The Complete Guide to Understanding Integers and Their Operations

Integers

Integers are a set of numbers that include both positive and negative numbers, as well as zero

Integers are a set of numbers that include both positive and negative numbers, as well as zero. They can be represented on the number line and are denoted by the symbol “Z”. In mathematical terms, integers are a subset of the real numbers.

Integers can be either whole numbers (such as -2, -1, 0, 1, 2), or their negatives, depending on whether they lie to the left or right of zero on the number line. They are used to represent quantities like temperature, elevation, or position where negative values indicate a decrease or direction opposite to a reference point.

Integers can be classified into different types, such as:

Positive Integers: These are the numbers greater than zero. They include numbers like 1, 2, 3, and so on.

Negative Integers: These are the numbers less than zero. They include numbers like -1, -2, -3, and so on.

Zero: This is neither a positive nor a negative integer. It lies at the origin of the number line.

To perform basic operations with integers, we can follow these rules:

1. Addition: To add integers, we add the numbers together. If the signs of the numbers are the same (both positive or both negative), we add their absolute values and keep the common sign. If the signs are different, we subtract the smaller absolute value from the larger and keep the sign of the number with the larger absolute value.

Example: -5 + 3 = -2

2. Subtraction: To subtract integers, we change the subtraction operation into addition and then follow the rules for addition.

Example: 7 – 4 = 7 + (-4) = 3

3. Multiplication: To multiply integers, we multiply the numbers together. If the signs of the numbers are the same, the result is positive. If the signs are different, the result is negative.

Example: (-2) × (-3) = 6

4. Division: To divide integers, we divide the numbers and apply the following rules:

– A positive number divided by a positive number results in a positive quotient.
– A negative number divided by a negative number results in a positive quotient.
– A positive number divided by a negative number results in a negative quotient.
– Zero divided by any non-zero number is zero.

Example: (-12) ÷ (3) = -4

Understanding integers and their operations can be helpful in various mathematical concepts, such as algebra, number theory, and even real-life scenarios involving positive and negative quantities.

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