## CHAPTER 2 - FRACTIONS AND DECIMALS

__OBJECTIVES__

- Identify the types of fractions and perform computations with them.
- Determine the least common denominator (LCD).
- Read, write, and round decimal numbers.
- Solve problems involving fractions and decimal numbers.
- Determine the relationship between fractions and decimal numbers.
- Perform arithmetic operations combined with fractions and decimal numbers.

__CHAPTER OUTLINE__

2.1 Fractions

2.2 Arithmetic Operations with Fractions

2.3 Decimal Numbers

2.4 Arithmetic Operations with Decimal Numbers

2.5 Converting Between Fractions and Decimal Numbers and Combined Order of Operations

2 Review Exercises

2 Self-Test Exercises

### Introduction

In the previous chapter, we learned about whole numbers and how to perform basic arithmetic operations with whole numbers. However, measurements and calculations of quantities, values, amounts, etc., cannot always be represented by whole numbers. Most of these involve portions of whole numbers, which are represented by **fractions** and **decimal numbers**.

Fractions and decimal numbers are used to express values that are a portion of a whole number. Fractions are widely used throughout mathematics, including in measurement, probability, and data applications. Decimal numbers are a special type of fraction that express numbers as a portion of powers of 10 (10, 100, 1,000, etc.).

Fractions and decimal numbers have different benefits. Fractions can be more precise than decimal numbers; for example, it is impossible to exactly represent the fraction [latex] $\displaystyle{\frac{1}{3}}$ [/latex] as a decimal number.

However, it is easier to read, write, and perform arithmetic operations with decimal numbers than it is with fractions. In addition, it is easier to determine the magnitude of numbers when they are expressed as decimal numbers rather than as fractions. For example, it is easier to recognize that the decimal number 7.75, as opposed to its fractional form [latex] $\displaystyle{\frac{31}{4}}$ [/latex], lies between the whole numbers 7 and 8.

In this chapter, we will learn about the different types of fractions and decimal numbers and the methods to convert them from one form to the other. As well, we will learn to perform arithmetic operations with fractions and decimal numbers, including powers and square roots.

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