# Subtraction

Last Updated: July 19, 2024

## What is Subtraction in Math?

Subtraction is one of the four fundamental operations in mathematics, serving as the inverse process of addition. It involves determining the difference between two numbers, where the first number (minuend) is reduced by the second number (subtrahend) to yield a result known as the difference. In simple terms, subtraction helps us figure out how much is left when a certain amount is taken away from another. For instance, if you have 10 apples and give away 4, subtraction allows you to calculate that you’re left with 6 apples (10 – 4 = 6). This operation is symbolized by the minus sign (“-“). Subtraction is a crucial mathematical skill, widely used in various aspects of daily life, from budgeting to measuring distances

## Subtraction Symbol and Parts

The subtraction operation is represented by the minus sign (“-“), a fundamental symbol in mathematics that signifies the action of taking one quantity away from another. Understanding the parts involved in a subtraction expression is crucial for grasping how the operation works.

### Symbol:

• Minus Sign (-): This symbol is used to indicate subtraction. It is placed between two numbers to show that the second number is subtracted from the first.

### Parts of a Subtraction Expression:

1. Minuend: The first number in a subtraction expression, from which another number is subtracted. It represents the starting quantity before subtraction takes place.

2. Subtrahend: The second number in the subtraction expression, which is taken away from the minuend. It represents the amount that is being subtracted from the first number.

3. Difference: The result of the subtraction operation. It is the remaining quantity after the subtrahend is taken away from the minuend.

### Example:

In the subtraction expression 8 – 3 = 5:

• 8 is the Minuend, the initial quantity.
• 3 is the Subtrahend, the amount subtracted from the minuend.
• 5 is the Difference, the result of the subtraction.

## Subtraction Table

Letβs have a look at the subtraction table of simple subtractions of numbers.

## Subtraction sums

Subtraction can be applied to numbers with varying digits, from single to double, triple, and beyond. The process is straightforward for single-digit numbers, as demonstrated in the following examples:

## Subtraction of Fractions

Subtracting fractions involves taking one fraction away from another. This process can vary slightly depending on whether the fractions have the same denominator (the bottom number) or different denominators. Understanding how to subtract fractions correctly is crucial for accurate mathematical calculations in a variety of contexts.

### Subtracting Fractions with the Same Denominator

When fractions have the same denominator, you only subtract the numerators (the top numbers) and keep the denominator the same.

Example:

• 5/8 – 3/8 = 2/8 or simplified to 1/4.

### Subtracting Fractions with Different Denominators

For fractions with different denominators, you first need to find a common denominator so that the fractions are comparable. Once you have a common denominator, you subtract the numerators as you would with like denominators.

Steps:

1. Find a Common Denominator: The easiest common denominator is usually the least common multiple (LCM) of the denominators.
2. Adjust the Fractions: Convert each fraction to an equivalent fraction with the common denominator.
3. Subtract the Numerators: Keep the common denominator and subtract the numerators.
4. Simplify the Fraction: If possible, reduce the resulting fraction to its simplest form.

Example:

• To subtract 1/4 from 3/5, find a common denominator, which in this case is 20. The fractions become 5/20 and 12/20. Then, 12/20 – 5/20 = 7/20

## Subtraction of Integers

Subtracting integers can be broken down into three scenarios:

1. Subtracting a positive number from another positive number.
2. Subtracting a negative number from another negative number.
3. Subtracting a negative number from a positive number.

To simplify these calculations, we can transform subtraction tasks into addition ones. This process involves two steps:

Step 1: Change the subtraction symbol to an addition symbol.

Step 2: Following the symbol change, invert the sign of the subsequent number.

The properties of subtraction of integers are tabulated below:

## Subtraction on Number line

To grasp the concept of subtracting numbers using a number line, let’s examine the following example.

Here, subtraction of 4 from 6 gives 2.

## Subtraction Word Problems

Solving word problems is a practical way to apply subtraction skills in real-world situations. Here are some examples of subtraction word problems across various contexts.

### Problem 1: Saving Money

Emma had \$45 saved up and she spent \$20 on a new book. How much money does Emma have left?

Solution: Subtract the amount spent from the initial savings: \$45 – \$20 = \$25. Emma has \$25 left.

A baker made 120 cookies in the morning and sold 75 of them by the afternoon. How many cookies does the baker have left?

Solution: Subtract the number of cookies sold from the total made: 120 – 75 = 45 cookies left.

### Problem 3: Marathon Distance

In a marathon, Peter has run 26 miles but still has 0.2 miles to go to finish the race. What is the total distance of the marathon?

Solution: Subtract the distance remaining from the distance covered: 26 + 0.2 = 26.2 miles for the total marathon distance.

### Problem 4: Library Books

Lucy borrowed 8 books from the library. If she returned 3 books, how many books does she still have?

Solution: Subtract the number of books returned from the total borrowed: 8 – 3 = 5 books still with Lucy.

### Problem 5: Birds in the Garden

There were 17 birds in the garden in the morning. By evening, 5 birds had flown away. How many birds are left in the garden?

Solution: Subtract the number of birds that flew away from the total number in the morning: 17 – 5 = 12 birds left.

## What Is a Subtract in Math?

Subtraction in math is the operation of deducting one number from another to find the difference. It’s a fundamental arithmetic process used to calculate how much remains when a quantity is taken from another.

## What Are the 3 Types of Subtraction?

The three types of subtraction include: 1) Taking Away, where one quantity is removed from another, 2) Comparison, determining the difference between two quantities, and 3) Finding the Missing Addend, identifying a number that, when added to a known quantity, reaches a given sum.

## What Is the Subtraction Symbol?

The subtraction symbol is the minus sign (“-“). It denotes the operation of subtraction, indicating that one number should be subtracted from another to find the difference.

## What Is Subtraction Class 4?

In Class 4 subtraction, students tackle more complex problems, including subtracting large numbers, understanding regrouping (borrowing), and applying subtraction in practical situations like word problems and money calculations.

## How to Do 3 Step Subtraction?

Three-step subtraction involves multiple layers of subtraction, often with regrouping. First, subtract the ones, then the tens (regrouping if necessary), and finally, subtract the hundreds or beyond, always moving from right to left across the number

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