Subtraction

Subtraction in math is the procedure of finding the difference between two or more numbers. It is one of the most basic arithmetic operations.

The minus sign (-) is used to represent subtraction.

Subtraction involves a minuend (starting number) and a subtrahend (the number to be subtracted), the result is called the difference.

For example, 15 – 5 = 10, where 15 is the minuend, 5 is the subtrahend, and 10 is the difference. Subtraction is used in various applications like comparing quantities, determining changes, or calculating what is left after removal.
 

The history of subtraction dates back to ancient times and civilizations, where it emerged alongside addition as a fundamental arithmetic operation.

As far as evidence goes, subtraction can be found in Babylonian and Egyptian mathematics, where the methods were recorded on clay tablets and papyrus.

The Romans and Greeks used subtraction, but it was difficult to use due to the existence of Roman numerals.

The numerical system simplified subtraction and helped develop the modern arithmetic methods that we use today.
 

Subtraction has a lot of properties that the students should follow. The properties of subtraction are given below:

Non-Commutative Property: 

In this property, the order of numbers matters while subtracting. Changing the order results in a different outcome.
Example: 5 – 3 ≠ 3 – 5

Non-Associative Property:

In this property, the grouping of numbers does not apply here, as it does in addition or multiplication.
Example: (8 – 3) – 2 ≠ 8 – (3 – 2)

Identity Property:

In this property, subtracting zero from a number does not change its value and the value remains the same.
Example: a – 0 = a

Inverse Relationship with Addition:

In this property, subtraction is the reverse of addition.
Example: If a + b =c, then c – b = a.

There are a lot of types of subtraction. These types are used in different contexts. Let us now see the different types of subtraction:

Simple Subtraction:

Simple subtraction is the procedure of finding the difference between two or more numbers. It involves basic subtraction without requiring complex steps like borrowing.

For example, if you have 7 apples and give 3 away, the difference is:
7 – 3 = 4.
Here, the minuend is 7, the subtrahend is 3 and the difference is 4

Subtraction of Decimals:

Subtraction of decimals is the procedure of finding the difference between two decimal numbers. It involves aligning the decimal points and subtracting digit by digit.

For example, Subtract 12.45 from 25.70
Align the decimal point: 25.70 – 12.45
Subtract digit by digit: 25.70 – 12.45 = 13.25.
So the difference is 13.25.

Subtraction of Fractions:

Subtraction of fractions is the procedure of finding the difference between two or more fractions. To subtract fractions, they must have a common denominator. If the fractions have different denominators, then using LCM convert them into common denominators. Then, subtract the numerators, while keeping the denominators unchanged.

For example, 
With same denominator:
5/8 – 3/8 = 5 - 3/8 = 2/8 = 1/4

With different denominators:
3/4 – 2/3
Find the common denominator: LCM of 4 and 3 is 12
Rewrite the fractions: 3/4 = 9/12, and 2/3 = 8/12.
Subtract: 9/12 – 8/12 = 1/12.

Subtraction of Negative Numbers:

Subtraction of negative numbers involves removing the negative value, which means – x  – = +. This is how the negative value is removed.

For example, 5 – (–3) = 5 + 3 = 8.
Here, – x  – = +. Hence, it becomes 5 + 3.
–4 – (–6) = –4 + 6 = 2
In general, a – (–b) = a + b.

Subtraction of Large Numbers:

Subtraction of large numbers involves finding the difference between two or more large numbers (multi-digit numbers). It is performed by aligning both numbers according to their place values. This also involves the process of borrowing from the other number.

For example, subtract 8,462 from 12,937.
Step 1: Align the numbers: 

Step 2: Subtract each digit from left to right, borrowing where it’s necessary.

Hence, the difference is 4,475.
 

Subtraction is the most basic concept in mathematics and is very important for students to understand concepts in other fields as well.

The mastery of subtraction helps students to understand number relationships, develop problem-solving abilities, and build critical thinking skills.

It plays a vital role in topics like algebra, data analysis, and geometry. Understanding this concept will help students a lot.

There are many applications of subtraction in daily life. Let us look over a few applications of subtraction in daily life:

• Financial Transactions: Subtraction helps in managing money, like calculating the change after making a purchase.
   
• Time Management: Subtraction helps in time management as it helps us in finding out the difference between two times.
   
• Cooking: When following a recipe, subtraction is used to adjust ingredients.
   
• Distance and Travel: Subtraction helps calculate how much distance remains from one destination to another.
   
• Inventory Management: Subtracting the sold items from stock helps know the remaining items.

If students are getting confused with the concept of subtraction. The students can follow the following tips and tricks to master subtraction:

Understanding Borrowing: 

While subtracting large numbers, students might sometimes need to borrow from the next higher place. This helps them to understand borrowing.

 Use a Calculator for larger numbers: 

While mastering subtraction in your mind is important, students might find it difficult to do it with larger numbers. At that time when it becomes difficult, students can use the calculator.

Practice Always:

Students must keep continuously practicing subtraction with different values and also solve word problems related to subtraction. This will help them to increase their speed in solving problems and understanding the concept better.