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Subtraction – Definition, Symbol, Examples, Practice Problems

Jo-ann Caballes

Updated on January 10, 2024

What Is Subtraction?

Subtraction is one of the fundamental operations in arithmetic that children learn early in their education. It’s a process we use to find the difference between two numbers, quantities, or objects. For instance, if a basket contains five apples and you remove two, you’re left with three. This operation can be expressed as a subtraction problem: 5 – 2 = 3. The concept of taking away or finding the difference is central to subtraction. It’s not just useful in mathematical computations but also applicable in various real-life situations, such as calculating change in a store, or determining how much of a pizza is left after some slices have been eaten.

What is Subtraction in Math?

In mathematics, subtraction serves as one of the fundamental pillars of basic arithmetic. It’s an operation that helps us calculate the difference between two numbers or quantities. In essence, subtraction represents the process of taking one number away from another. For example, if you have ten chocolates and you eat four, you’re left with six. That situation, expressed mathematically, is 10 – 4 = 6. This operation is so central to our daily lives that we use it frequently, sometimes without even noticing. For instance, it’s used when we calculate how many hours of sleep we can get before the alarm rings, or how much money remains after making a purchase.

Definition of Subtraction

In mathematical terms, subtraction is defined as the operation that tells the amount or quantity that remains when a number or quantity is taken from another. The result of subtraction is called the difference. For instance, in the subtraction problem 8 – 3 = 5, eight is the minuend (the number from which another number is subtracted), three is the subtrahend (the number that is to be subtracted), and five is the difference.

Symbol of Subtraction

The most common symbol of subtraction is the minus sign (-). It’s placed between two numbers to indicate that the second number (subtrahend) is to be subtracted from the first number (minuend). For example, in the expression 7 – 2, the minus sign is the symbol of subtraction, showing that 2 is to be subtracted from 7.

Formula of Subtraction Operation

The formula for the subtraction operation involves a minuend, a subtrahend, and a difference. It’s written in the format: Minuend – Subtrahend = Difference. For example, in the subtraction problem 15 – 6 = 9, 15 is the minuend, 6 is the subtrahend, and 9 is the difference.

What Is Minus in Math?

The minus sign (-) in math is a symbol used to represent subtraction, as well as negative numbers and the opposite of a number. When used for subtraction, it signifies that a number (the subtrahend) is to be subtracted from another number (the minuend). For example, in 10 – 3, the minus sign signifies that 3 is to be subtracted from 10. When used to represent negative numbers, the minus sign is placed before the number to indicate that it is less than zero. For instance, -5 is a negative number.

Uses of Minus Sign

The minus sign (-) has several uses in mathematics. Apart from representing subtraction and negative numbers, it’s used to denote the opposite of a number. For instance, the opposite of +5 is -5. It’s also used in equations to balance the two sides. For example, to balance the equation x + 2 = 5, we subtract 2 from both sides to get x = 5 – 2. Moreover, in the context of temperature, the minus sign is used to indicate degrees below zero.

How To Solve Subtraction Problems?

Solving subtraction problems typically involves three steps: identifying the minuend and subtrahend, performing the subtraction operation, and writing down the difference. For instance, to solve the subtraction problem 13 – 4, identify 13 as the minuend and 4 as the subtrahend. Subtract 4 from 13 to get the difference, which is 9. So, 13 – 4 = 9.

Subtraction Without Regrouping

Subtraction without regrouping (also known as subtraction without borrowing) occurs when the minuend (top number) in each column is larger than or equal to the subtrahend (bottom number). In this case, you simply subtract the smaller number from the larger number. For example, in the subtraction problem 63 – 27, you can subtract 7 from 3 and 2 from 6 without needing to borrow or regroup.

Subtraction With Regrouping

Subtraction with regrouping (also known as subtraction with borrowing) is a method used when the minuend (top number) in a column is smaller than the subtrahend (bottom number). In this case, you borrow 1 from the next higher place value column. For instance, in the subtraction problem 53 – 28, you can’t subtract 8 from 3 without regrouping. So, you borrow 1 from the tens place (making it 4), and the 3 becomes 13. Then you can subtract 8 from 13 and 2 from 4 to get the difference, 25.

