##### Chapter 1

## Number System

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

#### Introduction

**with numbers**. There are several different kinds of number structures in mathematics, such as binary, decimal, etc.

A number structure is a way of expressing numbers by writing. It is a mathematical notation for consistently representing numbers from a particular series using digits or other symbols. It reflects the arithmetic and algebraic structure of the figures and offers a specific representation for each number. We may also do mathematical operations like addition, subtraction, and division with it.

The meaning of any digit in a number can be calculated using the following formula:

- The digit
- Its position in the number
- The base of the number system

**Natural numbers **are a set of positive integers ranging from 1 to infinity, besides fractional and decimal numbers. They are sometimes classified as number counts.

Natural number types include:

- Prime numbers
- Even and Odd numbers
- Composite numbers
- Co-prime numbers
- Perfect numbers

**Whole numbers **are a set of positive integers that include 0 and range from 0 to infinity. They also exclude the fractional and decimal parts.

A fraction is a numerical value that denotes the components of a larger whole. If a number is separated into four bits, it is denoted by the symbol x/4. As a result, the fraction x/4 denotes 1/4th of the integer x. Fractions have a significant role in our everyday lives. There are many instances of fractions that you can see in everyday life. We have to share the delicious pizza with our friends and family, whether we want to or not. Four slices for three participants.

Fractions are classified into various forms based on the properties of the numerator and denominator. They are as follows:

- Like fractions
- Unlike fractions
**Equivalent fractions**- Mixed fractions
- Improper fractions
- Proper fractions

A fraction is a portion of a whole or a set of equivalent components. It is often necessary to equate two fractions to determine which is greater or smaller. There are two techniques for comparing fractions in mathematics.

**Using the Decimal Method to Compare Fractions**

Each fraction is translated to a decimal using the decimal system by dividing the numerator by the denominator. The decimal value is compared after separation.**Using the Same Denominator Method to Compare Fractions**

As we all know, any fraction includes two terms: the numerator and the denominator. The numerator is at the top, while the denominator is at the bottom. Consider the fraction 3/4 as an example. The numerator is 3, and the denominator is 4.

While arithmetic includes several other updated operations, the core operations are addition and subtraction, division, and multiplication.

**Addition**

The addition is one of the most fundamental arithmetic processes. The addition incorporates two or more ideas into a common word at the most basic shape.**Subtraction**

Subtraction is known as the antithesis of inclusion. It calculates the discrepancy between two numbers, i.e. the subtrahend minus the minuend. The distinction is positive if the minuend is larger than the subtrahend. The answer is negative if the minuend is smaller than the subtrahend, and 0 if the numbers are equivalent.**Multiplication**

Multiplication often transforms two quantities, such as addition and subtraction, into a single value referred to as the element. The multiplicand and multiplier, or both as variables, are the two initial values.The multiplication of two numbers is written as ab or a x b. It is sometimes represented as a*b (asterisk) in machine languages where only characters present on keyboards are used.**Division**

It is the opposite of differentiation. It finds the quotient of two numbers, which is the dividend separated by the divisor. If the dividend is greater than the divisor for every well-defined positive integer, the quotient is greater than 1; else, it is less than 1.

The terms within the brackets may be simplified explicitly. We may conduct division, multiplication, addition, and subtraction in the order specified within the bracket. This concept is a part of the BODMAS rule.

In this chapter, we learned about the basics of number systems. We gathered knowledge of fractions and their related concepts.

**What are the different types of number systems?**The number structure is nothing more than a way of representing or expressing quantities. The decimal number system, binary number system, octal number system, and hexadecimal number system are the most widely employed number systems.

**What is the significance of the number system?**The number scheme aids in representing numbers in a limited symbol range. In general, computers use binary numbers 0 and 1 to simplify calculations and reduce the amount of circuitry required, resulting in the least amount of space, energy usage, and expense.

**Explain fractions.**Fractions are integer quantities that are a fraction of a whole number. As a number or an object is separated into equivalent sections, each component becomes a fraction of the total. Where an is the numerator and b is the denominator, a fraction is written as a/b.

**In math, what are the three kinds of fractions?**Mixed fractions, improper fractions, and proper fractions are the three groups of fractions of mathematics.**What is the concept of a unit fraction?**

A division with a unit(one) numerator is known as a unit fraction.