Subtraction

Subtraction is one of the four basic arithmetic operations, used to find the difference between two or more numbers. It helps us understand how much one quantity is greater or smaller than another, or what remains after something is taken away. The subtraction symbol (–), also called the minus sign, represents this operation.

We use subtraction every day, for instance, to compare prices, find out how much is left, or calculate change after shopping.

The idea of subtraction has been around for thousands of years. Early records from Babylonian and Egyptian civilizations show subtraction written on clay tablets and papyrus scrolls. Later, the Romans and Greeks also practiced subtraction, though it was more difficult with Roman numerals.

With the invention of our modern number system, subtraction became much simpler, forming one of the most essential math operations we use today.





 

Every subtraction equation has three main parts:

Minuend – The starting number or the number from which another number is subtracted.

Subtrahend – The number that is being subtracted.

Difference – the result after getting Subtraction.

For example: \(15 – 5 = 10\), where 15 is the minuend, 5 is the subtrahend, and 10 is the difference.

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 \(c\ – b = a\).

Solving subtraction problems can be easy once you understand the steps. For one-digit numbers, we can subtract directly. But when we work with larger numbers, we arrange them in columns by place value: Ones, Tens, Hundreds, Thousands, and so on.

Sometimes, we need to borrow while subtracting, this is called subtraction with regrouping. We use regrouping when the minuend of the top number is smaller than the subtrahend of the bottom number. In such cases, we borrow 1 from the next column to make the subtraction possible.

For example,

\(\begin{array}{r} \phantom{0}52 \\ -37 \\ \hline 15 \end{array}\)


Here, since 2 is smaller than 7, we borrow 1 from the Tens place to make it \(12 – 7 = 5\). After borrowing, we subtract the Tens column: \(4 – 3 = 1\), so \(52 – 37 = 15\).

Learning both addition and subtraction together helps to understand how numbers increase and decrease, making it easier to solve everyday math problems.

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:

\(\frac{5}{8} - \frac{3}{8} = \frac{5 - 3}{8} = \frac{2}{8} = \frac{1}{4}\)

With different denominators:

\(\frac{3}{4} - \frac{2}{3}\)

Find the common denominator: LCM of 4 and 3 is 12.

Rewrite the fractions: \(\frac{3}{4} = \frac{9}{12}\), and \(\frac{2}{3} = \frac{8}{12}\).

Subtract: \(\frac{9}{12} - \frac{8}{12} = \frac{1}{12}\).

Subtraction of Negative Numbers

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

For example, \(5 – (–3) = 5 + 3 = 8\).

Here, (–) × (–) = +. 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 one of the most basic and essential concepts in mathematics. A strong understanding of subtraction lays the groundwork for learning advanced topics.
   
• Mastering subtraction helps students understand how numbers relate to one another, improving their logical thinking and problem-solving skills.
   
• Subtraction plays a key role in understanding algebra, geometry, and data analysis, making it a vital skill for future math learning.
   
• Using tools like a subtraction worksheet or an addition and subtraction worksheet helps the students to practice regularly, reinforce their skills, and build confidence in solving math problems.

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.

Keep Practicing: 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.

Check with Addition: After subtracting, add the difference to the smaller number. If the sum equals the larger number, the subtraction is correct.

Line Up Numbers Properly: Always align numbers according to their place values (ones, tens, hundreds, etc.). This reduces mistakes while subtracting.

Use Place Value for Regrouping: When practicing addition and subtraction with regrouping, use everyday items like pencils or blocks to demonstrate borrowing or carrying. Visual aids make it easier for kids to understand how numbers move between columns.

Practice with Repeated Subtraction: Encourage your child to solve division problems using repeated subtraction. For instance, 12 ÷ 3 can be shown as \(12 – 3 – 3 – 3 – 3 = 0\). This builds a strong link between subtraction and division.

Use Place Value to Teach Regrouping: When working on three-digit subtraction with regrouping, use visual aids like blocks, counters, or place value charts. Demonstrating how to borrow from the next column helps children clearly see how regrouping works in larger numbers.

Make Subtraction Part of Daily Life: Use real-life examples like “We baked 12 cookies and ate 5. How many are left?”. These examples make subtraction fun, practical, and easy to understand for young learners.

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.