Introduction to integers

Introduction to Introduction to IntegersIntegers

Integers Defined…Integers Defined…• An integer (pronounced IN-tuh-jer)

o is a whole number o Is not a fraction. o Is a number that can be positive, negative, or zero.

-6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6

opposite integers

negative integers positive integers

Four real life situations in which integers can Four real life situations in which integers can

be used.be used.

• Spending and earning money• Rising and falling temperatures• Stock market gains and losses• Gaining or losing metres in an NRL game.

Note: A positive integer does not have to have a + sign. For example, +3 and 3 are the same.

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10

Multiplying IntegersMultiplying Integers

Dividing IntegersDividing Integers

Adding and Adding and Subtracting with Subtracting with

IntegersIntegers

Using a number line you add by moving to the right.e.g. -2+3 = 1 (As shown on the diagram below).

Subtracting IntegersSubtracting IntegersSimilarly, when you are subtracting integers, you areMoving the arrow to the left.

No matter where you start on the numberline, you always move to the left. E.g. (-5) – 2 = -7

Adding and Adding and Subtracting IntegersSubtracting Integers

Some different, slightly more difficult examples

•3+(-7) becomes 3 – 7 = -4•-5 + (-2) becomes -5 – 2 = -7

•5-(-3) becomes 5 + 3 = 8•-6-(-3) becomes -6 + 3 = -3

The Problem:The Problem:• The highest elevation in Northern Lookout is

Snow Peak, which is 15 237 metres above sea level. The lowest elevation is Tree Valley, which is 368 metres below sea level. What is the distance from the top of Snow Peak to the bottom of Tree Valley?

SolutionSolutionWe can represent each elevation as an integer:  

Elevation Integer15 237 metres above sea level

+15 237

Sea level 0368 metres below sea level

-368

The distance from the top of Snow Peak to the bottom of Tree Valley is the same as the distance from +15 237 to -368 on the number line. We add the distance from +15 237 to 0, and the distance from 0 to -368, for a total of 15 605 metres.

• Integers are the set of whole numbers and their opposites

• Whole numbers larger than zero are called positive integers; whole numbers less than zero are called negative integers

• The integer zero is neither positive nor negative. • Two integers are opposites if they are the same

distance away from zero, but on opposite sides of the number line.

• Positive integers may be written with or without a sign.