Slideshow 1, Mr Richard Sasaki, Room 307 Inequalities and the Number Line

Objectives Recall how to use the number line.Recall how to use the number line. Recall which numbers are greater than, less than and equal to other numbersRecall which numbers are greater than, less than and equal to other numbers Represent this with inequalitiesRepresent this with inequalities

Chapter 1 Today we will start our regular maths lessons! The first chapter is all about negative numbers. Most people normally find Chapter 1 the easiest in each grade. In some ways, chapter 1 is the most important for each grade. We will be using negative numbers throughout the year so it’s important we get a strong basis. First we will look at the number line.

Number Sets Number sets are likely the most fundamental thing in maths. They group all numbers. We will learn about sets in Grade 8 but we should understand… The Integer Set - All “whole numbers”, positive, negative and zero… The Real Number Set - All integers, decimal numbers, fractions & irrational numbers… Note: The meanings of “Integer” and “Real Number” is important, try to remember them!

The Number Line The number line usually shows integers only but implies all real numbers (unless stated). It looks something like… It does include numbers like 1.5 or 7, even though it doesn’t show them. In fact, it includes all numbers from to.

The Number Line (Positive) Let’s look at a segment of the number line. We can easily see here which numbers are greater than others. Numbers on the are greater than numbers on the. right left This fact is always true. Look at 4 and 6 on the number line. Which is larger? larger How can we show this mathematically?

Inequalities We use inequalities to show how numbers differ. In this case we would write… This is read as. ). equal to 4 Why not?

Identifying Positions of Numbers Once again as mentioned before, all real numbers are included on the number line (and segments). Where is 4.5 on the number line? 4.5

Less than More than / Greater than We couldn’t label a number like this accurately enough. < > <> Decimal numbers / tenths / hundredths / real numbers

Less than or equal to Not equal to >> >< The gaps between numbers are uneven & getting smaller. The gaps should get smaller between values towards the left. Less than – The value is lower than (on the left of) Smaller than – The “weight” is less Larger than – The “weight” is greater More than – The value is higher than (on the right of) Integers – All whole numbers (including 0 and negative numbers) Natural Numbers – Counting Numbers (usually positive numbers only, it is disputed whether 0 is included or not.)