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# Addition & Subtraction Of Integers

## What is an integer?

An integer is a number that can be expressed without the use of fractions or decimals

The set of integers is denoted by Z, which includes:

1. Zero – it is defined as an integer that is neither negative nor positive.
2. Positive Integers – positive integers are those numbers greater than zero such as 1, 2, 3, 4, …
3. Negative Integers – negative integers are those numbers less than zero such as -1, -2, -3, -4, …

Take note:

1. There is no such thing as negative zero.
2. No need to put + sign on a positive integer.
3. A number with no negative or positive sign is considered as a positive integer.

Generally, the term “addition” refers to the process of increasing the value of something. However, in the case of integers, the addition operation may result in an increase or decrease in the given number’s value.

Here’s a list of rules for adding integers:

• The sum of an integer and its opposite or additive inverse is 0. Say for, example, 5 + (-5) = 0.
• If we add 0 to any integer, the result will be the same number. For instance, 3 + 0 = 3.
• If we add two positive integers,  the sum will always be a positive number that is greater than both given integers.
• If we add two negative integers, the result will always be a negative number that is smaller than the given integers.
• If we add a positive integer and a negative integer, the process will become subtraction. Then, the greater number will determine the sign of the result.

The table below shows a summary of the rules in adding integers depending on its sign.

When adding positive integers, we simply add the numbers – just how we add whole numbers. The result of two positive integers will always be a positive number and should be greater than the given numbers.

The table below shows example of adding two positive integers.

When adding negative integers, the first thing to do is get its absolute value. Absolute value is the distance of a number from zero. For instance, the absolute value of -9 is 9. The result of adding negative integers will always result to a negative value.

1. Get the absolute value of the given numbers.
3. Place the negative sign on the final answer.

Example #1

What is the sum of -10 and -25?

Solution

Example #2

Determine the sum of -98 and -45.

Solution

Example #3

What is the result of adding -103 and -567?

Solution

### Adding positive and negative integers

When adding unlike signs, subtract the absolute values of two integers and then add the sign of the number to the greater absolute value.

Case 1: When the absolute value of the greater number is positive, the result is always positive.

To add unlike signs if the absolute value of the greater number is positive:

1. Get the absolute value of the given numbers.
2. Subtract the numbers.

Example #1

What is the sum of 10 and -3?

Solution

Example #2

Determine the result of adding -7 and 23.

Solution

Example #3

What is the sum of 98 and -42?

Solution

Case 2: When the absolute value of the greater number is negative, the result is always negative.

To add unlike signs if the absolute value of the greater number is negative:

1. Get the absolute value of the given numbers.
2. Subtract the numbers.
3. Write the negative sign on the final answer.

Example #1

Determine the sum of -25 and 9.

Solution

Example #2

What is the sum of 19 and -37?

Solution

Example #3

Find the sum of -108 and 49.

Solution

## How to subtract integers?

Subtraction generally refers to a reduction in value. However, since we have a positive and negative integers, the difference may increase or decrease in value.

Here’s a list of rules for subtracting integers:

• Subtracting a positive integer from a positive integer will result to a decrease in number.
• Subtracting a negative integer from a positive integer will result to an increase in number.
• Subtracting a positive integer from a negative integer will result to a decrease in number.

### Subtracting positive integers

When subtracting two positive integers, there are two cases that we need to consider.

• Case 1: If the minuend is greater than the subtrahend, then the final result is a positive number.
• Case 2: If the subtrahend is greater than the minuend, then the final answer is a negative number.

Case 1: When the minuend is greater than the subtrahend.

To subtract two positive integers if the minuend is greater than the subtrahend, simply subtract the numbers like subtracting a whole number.

The table below shows example of subtracting two positive integers if the minuend is greater than the subtrahend.

Case 2: When the subtrahend is greater than the minuend.

To subtract integers if the subtrahend is greater than the minuend:

1. Switch the position of number of the subtrahend and minuend.
2. Subtract accordingly.
3. Write negative sign on the final answer.

Example #1

What is the difference of subtracting 6 from 4?

Solution

Example #2

Find the result of 13 – 25.

Solution

Example #3

What is the difference if we subtract 162 from 57?

Solution

### Subtracting negative integers

When subtracting two negative integers, there are two cases that we need to consider.

• Case 1: If the absolute value of the minuend is greater than the absolute value of the subtrahend, the final result is a negative number.
• Case 2: If the subtrahend is greater than the minuend, then the result will always be a positive number.

Case 1: When the absolute value of the minuend is greater than the absolute value of subtrahend.

To subtract two negative integers if the absolute value of the minuend is greater than the absolute value of the subtrahend:

1. Multiply minus sign by the sign of the subtrahend.
2. Get the absolute value of the integers.
3. Subtract the numbers.

Example #1

What is the difference between -13 and -7?

Solution

Example #2

What is the result of subtracting -19 from -45?

Solution

Case 2: When the absolute value of the subtrahend is greater than the absolute value of minuend.

To subtract two negative integers if the absolute value of the subtrahend is greater than the absolute value of the minuend:

1. Multiply minus sign by the sign of the subtrahend.
2. Get the absolute value of the integers.
3. Switch the position of the subtrahend and minuend.
4. Subtract the numbers.

Example #1

What is the difference between -6 and -15?

Solution

Example #2

Determine the result of subtracting -51 from -29.

Solution

### Subtracting positive and negative integers

When subtracting integers with unlike sign, there are two cases that we need to consider:

• Case 1: If the minuend is a positive integer and the subtrahend is a negative integer, the result will be positive.
• Case 2: If the minuend is a negative integer and the subtrahend is a positive integer, the result will always be negative.

Case 1: When the minuend is a positive integer and the subtrahend is a negative integer.

To subtract two integers with unlike signs:

1. Multiply minus sign by the sign of the subtrahend.

Example #1

Find the difference of subtracting -19 from 31.

Solution

Example #2

What is the difference of subtracting -53 from 23?

Solution

Case 2: When the minuend is a negative integer and the subtrahend is a positive integer.

To subtract two integers with unlike signs:

1. Multiply minus sign by the sign of the subtrahend.
2. Get the absolute value of numbers.
4. Write negative sign on the final answer.

Example #1

What is the result of subtracting 15 from -8?

Solution

Example #2

Determine the difference of subtracting 71 from -43

Solution