Subtraction Table

A subtraction table is a chart that shows the results of subtracting one number from another. The minuend (from which subtraction is made) is listed down the left column, and the subtrahend (which is subtracted) across the top row. The difference can be found where the row and column of the minuend and subtrahend meet. Subtraction tables are great tools for children learning subtraction, as they provide a visual representation of the operation and can help improve speed and accuracy.

Subtraction Sums

Subtraction sums refer to the problems or exercises that involve the operation of subtraction. They may consist of simple problems like 7 – 3, or more complex ones that involve larger numbers, decimals, fractions, or integers. Practice with a variety of subtraction sums can help children improve their fluency and understanding of the subtraction operation.

Subtraction of Fractions

The subtraction of fractions involves a few steps. If the fractions have the same denominator (also known as like fractions), you simply subtract the numerators and keep the denominator. For example, 5/8 – 3/8 = 2/8, which simplifies to 1/4. If the fractions have different denominators (also known as unlike fractions), you first need to find a common denominator, adjust the numerators accordingly, then subtract.

Subtraction of Integers

Subtraction of integers can be a bit tricky due to the presence of positive and negative numbers. However, it can be simplified by understanding that subtracting a number is the same as adding its opposite. For example, to subtract -3 from 5 (5 – (-3)), you add the opposite of -3 (which is 3) to 5, resulting in 8.

Subtraction on Number Line

Subtraction on a number line provides a visual method for subtracting numbers. To subtract a number, you start at the minuend and move to the left the number of steps equal to the subtrahend. For example, to subtract 3 from 7 on a number line, you start at 7 and move three steps to the left, landing on 4.

Subtraction Word Problems

Subtraction word problems are practical scenarios that require the use of subtraction to solve. They are often used in math education to apply subtraction skills to real-world situations. For example, “John has 15 candies. He gives 7 to his friend. How many candies does John have now?” requires the subtraction operation to solve (15 – 7 = 8).

Properties of Subtraction

There are several properties of subtraction, including the property of non-commutativity (changing the order of the numbers changes the result, i.e., a – b ≠ b – a) and the property of non-associativity (changing the grouping of the numbers changes the result, i.e., (a – b) – c ≠ a – (b – c)).

Solved Examples On Subtraction

Here are some solved examples on subtraction:

1. 10 – 5 = 5
2. 7 – 2 = 5
3. 15 – 8 = 7

Each example follows the same format: Minuend – Subtrahend = Difference.

Practice Problems On Subtraction

Practice problems are an excellent way to reinforce your understanding of subtraction. Here are a few practice problems on subtraction:

1. 12 – 7 = ?
2. 9 – 4 = ?
3. 6 – 3 = ?

Try solving these problems to test your subtraction skills!

Conclusion

Frequently Asked Questions On Subtraction

What is subtraction?

Subtraction is a fundamental arithmetic operation that is integral to our daily mathematical calculations. It is the process of deducting a quantity, often referred to as the subtrahend, from a larger quantity known as the minuend. Subtraction is used to determine the difference between these two numbers or quantities. Conceptually, subtraction can be thought of as the operation of “taking away.” It’s crucial in various real-world scenarios, such as when we calculate the remaining amount of money after making a purchase or determining the time left for an event to start.

What is the symbol for subtraction?

The symbol for subtraction is the minus sign (-). It is used between two numbers to denote that the number following the sign should be subtracted from the number preceding it. This symbol is universally recognized in mathematics and signifies the operation of subtraction. For example, in the arithmetic expression “7 – 2”, the minus sign indicates that 2 should be subtracted from 7.

What is the formula for subtraction?

The standard formula for subtraction is expressed as: Minuend – Subtrahend = Difference. Here, the minuend is the initial quantity from which another quantity, the subtrahend, is subtracted. The result of this operation is known as the difference. To illustrate, let’s consider the subtraction operation “9 – 4 = 5”. Here, 9 is the minuend, 4 is the subtrahend, and 5 is the difference. This formula provides the basic framework for understanding and performing subtraction operations.

Jo-ann Caballes

5 articles

As a seasoned educator with a Bachelor’s in Secondary Education and over three years of experience, I specialize in making mathematics accessible to students of all backgrounds through Brighterly. My expertise extends beyond teaching; I blog about innovative educational strategies and have a keen interest in child psychology and curriculum development. My approach is shaped by a belief in practical, real-life application of math, making learning both impactful and enjoyable.