Subtraction: There is a misconception that Mathematics is just the use of complicated formulas and calculations which won’t be ever applied in real life, but you will be amazed to see Mathematics emerge from unexpected situations. Don’t BELIEVE me????

Note some of the daily activities mentioned here: Activities such as adding new friends, subtracting negative thoughts, ways to multiply the pocket money we earn and dividing pizza among your friends. Wait a Second!!!!!

We just talked about the \(4\) basic operation used in Mathematics. So, in this article, we are going to cover one of the prime basic operations used in Mathematics.

What is Subtraction?

Let’s start with when we were in kindergarten and learned the rhymes taught by our Mother/ Teacher. Rhymes such as ‘Ten Green Bottles’, ‘Five Little Monkeys’ and ‘Five Little Ducks’

Does that Ring a Bell!!!!!

Of course, it does! These rhymes helped us to practice the process of subtracting one each time.

Hence, subtraction is one of the basic arithmetic operations representing the operation of removing objects from a collection. Subtraction is denoted by the symbol “-“. Subtraction is notified as a minus in most situations, but still, we have a vast terminology used for subtraction based on the situations. The synonym of subtraction is subtract, take away, minus, decrease, leave, how many leftovers, how much less, etc.

For example, what is \(10\) minus \(4\)? If I subtract \(27\) apples out of \(155\) apples from a carton, how many will there be left? What is the difference between \(579\) and \(141\)?

Subtraction Meaning

In simple words, subtraction is the operation of finding the difference between two numbers. When we apply subtraction to a collection, then the number of things in the collection reduce or become less.

In the subtraction problem, \(100–30 = 70,\) the number \(100\) is the minuend, the number \(30\) is the subtrahend, and the number \(70\) is the difference. Hence, the minuend, subtrahend and difference are parts of a subtraction problem.

Have a look at another example from the figure given below.

What is Subtraction Without Borrowing?

There are very easy and hassle-steps to do subtraction without borrowing and following these steps one can learn subtraction without borrowing in no time

1. Place the subtrahend below the minuend so that the ones-place numbers fall in the same column.
2. Now subtract each column separately and in order, starting with the ones-place column.
3. And lastly, place the answer of the subtractions below each one of the columns, but in order.

It’s easy, right? Let’s understand it with an illustration.

Subtract \(15\) from \(38.\)

We need to write down \(38\) and below it, \(15,\) making sure that \(5\) is just below \(8.\)
\(3\;\;\;8\;\)
\( – 1\;\;\;5\)
We start off by subtracting the ones-place column: \(8\;–\;5\; = \;3\) and we write the \(3\) under the same column.
Now, solve the \(10 s\) place column \(3\;–\;1\; = \;2,\) and we write the \(2\) below the column.
\(3\;\;\;\;8\)
\(\underline { – 1\;\;\;5} \)
\(2\;\;\;\;3\)
As you can see above, the answer is \(23.\)

What is Subtraction with Borrowing?

Can I borrow your pen? Can I borrow your notes to complete my notes? I am short of some money; can I borrow some amount from you? We almost use the word borrow at least once a day.

Let’s do some bungy-jumping how subtraction is done with the help of borrowing. The other name for borrowing is regrouping. We borrow something whenever we don’t have enough.

For example: In subtraction of two-digit numbers, the method of borrowing consists of taking a ten from the subtrahend and breaking it down into units to have enough units to subtract from the minuend.
Let’s understand it with the help of an example.

Up for another example???

Check out the other example.

So, we use the borrowing method when we must subtract one number that is greater than another (the subtrahend is greater than the minuend). So, \(47 – 25\) would not need borrowing or regrouping because if we look at one’s place, we can take away \(5\) form \(7.\) Bur \(40-25\) would use borrowing or regrouping because we can’t subtract \(5\) from \(0.\)

How to Do Subtraction on the Number line?

The number line is a horizontal straight line on which numbers are marked at regular intervals. The number line extends indefinitely on both sides of zero.

Before we go further, keep two important points in mind about the placement of numbers on a number line.

1. A number on the left is always less than a number on the right.
2. And a number on the right is always greater than a number on the left.

Let us understand the concept of subtraction on the number line with the help of an example.

