Subtracting Integers

Subtracting Integers: Subtraction of integers is a fundamental operation in mathematics that involves finding the difference between two integers. Understanding how to subtract integers is important for various mathematical applications including algebra, geometry, and calculus.

To perform integer subtraction, invert the sign of the number being subtracted (the subtrahend). When subtracting numbers that share the same sign, simply add their absolute values together and retain the shared sign in the answer. On the other hand, if the numbers have different signs, calculate the absolute difference between them and assign the result the sign of the number with the larger absolute value.

In this article, we will discuss subtracting integers in detail, and will learn how to subtract integers of the same sign, and of different signs, along with the properties of subtraction of integers.

Subtracting Integers in Math

Subtracting integers involves finding the difference between two numbers, taking into account their signs. It’s the process of finding how much one number is less than or greater than another on the number line.

Subtracting integers involves finding the difference between two integers, considering their signs. When subtracting integers, it’s essential to understand the concept of positive and negative numbers and how they interact with each other.

Subtracting Integers Definition

Subtraction of integers involves finding the difference between two integers where one integer is being taken away from another. Subtracting integers means operating subtraction on positive and negative whole numbers.

Subtrahend and Minuend

Subtrahend is the number being subtracted while the minuend is the number from which another number is subtracted.

In the expression ‘a – b’ where a is the minuend and b is the subtrahend, the result represents the difference between the two numbers. In other words, the number from which another number is subtracted is called the minuend, and the number being subtracted is called the subtrahend.

How to Subtract Integers

To subtract integers, subtract the numbers as usual and apply the rules for signs mentioned above. Rules for Subtracting Integers are listed below:

Step 1: To subtract integers, follow these steps:

Step 2: Identify the minuend (the number from which another number is subtracted) and the subtrahend (the number being subtracted).

Step 3: If the signs of both integers are the same, subtract their absolute values and assign the same sign to the result.

Step 4: If the signs are different, subtract their absolute values, and the result takes the sign of the integer with the greater absolute value.

The result obtained is the difference between the two integers.

Subtracting Integers Rules Chart

Subtracting Integers Rules Chart

Rules on Subtracting Integers

Various rules of operation are,

• Subtracting integers with the same sign: Subtract the absolute values and keep the sign of the larger number.
• Subtracting integers with different signs: Treat it as adding the opposite. Subtract the absolute values and take the sign of the number with the greater absolute value.
• Subtracting a positive integer from another positive integer results in a positive integer.
• Subtracting a negative integer from another negative integer results in a positive integer.
• Subtracting a negative integer from a positive integer results in adding the two numbers.
• When subtracting integers with different signs, subtract the absolute values and keep the sign of the number with the greater absolute value. Example: (-7) – 3 = -10
• When subtracting integers with the same sign, subtract the absolute values and keep the common sign. Example: (-4) – (-2) = -2
• Subtracting from Zero: Subtracting an integer from zero is straightforward, it retains the sign of the integer being subtracted. Example: 0 – (-5) = 5

Positive – Positive	Positive – Negative	Negative – Positive	Negative – Negative
Positive	Negative	Negative	Positive
Negative	Positive	Negative	Positive

Subtracting Integers with Same Sign

When subtracting integers with the same sign, the process is straightforward. Simply subtract the absolute values of the numbers and keep the sign of the larger number.

Here are the steps for subtracting integers with the same sign :

Step 1: Identify the sign of the integers you’re subtracting. If they have the same sign, proceed to the next step.

Step 2: Subtract the absolute values of the integers. Ignore the signs while performing subtraction.

Step 3: Assign the common sign to the result. Since the integers have the same sign, the result will also have that sign.

Example: Subtracting (-7) – (-3):

Both integers have a negative sign, so they have the same sign.

Subtract the absolute values:

|-7| – |-3| = 7 – 3 = 4

Result takes the negative sign, so the answer is -4.

Subtracting Integers with Different Signs

When subtracting integers with different signs, it’s akin to adding the opposite. Subtract the absolute values and take the sign of the number with the greater absolute value.

Here are the steps for subtracting integers with different sign :

Step 1: Determine the signs of the integers you’re subtracting. If they have different signs, proceed to the next step.

Step 2: Subtract the absolute values of the integers. Ignore the signs while performing subtraction.

Step 3: Assign the sign of the number with the greater absolute value to the result.

Example: Subtracting (-7) – 3:

Signs of the integers are different.

Subtract the absolute values:

|-7| – |3| = 7 – 3 = 4

Since 7 has the greater absolute value and it’s negative, the result takes the negative sign so the answer is -4.

Subtracting Integers on Number Line

Subtracting integers on a number line involves moving to the left (for subtraction) or to the right (for addition) from a starting point. When subtracting integers, move to the left if subtracting a positive integer and to the right if subtracting a negative integer. On a number line, it is thus the subtracting of integers involves moving to the left for positive integers and to the right for negative integers.

To subtract integers on a number line, follow these steps:

Step 1: Start at the initial position: Locate the first integer on the number line.

Step 2: Move to the left or right: Depending on whether you are subtracting a positive or negative integer, move in the opposite direction along the number line.

Step 3: Number of steps: Move the number of steps equal to the absolute value of the integer being subtracted.

