GRADE 8 MATHS CHAPTER 2 - INTEGERS

In Chapter 1, we discussed Whole Numbers ( Natural Numbers and 0), If we include negative numbers in this set then we have a new set of numbers, which is called INTEGERS.

The symbol for integers is Z.

Let us talk about few examples of integers in our daily life.

  • You have bank account balance of R200 and you withdraw R300 from ATM machine, You have a balance of -R100

  • You are in a big multi story mall and you have parked your vehicle in the 2nd basement. The number in the lift will be -2.

  • Temperature in winter drops from 12 degrees celsious during the day to -3 degrees at night.
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Floor and elevator signage, by G_Nikolakopoulou…
Meteorology thermometer isolated on white background_ Thermometer shows air temperature minus 14 degrees celsius or plus 7 degrees fahrenheit Stock Photo

Counting of Integers on a number line.


  • What is Integer_

Counting in Three's


Counting in Five's


Exercise 1 


Comparing and Ordering of Integers.


Exercise 2  : Compare and order the integers.

a.  Fill in the blank with one of the sign in between two integers (< , = , >).


a.  Arragne the following number in ascending order (Smallest to biggest).


b.  Arragne the following number in descending order (Biggest to smallest).


Addition/Subtration of Integers

- We use same rules for addition/subtraction as we used to use in lower grades.

- Keep in mind the number line.

- For addition, we move to the right on a number line, and for subtraction, we move to the left on a number line.


Example :


RULES OF BRACKET ( VERY IMPORTANT)

- If we don't have bracket like example above, then we can continue our examples like normal. (for addition, move right and for subtraction move left on a number line)

- But, if there is a bracket, we have to be very careful in opening a bracket.

- ONLY ONE RULE, YOU NEED TO KEEP IN MIND.

 + OUTSIDE BRACKET  THEN OPEN BRACKET WITH SAME SIGN

 - OUTSIDE BRACKET, THEN OPEN BRACKET WITH DIFFERENT SIGN.

EXAMPLES :



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ONLY ONE RULE FOR  MULTIPLICATION AND DIVISION



one negative, then answer is negative

two negative, then answer is positive

three negative, then answer is negative

four negative, then answer is positive


EXAMPLES :



SQUARES AND CUBES

- Squares meaning number multipies itself twice.

- Cube means the number multiplies itself thrice.

PLEASE MEMORISE SQUARES AND CUBES BELOW. THEY WILL BE VERY HELPFUL GOING FORWARD.

                                                                               

 - When we square or cube integers, rules of multiplication app

Examples :


Exercise 1 :


SQUARE ROOTS AND CUBE ROOTS ARE OPPOSITE METHOD OF SQUARE AND CUBES.

SQUARES / CUBES 


SQUARE ROOT / CUBE ROOT


Exercise 2 :

Calculate the following, WITHOUT THE USE OF CALCULATOR.


Exercise 3


Examples of mixed questions :


Exercise 4


Revision Exercise

a. Read the following pattern and find the values of unknown letters.

          w;  -12 ; -8 ; -4 ;  p ; q ; 8 ; 12; r

b. Look at the number line below and find the values of x , y and z.

          

c. Arrange the following integers in descending order.

           -20 ; -100 ; 45 ; 0 ; 145; -150 ; 22 ; -23453344 ; 54640 ; -237

d. Arrange the follwing integers in ascending order.

           230 ; -50 ; -200; 2; 0 ; -30 ; -1000; 2300; 545 ; 600 ; -457

e. Fill in the gap (blank) with one of the following sign < ; > or =.


f. Calculate the following examples without the use of calculator.