Mathematics Operations of Integers

Integers are all the numbers in Mathematics, excluding fractions. There are four operations of integers, addition, subtraction, multiplication, and division. Integers include positive numbers, negative numbers, and also zero. Addition includes adding two integers together, subtraction includes subtracting the smaller integer from the larger one, multiplication includes the product of the integers.

Read Also: Fractions on Number Line

Key Takeaways: Integers, number line, addition, subtraction, multiplication, division

---

What are Integers?

[Click Here for Sample Questions]

Integers are all the numbers in Mathematics, excluding fractions. Integers include numbers with both the signs, negative and positive and zero. The fractions are not included in the integers. Integers can undergo all the arithmetic operations.

For example: 1, -17, 0, etc.

All the integers can be represented on a number line. The numbers on the right of 0 are positive, and the numbers on the left of 0 are negative.

Integers

Check Important Notes for Rational Numbers on Number Line

---

Operations of Integers

[Click Here for Sample Questions]

Operations of integers include all the arithmetic equations that can be carried out for integers. There are four types of operations which can be carried out with integers. The four different arithmetic operations are as follows.

Addition

The operation addition includes adding the two integers. Addition can be applied to both positive and negative integers. Scenarios with positive and negative integers are as follows:

• Both are positive integers: This causes the addition of both the integers and then a greater integer is obtained. For example, 2+5=7, 7 is greater than 2 and 5.
• Both are negative integers: This causes the addition of both the integers and then a smaller integer is obtained. For example, -2 + (-5) = -7, -7 is smaller than -2 and -5.
• One is positive, and another is a negative integer: This scenario does not result in addition. This results in subtraction which is explained below.

Subtraction

The operation subtraction includes adding the two integers. Subtraction can be applied to both positive and negative integers. Scenarios with positive and negative integers are as follows:

• Both integers have the same sign: This causes subtraction of the smaller integer from the larger integers.
  • Positive integers: For example, (+5) - (+2) = 5-2 = 3.
  • Negative integers: For example, (-5) - (-2)= -5+2 = -3.
• Both integers have different signs: This can result in addition or subtraction. It depends on the nature of signs present.
  • For example : (+5) - (-2)=5+2 = 7.
  • -2 - (+5)= -2-5=-7

Also Read: Natural numbers

Multiplication

Multiplication results in the formation of larger, or smaller integers from the integers involved.

• Both integers have the same sign: When both integers have the same sign, it always results in a positive sign.

Positive integers: For example, (+5) X (+2)= 10.

Negative integers: For example, (-5) X (-14)= 70.

• Both integers have different signs: When both integers have different signs, it always results in a negative sign. For example : (+5) X (-2)= -10.

Division

Division results in the formation of smaller integers from the integers involved. The result can also be a fraction.

• Both integers have the same sign: When both integers have the same sign, it always results in a positive sign.

Positive integers: For example, (+14) \(\div \) (+2)= 7

Negative integers: For example, (-2) \(\div \) (-14)= 1/7

• Both integers have different signs: When both integers have different signs, it always results in a negative sign. For example : (+15) \(\div \) (-3)= -5.

Check More: Degree of Polynomials

---

Things to Remember

[Click Here for Sample Questions]

• Integers are all the numbers in Mathematics, excluding fractions. Integers include numbers with both the signs, negative, positive and zero.
• There are four operations of integers, addition, subtraction, multiplication, and division.
• Addition of different integers with the same sign results in the sum of integers with the same sign.
• Addition of different integers with different signs will result in the difference of integers with the sign of greater value, it also causes subtraction of the smaller integers from the larger integers.
• Similar is the case with subtraction.
• Multiplication and division of two same signed integers will result in a positive value and in the case of two different signed integers will result in a negative value.

Read More: Roots of Polynomials

---