Integers

Mathayomsuksa 3

Vocabulary

integers

Vocabulary

positive number

Vocabulary

negative number

Vocabulary

addition

Vocabulary

subtraction

Structure

ModifiersA modifier can be an adjective, an

adverb, or a phrase or clause acting as an adjective or adverb In every case, the basic principle is the same: the modifier adds information to another element in the sentence.

Look at the following examples below

On a number line, a movement to the left is used to show subtracting a positive number.

A positive number

prepositional phrase

adjective

Integers

The positive whole number 1, 2, 3, 4, ……….., and the negative whole number -1, -2, -3, -4, ……., are marked on it.

Negative Integers:Less than zero

Positive Integers:More than zero

Zero is neither negative or positive

Order of Integers

Integers are arranged in order on the numberline so that for any two integers, the smallerintegers always lie to the left of the largeintegers For example, 3 lies to the left of 5, since 3 is

less than 5. -3 lies to the left of -1, since -3

is less than -1.

The symbol < that means is smaller than may be used for ordering the integers as follow: … -4 < -3 < -2 < -1 < 0 < 1 < 2 < 3 < 4 < 5 …

The symbol > that means is greater than can also be used for ordering the integers in the opposite direction: … 5 > 4 > 3 > 2 > 1 > 0 > -1 > -2 > -3 > -4 …

Addition and Subtraction of Integers

Addition of Integers on a Number LineOn a number line, ‘a movement to the right ’ is used to show ‘adding a positive number ‘ while ‘ a movement to the left ‘ is used to show ‘adding a negative number ‘.For example, -3 + 5 = 2

+5

-3

Subtraction of Integers on a Number Line

On a number line, ‘ a movement to the left ‘ is used to show ‘ subtracting a positive number ‘ while ‘ a movement to the right ‘ is used to show ‘ subtracting a negative number ‘.For example, -3 - (-5) = 2 5

-3

The Rule of Integers

• The sum of an integer and its opposite is zero.

Example -20 + 20 = 0

• To add two negative integers, we find the sum of their absolute values and take the negative sign for the answer.

Example -25 + (-17) = -(25+17) = -42

• To add two integers of different signs, we find the different between their absolute values and take the same sign as that of the integers which has the larger absolute value for the answer

Example -17 + 12 = -(17-12) = -5 -12 + 17 = 17 – 12 = 5

• To subtract an integer, add its opposite.Example -15 – 20 = -15 + (-20) = -35

15 - (-20) = 15 + 20 = 35

• Note that when we write 15 – (-20), the symbol ‘ - ’ between the two number is the subtractive sign. The symbol ‘ - ’ in ‘ -20 ’ is the sign of

number; the number is ‘ negative 20 ’.

For Example

9 + (-5) =

+9

-5

4

Speed Test Games1) An aeroplane was flying at a height of

2000 m. In order to clear a mountain, it had to climb a further height of 2000 m. After that, it descended 3000 m and flew for some time before it climbed another 2000 m again to avoid a thunderstorm. What was its height then ?

Answers

2) The highest point of an iceberg is +62 m from sea level. Its lowest point is -103 m from sea level. What is the height of the iceberg?

Answer

iceberg

sea level

3) The table below records the result of a game.

R8 represents a red card of 8, B6 a black card of 6 and

so on. A score of -8 points is given for R8, a score of 6 points for B6 and so on.(a) Find the total score of (i) player A and (ii) player B(b) Who had the higher score?(c) By how many more points did the winner beat the

loser? Answer

Round 1 2 3 4 5 6Player A R8 B2 R3 B7 R3 B3Player B B6 R5 R8 B5 B7 R10

Answers1)

+ - +

=

Its height then was 3000 m

Question

2000 m 3000 m2000 m 2000 m

3000 m

2) -

+ =

Its height of the iceberg is 165 mThe height cannot be a negative number.

Question

+62 -103

16562 103

3) (a) (i) = (-8) + 2 + (-3) + 7 + (-3) + 3 = -2(ii) = 6 + (-5) + (-8) + 5 + 7 + (-10) = -5

(b) Player A

(c) 3

Speed Test Game

a) 9+(-50) = b) -12 - (-5) =

c) -20 + (-8) = d) -45 + 18 =

e) -23 + (-50) = f) 10 + (-40) =

g) -15 - (-8) = h) -15 + 25 =

I ) 32 + (-27) = j) 82 - (-18) =

-41

-28

-73

-7

5

-7

-27

-30

10

100