An integer is a whole number that can be positive, negative, or zero. It does not include fractions or decimals.

- ... -3, -2, -1, 0, 1, 2, 3 ...

Integers can be categorized into three types: positive integers, negative integers, and zero.

Positive integers are whole numbers greater than zero. They are written without a sign.

Examples: 1, 2, 3, 4, ...

Negative integers are whole numbers less than zero. They are written with a negative sign ("-").

Examples: -1, -2, -3, -4, ...

Zero is a whole number that represents the absence of quantity. It is neither positive nor negative.

Example: 0

Integers can be represented on a number line, with positive integers to the right of zero and negative integers to the left of zero.

When adding integers with the same sign, add their absolute values and keep the sign.

Example: (-3) + (-5) = -8

When adding integers with different signs, subtract the smaller absolute value from the larger absolute value and keep the sign of the number with the larger absolute value.

Example: (-3) + 5 = 2

Subtracting an integer is the same as adding its opposite.

Example: (-7) - (-4) = (-7) + 4 = -3

When multiplying integers with the same sign, the product is positive. When multiplying integers with different signs, the product is negative.

Example: (-2) * 3 = -6

When dividing integers, the quotient has the same sign as the dividend if both numbers have the same sign. If the numbers have different signs, the quotient is negative.

Example: (-10) / (-2) = 5

When working with integers, it's important to understand the concepts of positive and negative numbers, as well as the rules for performing operations with integers. Here are some key points to remember when studying integers:

- Integers include positive numbers, negative numbers, and zero.
- Integers can be represented on a number line.
- Adding and subtracting integers involves considering the signs of the numbers.
- Multiplying and dividing integers also have rules based on the signs of the numbers being multiplied or divided.

Practice with various integer operations and familiarize yourself with the rules for each operation. Drawing number lines and using visual aids can also be helpful in understanding how integers work.

Remember that integers are used in many real-world situations, such as calculating temperatures, distances, and financial transactions. Understanding integers is an important foundational skill in mathematics.

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Geometry (NCTM)

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

Identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes.

Use visualization, spatial reasoning, and geometric modeling to solve problems.

Use geometric models to solve problems in other areas of mathematics, such as number and measurement.