Subtract \(2\) from \(6\) on a number line

Firstly, mark both the integers on the same number line. Then count how many steps are required from the integer \(2\) to reach \(6.\)

Uses of Subtraction With Regrouping

Subtraction with regrouping is very useful in our daily life. Some examples are given below:

1. To measure distance
2. To measure time 
3. To deal with money
4. Shopping at the grocery store or supermarket
5. Cooking and baking and so on.

How to Do Subtraction of Large Numbers?

The method of subtraction remains the same whether the numbers to be subtracted are small or large.

The steps involved in subtraction are as follows.

1. Write the numbers in the place value chart one below the other. The greater number will come above the smaller number.
2. Subtraction is done column-wise, from right to left. So, make sure to start subtracting the lowest (one’s) place and move to the higher places.
3. Regroup or borrow if the digit of minuend of a place is smaller than the digit of the subtrahend.

For example, subtract \(14,16,300\) form \(6,23,42,750.\)

Verifying subtraction result:

After carrying out the subtraction operation, always check for the correctness of the answer obtained.

To do that, add the difference obtained to the subtrahend. If you get the same answer as the minuend, then the answer is correct; otherwise, the answer is incorrect and you need to do the subtraction again.

Lets us understand the concept with the example taken above.

Here, after adding, we get \(6,23,42,750\) which is the same as minuend.

What are Subtraction Rules?

We know that addition and subtraction are inverse operations. So, every subtraction problem can be written as an addition problem.

While writing any subtraction problem, we have to take the sign of subtrahend inside the bracket and add the addition operator between both the terms. This is one way of solving subtraction questions.

Let us learn and understand the rules of subtraction to ease out the calculations while dealing with operations on numbers.

(i) Subtraction of two positive numbers: While subtracting two positive numbers, take the difference of absolute values of both numbers and assign the sign of the greater number before the answer.
For example:

\(20 – 13 = 7\) \(5 – 12 = – 7\)

(ii) Subtraction of a positive number and a negative number: While subtracting a positive number and a negative number, take the sum of the absolute values of both the numbers and assign the sign of minuend with the answer.
For example:

\(5 – \left( { – 15} \right) = 20\) \(\left( { – 12} \right) – 7 = – 19\)

(iii) Subtraction of two negative numbers:  While subtracting two negative numbers, the sign of subtrahend has to be changed. Then, take the difference of the absolute values of both the numbers and assign the sign of the greater number.
For example:

\(\left( { – 5} \right) – \left( { – 7} \right) = – 5 + 7 = 2\) \(\left( { – 16} \right) – \left( {14} \right) = – 16 – 14 = – 30\)

What are Properties of Subtraction?

1. Closure property: If \(x\) and \(y\) are two whole numbers, then \(x-y\) is not necessarily a whole number.

(i) If \(x = 20\) and \(y = 17,\;x – y = 20 – 17 = 3,\) which is a whole number. (ii) If \(x=0\) and \(y = 20,\;\;x – y = 0 – 20 = – 20,\) which is not a whole

2. Commutative property: If \(x\) and \(y\) are two whole numbers, then

(i) if \(x=20\) and \(y = 17,\;x – y = 20 – 17 = 3,\) and \( – x = 17 – 20 = – 3\) Therefore, \(x – y \ne y – x\)

3. Associative property: For any three whole numbers \(x,y\) and \(z.\)
\(x – \left( {y – z} \right) \ne \left( {x – y} \right) – z,\) that is, the subtraction of whole numbers does not satisfy associativity.

(i) for \(x = 20,\;y = 15\) and \(z = 12\) \(x – \left( {y – z} \right) = 20 – \left( {15 – 12} \right) = 20 – 3 = 17\) \(\left( {x – y} \right) – z = \left( {20 – 15} \right) – 12 = 5 – 12 = – 7\) Therefore, \(x – \left( {y – z} \right) \ne \left( {x – y} \right) – z\)

4. Distributive property: For any three whole numbers \(x,y\) and \(z\)
\(x \times \left( {y – z} \right) = x \times y – x \times z\)

(i) For \(x = 10,\;y = 15\) and \(z=15\) \(x \times \left( {y – z} \right) = 10 \times \left( {15 – 5} \right) = 10 \times 10 = 100\) \(x \times y – x \times z = 10 \times 15 – 10 \times 5 = 150 – 50 = 100\) Therefore, \(x \times \left( {y – z} \right) = x \times y – x \times z\)

5. Existence of identity: For any whole number \(x,\;x – 0 = x\) and \(0 – x \ne x\)
Thus, for subtraction, no identity number exists.

