Integers in the Number System

Number System

Integers

• A set of whole numbers and their negatives (including zero)
• Can be positive, negative, or zero
• Examples: ..., -3, -2, -1, 0, 1, 2, 3, ...
• Can be represented on the number line
• Properties:
  • Closure: The result of adding or multiplying two integers is always an integer
  • Commutative property: The order of integers does not change the result of addition or multiplication
  • Associative property: The order in which integers are added or multiplied does not change the result

Decimals

• A way to represent fractions using a base-10 number system
• Consist of a whole number part and a fractional part separated by a decimal point
• Examples: 0.5, 3.14, 2.78
• Can be converted to fractions
• Can be used to represent repeating or non-repeating decimals

Whole Numbers

• A set of non-negative integers (including zero)
• Examples: 0, 1, 2, 3, 4, 5, ...
• Properties:
  • Closure: The result of adding or multiplying two whole numbers is always a whole number
  • Commutative property: The order of whole numbers does not change the result of addition or multiplication
  • Associative property: The order in which whole numbers are added or multiplied does not change the result

Fractions

• A way to represent part of a whole
• Consist of a numerator (top number) and a denominator (bottom number)
• Examples: 1/2, 3/4, 2/3
• Can be simplified by dividing both numerator and denominator by their greatest common divisor
• Can be converted to decimals
• Types:
  1. Proper fractions: Numerator is less than the denominator
  2. Improper fractions: Numerator is greater than or equal to the denominator
  3. Mixed fractions: A combination of a whole number and a proper fraction

Number System

• Integers are a set of whole numbers and their negatives, including zero.
• Integers can be positive, negative, or zero.
• Examples of integers include ..., -3, -2, -1, 0, 1, 2, 3, ...
• Integers can be represented on the number line.

Properties of Integers

• Closure: The result of adding or multiplying two integers is always an integer.
• Commutative property: The order of integers does not change the result of addition or multiplication.
• Associative property: The order in which integers are added or multiplied does not change the result.

Decimals

• Decimals are a way to represent fractions using a base-10 number system.
• Decimals consist of a whole number part and a fractional part separated by a decimal point.
• Examples of decimals include 0.5, 3.14, 2.78.
• Decimals can be converted to fractions.
• Decimals can be used to represent repeating or non-repeating decimals.

Whole Numbers

• Whole numbers are a set of non-negative integers, including zero.
• Examples of whole numbers include 0, 1, 2, 3, 4, 5, ...

Properties of Whole Numbers

• Closure: The result of adding or multiplying two whole numbers is always a whole number.
• Commutative property: The order of whole numbers does not change the result of addition or multiplication.
• Associative property: The order in which whole numbers are added or multiplied does not change the result.

Fractions

• Fractions are a way to represent part of a whole.
• Fractions consist of a numerator (top number) and a denominator (bottom number).
• Examples of fractions include 1/2, 3/4, 2/3.
• Fractions can be simplified by dividing both numerator and denominator by their greatest common divisor.
• Fractions can be converted to decimals.

Types of Fractions

• Proper fractions: Numerator is less than the denominator.
• Improper fractions: Numerator is greater than or equal to the denominator.
• Mixed fractions: A combination of a whole number and a proper fraction.

Number System

• A fraction represents part of a whole and consists of a numerator (top number) and a denominator (bottom number).
• The numerator tells how many equal parts are being referred to, and the denominator tells how many parts the whole is divided into.
• Examples of fractions include 1/2, 3/4, and 2/3.
• Fractions can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD).

Whole Numbers

• A whole number is a positive integer, including 0.
• Examples of whole numbers include 0, 1, 2, 3, and so on.
• Whole numbers can be added, subtracted, multiplied, and divided (except by 0).
• Whole numbers can be represented on a number line.

Decimals

• A decimal is a way to represent a fraction with a denominator that is a power of 10.
• Examples of decimals include 0.5, 3.14, and 2.78.
• Decimals can be added, subtracted, multiplied, and divided (except by 0).
• Decimals can be converted to fractions by dividing by a power of 10.

Integers

• An integer is a whole number, either positive, negative, or zero.
• Examples of integers include ..., -3, -2, -1, 0, 1, 2, 3, and so on.
• Integers can be added, subtracted, multiplied, and divided (except by 0).
• Integers can be represented on a number line.

Percentages

• A percentage is a way to represent a fraction with a denominator of 100.
• Examples of percentages include 25%, 50%, and 75%.
• Percentages can be converted to decimals by dividing by 100.
• Percentages can be used to represent proportions, ratios, and increases/decreases.
• Examples of percentage calculations include:
  • Increase: 25% of 100 = 25
  • Decrease: 25% of 100 = -25 (subtracted from 100)
  • Proportion: 25% of 80 = 20