Step 4: Final position: The final position is where you end up on the number line after the subtraction.

For example, subtracting -3 from 5:

Step 1: Start at 5 on the number line.

Step 2: Since we are subtracting a negative integer (-3), move to the right (positive direction).

Step 3: Move 3 steps to the right.

Step 4: End up at 8 on the number line, which is the result of 5 – (-3) = 8

Subtracting Integers on a Number Line

Subtracting Integers – Properties

When subtracting integers, several properties hold true:

• Closure property: The difference of any two integers is always an integer.
• Associative property: Subtraction is associative, meaning the grouping of integers being subtracted does not affect the result. For example, (a – b) – c = a – (b – c).
• Identity property: Subtracting zero from any integer leaves the integer unchanged.
• Inverse property: The difference between an integer and its additive inverse (its negative) is always zero.
• Subtraction of integers is not commutative.
• Subtraction of integers is associative.
• Subtraction of integers is distributive over addition.

People Also Read:

• Rational Numbers
• Integers
• Arithmetic Operations
• What is the rule for subtracting negative numbers?

Subtracting Integers Examples

Question 1: Joe had $50 in his wallet. He spent $25 on groceries. What is the balance in his wallet now?

Solution:

Joe had $50 initially

He spent $25 on groceries

To find the balance, subtract the amount spent from the initial amount:

$50 – $25 = $25

Question 2: A submarine descended 300 meters below sea level. Later, it ascended 150 meters. How far below sea level is the submarine now?

Solution:

Submarine descended 300 meters below sea level.

It then ascended 150 meters.

To find the current depth, subtract the ascent from the descent:

300 meters – 150 meters = 150 meters below sea level.

Question 3: In a football game, a team lost 15 yards on one play and gained 20 yards on the next. What is the net change in yards for the team?

Solution:

Team lost 15 yards and gained 20 yards.

To find the net change, subtract the lost yards from the gained yards:

20 yards – 15 yards

= +5 yards

Question 4: Sarah has a debt of $200. She paid back $50. What is her remaining debt?

Solution:

Sarah had a debt of $200.

She paid back $50.

To find remaining debt, subtract the amount paid back from the initial debt:

$200 – $50 = $150

Question 5: A temperature drops by 8 degrees Celsius overnight and then rises by 5 degrees Celsius during the day. What is the net change in temperature?

Solution:

Temperature dropped by 8 degrees Celsius and then rose by 5 degrees Celsius.

To find the net change, subtract the decrease from the increase:

5 °C – 8 °C

= -3 °C

Subtracting Integers Worksheet

Problem 1: A lift was at the 5th floor. It descended 3 floors and then ascended 7 floors. Which floor is the lift on now?

Problem 2: Mary has a collection of 15 books. She gave away 7 books to her friend. How many books does Mary have left?

Problem 3: In a quiz, a student scored -5 points in one round and then scored 10 points in the next round. What is the student’s total score?

Problem 4: A company had a profit of $500 last month but incurred a loss of $300 this month. What is the net profit or loss for the company over these two months?

Problem 5: A car traveled 50 kilometers north and then turned around and traveled 30 kilometers south. How far is the car from its starting point?

FAQs on Subtracting Integers

What is the rule for subtracting integers?

Table of Rules for Subtracting Integers

Signs of Integers	Operation	Sign of Answer
(+) – (+)	Subtract	Sign of Larger Integer
(-) – (-)	Subtract	Sign of Larger Integer
(+) – (-)	Add	+
(-) – (+)	Add	–

What is an example of a subtraction of integers?

An example of a subtraction of integers is subtracting (-6) from 11, that is 11 – (-6), i.e. 11 + 6 = 17.

What are the rules for subtracting positive and negative numbers?

Subtracting positive number from negative number results in the sum of modulus of both number with negative sign in front of them.

Can result of subtracting two integers be a fraction?

No, the result of subtracting two integers is always an integer.

What happens when the subtrahend is greater than the minuend?

When the subtrahend is greater than the minuend, the result is negative.

What does subtracting a negative number mean?

Subtracting a negative number is equivalent to adding its positive counterpart.

Is subtraction commutative?

No, subtraction is not commutative; changing the order of the numbers being subtracted changes the result.

Can you subtract a positive number from a negative number?

Yes, subtracting a positive number from a negative number is equivalent to adding their absolute values with the negative sign.

What about subtracting integers with different signs?

When subtracting integers with different signs, treat it as adding the opposite. Subtract the absolute values and take the sign of the number with the greater absolute value.

Can you explain subtracting integers using a number line?

Yes, on a number line, moving to the left represents subtraction, while moving to the right represents addition. Subtracting integers means moving to the left on the number line.

What happens when you subtract a negative integer?

Subtracting a negative integer is equivalent to adding a positive integer. It results in an increase in value.

Is subtracting integers different from adding integers?

Yes, subtracting integers involves finding the difference between two numbers, whereas adding integers involves finding the sum of two numbers.

Can you subtract more than two integers at once?

Yes, you can subtract more than two integers at once by subtracting one number at a time or using parentheses to group the numbers.

What is the subtracting integers formula?

There is no formula for subtracting integers. Only sign of the integers is taken into consideration while performing normal subtraction.