Introduction

A set of positive and negative integers, including zero, is known as an integer. A visual representation of integers on a number line refers to the definition of integers on a number line. On a number line, integers assist us in performing various arithmetic operations. For example, integers are represented by utilizing a number line. A number line is a graph that depicts numbers in a straight line. It is made up of positive numbers like 1, 2…, negative integers like – 1, – 2…, and 0, which are neither positive nor negative.

Addition and Subtraction of Integers on Number Line

We will now learn to perform arithmetic operations on integers on a number line, such as addition and subtraction.

Points to Remember When Performing Integer Arithmetic Operations on a Number Line:

  • Always begin with “0.”
  • If the number is positive, move to the right side.
  • If the number is negative, move to the left side.

Addition of Integers on Number Line

On a number line, you add integers by glancing at the sign of the second addend. We go towards the right side if we add a positive number to the given integer, and we move towards the left side if we add a negative number to the given integer. Let’s look at a few examples of integer addition on a number line.

Subtraction of Integers using Number Line

On a number line, subtracting integers is done by looking at the sign of the subtrahend. To deduct a positive integer, interchange the number line to the left, and to remove a negative integer, move the number line to the right.

Multiplication and Division of Integers

Integer multiplication and division are two of the most basic operations on integers. Multiplication of integers is the same as repetitive addition, which involves repeatedly adding an integer. 4 × 3 indicates, for example, adding 4 three times, i.e., 4 + 4 + 4 Equals 12. Equal grouping or dividing an integer into a certain number of groups is called integer division. For example, -6 ÷ 2 divides -6 into two equal pieces, yielding -3.

Multiplication of Integers

Integer multiplication is the process of adding positive and negative numbers repeatedly, or we can say integers. When it comes to the multiplication of integers on a number line, the following considerations must be made:

  • Two positive numbers multiplied
  • Two negative numbers multiplied
  • One positive and one negative number multiplied
  • Positive x Positive = Positive = 2 × 5 = 10 when multiplying integers with two positive signs.
  • Negative x Negative = Positive = –2 × –3 = 6when multiplying integers with two negative signs.
  • Negative x Positive = Negative = –2 × 5 = –10 when multiplying integers with one negative and one positive sign.

Multiplication of Integers Rules and Steps

Integer multiplication is fairly similar to regular multiplication. However, because integers include both negative and positive numbers, we must remember certain rules or conditions while multiplying them, as we saw in the previous section. So, let’s have a look at how to multiply integers.

Step 1: Determine the integers’ absolute value.

Step 2: Calculate the absolute value of the product of the absolute values

Step 3: Determine the sign of the number according to the rules or criteria once the product has been obtained.

Division of Integers

The grouping of elements is involved in integer division. It consists of both positive and negative numbers. The division of integers, like multiplication, involves the same circumstances.

  • Subtracting two positive numbers
  • Dividing a negative number by a positive number
  • Dividing two numbers, one positive and one negative

When two positive signs are used to divide numbers, Positive = Positive 16 ÷ 8 = 2.

Negative Negative Equals Positive –16 –8 = 2 when two negative signs divide integers.

Negative Positive = Negative – –16 ÷ 8 = –2when dividing numbers with one negative and one positive sign.

To summarise and make things simple, the two most important elements to keep in mind when multiplying or dividing integers are:

  • The response is always negative when the signs are different.
  • When all signals are positive, the answer is always yes.

Multiplication and Division of Integers Tips and Tricks:

  • There is no such thing as the lowest or largest integer.
  • 1 is the lowest positive integer, and -1 is the largest negative integer.
  • The PEMDAS rule applies to integer operations. Brackets, Squares, Powers, Square Roots, Division, Multiplication, Addition, and Subtraction are all examples of “operations.”

Conclusion

The basic arithmetic operations (addition, subtraction, multiplication, and division) will be included in integer operations. In mathematics, integers on the number line include all positive, negative, and zero values but do not include fractions. As a result, working with integers on the number line is simple.