6. Existence of inverse: Since subtraction for every non-zero whole number does not have an identity number, its inverse does not exist.

Tips and Tricks for Subtraction

Here we have provided some of the best tips and tricks for subtraction which will help students do their homework easily.

Trick 1: While solving questions based on addition and subtraction related to composite numbers, whole numbers are added together and fractions are added or subtracted together. But if the sum of the fractions, then comes as a composite number, then the whole number present in it is again added to the sum of the whole numbers.

Trick 2: In the questions based on addition and subtraction related to whole numbers, the digits of units, tens, hundreds, thousands and ten thousand of the numbers present in the given expression are added and subtracted together respectively. The unit’s digit obtained from the sum of the units’ digits is placed in the unit’s place for that expression and the remaining number is added to the sum of the ten’s digits.

Trick 3: If the total numbers present in the addition of decimal numbers are formed by repetition of the same digit and the first, second, third and fourth numbers after the decimal are of only one, two, three and four digits respectively, then while solving such questions, the repetition The unit digit of the product obtained by multiplying one digit by 1, 2, 3 and 4 respectively is placed in the place of the unit, tens, hundred and thousand of the sum, respectively. Simultaneously the score on your left-hand side is added. Lastly, the decimal is placed after four digits from the right side of the sum.

Trick 4: Before solving the questions based on addition and subtraction of decimal numbers, the total number present in them is equal to the maximum number after the decimal, by putting zero (0) after the decimal. After this, the operation of addition and subtraction is done.

Solved Examples – Subtraction

Q.1. \(211\) birds were sitting on a tree. \(39\) birds flew away from a tree.
Ans: Given, \(211\) birds are sitting on a tree.
\(39\) birds flew away from the tree.
Birds left on the tree \(= 211 – 39 = 172\)
Therefore, the number of birds on the tree is equal to \(172.\)

Q.2. What is the result of the operation \(96,78,913 – 10,00,000\)
Ans: We must subtract \(10,00,000\) from \(96,78,913.\)
\(96\;,78\;,913\)
\(\underline { – 1\;0,00,000} \)
\(86,78,913\)
Hence, the required answer is \(86,78,913\)

Q.3. The difference between the two numbers is \(43,152.\) If the greater number is \(84,769,\) find the smaller number.
Ans: Given that the greater number is \(84,769\)
Difference between two numbers \(43,152\)
Therefore, smaller number \(= 84,769 – 43,152 = 41,617\)
Therefore, the smaller number is \(41,617.\)

Q.4. Subtract \(7\) from \(25\) on a number line.
Ans: Draw a number line and mark both the numbers on the number line and jump \(7\) steps towards the left side. After jumping \(7\) steps, the number you landed on is the required answer.

Q.5. Use a number line to find \(78-45.\)
Ans: We are asked to subtract two numbers on a number line. The subtraction is to be done as follows:

Summary

In this article, we learned the meaning of subtraction, where it is applied in real life and how the application of subtraction is a useful operator in day-to-day life. We also learned what is minuend and subtrahend. We thoroughly learned about the properties and how to do subtraction with borrowing. We learned about number line and how to subtract numbers on a number line.

Frequently Asked Questions (FAQ) – Subtraction

Q.3. What is the formula of subtraction?
Ans: To do subtraction on the integers, use the (minus sign) arithmetic operator.

Q.4. What is the symbol of subtraction?
Ans: Subtraction is one of the basic arithmetic operations that represents the operation of removing objects from a collection. Subtraction is denoted by the symbol “-“.

Q.5. What are the subtraction terms?
Ans: The terms of subtraction are called minuend and subtrahend.

Now that you are provided with all the necessary information about subtraction, we hope this article is helpful to you. If you have any queries on this page, post your comments in the comment box below and we will get back to you as soon as possible.

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