1-646-564-2231

# Subtraction: Formula, Properties, Examples

Subtraction is one of the basic math operations. It is the process of taking away a number from another. This arithmetic operation is denoted by a subtraction symbol (-). Read on to learn all about calculating the difference between two or more numbers.

Here’s what we’ll cover:

• What is subtraction?
• Subtraction formula
• Properties of subtraction
• How to subtract numbers?
• Subtraction without regrouping
• Subtraction with regrouping
• Word problems on subtraction
• Verifying subtraction results
• How to subtract fractions?
• How to subtract decimals?
• Practice problems

## What is Subtraction?

Subtraction is an arithmetic operation of taking the difference between two numbers.  For instance, if x= a-b, then a is called the minuend, b is the subtrahend, and the symbol between the a and b is called the minus sign. The final result after subtracting subtrahend from minuend is called the difference of the two numbers. The expression “a-b” is read “a minus b.”

Subtraction Formula: Minuend – Subtrahend = Difference

### Properties of Subtraction

The properties of subtraction are as follows:

• It is the reverse of addition.
• If we subtract a number from itself, it gives 0.
• For any two whole numbers, x and y, if x > y then x – y is a whole number and if x < y, then x – y is never a whole number. The subtraction of a bigger real number from a smaller number gives a negative real number. For example, 110 – 100 = 10, is a whole number but 100 – 110 = -10 is not a whole number.
• For any two whole numbers, x and y, x – y ≠  y – x. Hence, unlike addition, subtraction of the whole number is not commutative. For example, 15 – 7 = 8 but  7 – 15 ≠ 9.
• For any three whole numbers say x, y, and z (x – y) – z ≠ x – (y – z). So, the subtraction of whole numbers isn’t associative.
• The subtraction property of equality means balancing an equation by using the same mathematical operation on the two sides of the equation. Suppose there are 15 stars in two boxes. So, if we take away 2 stars from box 1 then, to balance this equation in both the boxes we need to take away 2 stars from the other box also.
• We can also extend the subtraction of real numbers to complex numbers.

### How to Subtract Numbers?

To solve subtraction problems, we can easily subtract one-digit numbers, but for larger numbers, we use the place value method and split the numbers into columns like Ones, Tens, Hundreds, Thousands, and more. Subtracting numbers often have cases where we will have to borrow one number from the next.

Subtraction involving borrowing is also called subtraction with regrouping. We borrow one number from the preceding column when the minuend is smaller than the subtrahend. This borrowing makes the minuend bigger than the subtrahend. The following example will help to understand this method.

Note: While subtracting, we always subtract the smaller number from the larger number.

#### Subtraction Without Regrouping

Example: Subtract 2532 from 4856.

Step 1: Begin with the digit at ones place. (6 – 2 = 4)

Step 2: Next, we will solve the tens place. (5 – 3 = 2)

Step 3: Subtract the digits at hundreds place. (8 – 5 = 3)

Step 5: Finally, solve the digits at thousands place. (4 – 2 = 2)

Step 6: So, the difference between the two given numbers is: 4856 – 2532 = 2324.

#### Subtraction With Regrouping

Example: Subtract 3278 from 4462.

Solution: The following steps will help you solve subtraction problems with regrouping.

Step 1: We will begin subtracting the digits at ones place. Since 8 is greater than 2, we will borrow 1 from the tens column and 2 will become 12. Now we will subtract, 12 – 8 = 4 ones.

Step 2: As 6 donated 1 to the ones column in the previous step, it will become 5. Here, 7 is greater than 5, so we will borrow 1 from the preceding column. Now, it will become 15 and 15 – 7 will be 8 at tens place.

Step 3: Since in the previous step 4 donated 1 to the tens column, we are left with 3 at the hundreds place. Now, we will subtract the digits in the hundreds place, i.e., (3 – 2) and we will get 1.

Step 4: Now, we will subtract the digits at the thousands place. So, 4-3 will be 1 at the thousands place.

Step 5: Therefore, the difference between the two numbers: 4462 – 3278 = 1184

## Word Problems on Subtraction

### Verifying Subtraction Results

We can verify the answer as follows:

• Add the difference and the subtrahend. If you obtain the minuend as the sum, then your answer is correct.
• For example, 2233- 1000 = 1233. Here,  1000 is subtrahend and 2233 is minuend. The difference is 1233.
Now adding difference + subtrahend = minuend.
So, 1233 + 1000 = 2233. Hence, the answer is correct as the sum equals the minuend.

#### How to Find Missing Minuends?

Often subtraction problems require you to find a missing minuend in the given question. Consider the following example to understand this better.

### How to Subtract Fractions?

Adding and subtracting fractions is one of the most common arithmetic operations. The following steps will help you subtract fractions:

Step 1. Firstly, we will ensure that the denominators of both the fractions are the same.

Step 2. If the denominators are the same, subtract the numerators. Next, we will place the answer over the same denominator.

Step 3. Lastly, simplify the fraction if required.

### How to Subtract Decimals?

Follow the steps given below to subtract decimals:

• Firstly, we will write down the two numbers, one below the other and ensure the decimal points are lined up.
• We add zeros to make the numbers of the same length.
• Then. We will subtract normally. We must keep in mind the place of the decimal point and put the decimal point in the answer.

### 1.What are some facts about subtraction?

Subtraction is really just the opposite of addition.

Subtraction is a process that can be used to find the difference between two numbers. The result of subtracting a number from another number is called the difference. For example, if you have $5.00 and spend$3.00 on an ice cream cone, then you have $2.00 left over. The amount you spent is$3.00 less than the amount you started with, which means that your total change in money (the difference) is \$2.00.

Subtraction can be written as a subtraction equation or as an equation that shows how many times to multiply one number by another number before adding them together to get another number (like 3 + 2 = 5).

### 2.What are the rules for addition and subtraction?

The rules for addition and subtraction are pretty simple.

To add numbers, you simply put them together. For example, if you want to add 1 + 2, you would write down a 1 in the first spot, then a 2 in the next spot. The result is 3!

Subtraction is just like addition, except instead of adding two numbers together, you’re taking one number away from another. So if I have 6 apples and eat 4 of them, I’ll have 2 apples left over. That means I subtracted 4 apples from my original 6-apple total to get my final 2-apple total!

### 3.What are seven names for subtraction?

Here are 7 names for subtraction:

1. difference

2. less than

3. leftover

4. deficit

5. shortage

6. shortfall

7. Surplus

### 4.What are the 3 parts of subtraction?

The three parts of subtraction are

1. the minuend, which is the number you’re taking away from another number;

2. the subtrahend, which is the number you’re subtracting from another number; and

3. the difference, which is what you’re left with after subtracting one number from another.

### 5.What is the first number in a subtraction process?

The first number in a subtraction process is the number you’re taking away. In other words, if you wanted to subtract 3 from 5, then 3 would be the first number.

## More Related TOPICS

### Use Models to Subtract Mixed Numbers

Key Concepts Using models to subtract mixed numbers Subtract mixed numbers Addition and subtraction of mixed

### Use Models to Add Mixed Numbers

Key Concepts Using models to add mixed numbers Adding mixed numbers Introduction  In this chapter, we

### Find Common Denominators

Key Concepts Equivalent fractions and common denominators Finding common denominators Introduction In this chapter, we will