# 3.1: Required Math Concepts

- Page ID
- 2316

## Numeral System and Notation

### Numbers

#### Natural numbers

#### Whole numbers

- Counting Numbers: 1, 2, 3, …
- Whole Numbers: 0, 1, 2, 3, …

#### Integers

{…,−3,−2,−1,0,1,2,3,…}. It is useful to note that the set of integers is made up of three distinct subsets: negative integers, zero, and positive integers. In this sense, the positive integers are just the natural numbers. Another way to think about it is that the natural numbers are a subset of the integers.

### Fractions

**Fractions** are a way to represent parts of a whole. It is written where and are integers and In a fraction, is called the numerator and is called the denominator. The denominator represents the number of equal parts the whole has been divided into, and the numerator represents how many parts are included. The denominator, cannot equal zero because division by zero is undefined.

of the circle. This type of model is called a fraction circle. Other shapes, such as rectangles, can also be used to model fractions.

represent? The fraction means two of three equal parts.

#### Improper and Proper Fractions

numerator is greater than or equal to the denominator, so its value is greater than or equal to one. Fractions such as , , , and are called improper fractions.

, , and are proper fractions.

#### Equivalent Fractions

and have the same value, 1. Figure shows two images: a single pizza on the left, cut into two equal pieces, and a second pizza of the same size, cut into eight pieces on the right. This is a way to show that is equivalent to . In other words, they are equivalent fractions.

is equivalent to .

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