Slideshow 1, Mr Richard Sasaki, Room 307

Slideshow 1, Mr Richard Sasaki, Room 307

Inequalities and the Number Line

Inequalities and the Number Line

Objectives

• Recall how to use the number line.• Recall which numbers are greater than,

less than and equal to other numbers• Represent 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 SetsNumber 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… 0 ,1 ,2 ,3 ,……,−2,−1 ,

The Real Number Set -

All integers, decimal numbers, fractions & irrational numbers…

0 ,1 ,2 ,3 ,……,−2,−1 , ,12,13,…,23,…,𝜋 ,√2 ,…

Note: The meanings of “Integer” and “Real Number” is important, try to remember them!

The Number LineThe number line usually shows integers only but implies all real numbers (unless stated).

It looks something like…

0 1 2 3 4 5-1-2

-3-4-5It does include numbers like 1.5 or 7, even though it doesn’t show them.In fact, it includes all numbers from to .−∞∞

−∞ ∞

Note: Infinity ( isn’t really a number. It’s like a boundary that is unmeasurable or an amount that is uncountable.

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 .

rightleftThis fact is always

true.Look at 4 and 6 on the number line.

Which is larger?

larger

How can we show this mathematically?

InequalitiesWe use inequalities to show how numbers differ.

In this case we would write…

6>4This is read as .

is greater than

We shouldn’t write , this is bad practice, but we can say . is less than

We also shouldn’t write (

is greater than or).equal to

4Why not?Of course, 6 cannot be equal to 4. carries the meaning

of and .

Identifying Positions of NumbersOnce 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

Where is on the number line?

52

Where is on the number line?

13

Where is on the number line?

3.1

Less thanMore than / Greater than

2.5 92

We couldn’t label a number like this accurately enough.

< >< >

Decimal numbers / tenths / hundredths / real numbers

0.36514

13

Less than or equal toNot equal to

> >

> <

The gaps between numbers are uneven & getting smaller.940

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 lessLarger than – The “weight” is

greaterMore 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.)