. Subtraction without converting into pence

Let us understand both of these methods.

Subtraction of the amounts with conversion into pence

Subtraction in money by using the conversion method, we convert pounds and pence into pence and then subtract the smaller amount of pence from the greater amount. The obtained numbers are subtracted as ordinary numbers and if required finally we put a dot after two digits from the right. The difference is expressed in pounds and pence. The following steps are included in this process – 

  1. First of all, we convert all the given money into pence. 
  2. Then we subtract the smaller pence from the larger one and obtain the result. 
  3. Finally, we divide the result obtained in the above step by 1000 to obtain the amounts in pounds and pence.

 Let us understand the above steps through an example.

Example

Suppose we want to subtract £ 34.05 from £ 58.49

Solution

We have been given the amounts £ 34.05 from £ 58.49

Going by the above steps, first, we will convert the given amounts in pence. We know that

£ 1 = 100 p

Therefore, we have,

£ 34.05 = 34.05 x 100 = 3405 p

£ 58.49  = 59.49 x 100 = 5949 p

Now we have two values 3405 p and 5949 p. We can subtract the larger value from the smaller one, in the same manner, we find the difference between two whole numbers. We will get,

5949 p – 3405 p = 2444 p

Now we have obtained our result in pence. To convert it back into pounds, we will have to divide the result by 100. We will now have,

2444 p = £ 2444100  = £ 24.44

Hence, we can say that the difference of £ 34.05 from £ 58.49 = £ 24.44

Subtraction of the amounts without conversion into pence

If we want to find the difference of two or more amounts of money without first converting into pence, we will have the go through the following steps – 

  1. Arrange the pounds and pence in columns just the way you place decimal numbers for addition.
  2. Find the difference of the given amounts as ordinary numbers.

In other words, for performing subtraction in money by using without conversion method we arrange the amount in columns i.e., pounds under pounds, pence under pence and dot under dot. Now subtract as usual as ordinary numbers.

Let us understand this by an example.

Suppose we want to find the value of £ 11.6 – £ 9.847

Solution

We have been given the decimals, £ 11.6 and £ 9.847 and we are required to find their difference. Recall that in subtraction of decimal numbers we will have to convert these decimals into like decimals. Therefore, 

£ 11.6 = £ 11.600

£ 9.847 is already a like decimal so no conversion is required.

Next, we will subtract these fractions just as we add the whole numbers. We will get,

11.600
-9.847
——–
1.753
——–

Therefore, £ 11.6 – £ 9.847 = £ 1.753

Addition and Subtraction of Money in Everyday situations

The addition and subtraction of money is something we perform almost every day in our lives. Let us understand the importance of understanding how to add and subtract values that represent money through some examples.

Example 1 Maria had £ 305.80 in her bank account. She deposited £ 250.25 more and then withdrew £ 317.50 from her account. What is the balance now in her account?

Solution Let us first define what is given and what needs to be calculated. We have been given that Maria had £ 305.80 in her bank account. She deposited £ 250.25 more and then withdrew £ 317.50 from her account. We are required to find the balance in her account now. Therefore,

Initial amount in Maria’s account = £ 305.80 …………………. ( 1 ) 

Amount deposited by Maria = £ 250.25 …………………. ( 2 ) 

Total amount in Maria’s account = ( 1 ) + ( 2 )  

= £ 305.80 + £ 250.25 

= £ 556.05 …………………………… ( 3 ) 

Now, from this total amount, we subtract the amount Maria had withdrawn, i.e. £ 317.50

Therefore, money left in her account = ( 3 ) – £ 317.50

= £ 556.05 – £ 317.50

= £ 238.55

Hence, money left in Maria’s account = £ 238.55

Example 2 Peter is trying to save £ 1000. He currently has £ 747.50 in his bank account. He just earned another £ 25.50 by helping his mother arrange the things around the house and got £ 35 for his birthday. How much more does Peter need to save to meet his goal?

Solution We have been given that Peter wants to save £ 1000. He currently has £ 747.50 in his bank account. He just earned another £ 25.50 by helping his mother arrange the things around the house and got £ 35 for his birthday. Now, first, let us summarise the amount Peter has with him at the moment. We get,

Money in Peter’s bank account = £ 747.50

Money received by Peter by helping his mother = £ 25.50

Money received by Peter for his birthday = £ 35

Total money that Peter has = £ 747.50 + £ 25.50 + £ 35 = £ 808

Money that Peter want’s to save = £ 1000

Money that Peter needs to meet his goal = £ 1000 – £ 808

= £ 192

Hence, Peter needs to save £ 192 more to meet his goal. 

Example 3 Samina purchased a syrup for £ 36.00, a cookies box for  £ 29.50 and a hair oil bottle for  £ 32.50. She gave the shopkeeper £ 100, how much money did the shopkeeper return as balance?

Solution We have been given that Samina purchased a syrup for £ 36.00, a cookies box for £ 29.50 and a hair oil bottle for £ 32.50. She gave the shopkeeper £ 100. We are required to find the money returned by the shopkeeper as a balance. In order to do so, first, let us summarise the items purchased by Samina.

Cost of syrup purchased by Samina =  £ 36.00

Cost of cookies box purchased by Samina = £ 29.50

Cost of hair oil bottle purchased by Samina = £ 32.50

Total shopping by Samina = £ 36.00 + £ 29.50 + £ 32.50 = £ 98

Now, Samina gave £ 100 to the shopkeeper. Therefore

Change returned by the shopkeeper = £ 100 – £ 98 = £ 2.00

Hence, Samina got £ 2.00 from the shopkeeper as a change.

Key Facts and Summary

  1. A currency is the system of money used in a country or we can say that a currency is a system of money in common use, especially for people in a nation.
  2. £ 1 = 100 p
  3. $ 100 = 100 cents
  4. The addition and subtraction of money are similar to the addition and subtraction of numbers. Just like numbers, we place pence and pounds in different columns.  
  5. For performing addition in money by using without conversion method we arrange the amount in columns i.e., pounds under pounds, pence under pence and dot under dot. Now add as usual as ordinary numbers.
  6. For performing subtraction in money by using without conversion method we arrange the amount in columns i.e., pounds under pounds, pence under pence and dot under dot. Now subtract as usual as ordinary numbers.

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