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Integers

ADDITION AND SUBTRACTION OF INTEGERS

BACKGROUND KNOWLEDGE

Numbers - whole numbers and integers.

a). Which of the following are whole numbers?

- 3, 3, 0.55, 102, 6, 9, -1.5, 0, -6

Solution
The whole numbers are -3,3, 102, 6, 9, -6 and 0

b). Identify the integers represented by the letters a, b, c and d

ADDITION AND SUBTRACTION OF INTEGERS

BACKGROUND KNOWLEDGE

Numbers - whole numbers and integers.

a). Which of the following are whole numbers?

- 3, 3, 0.55, 102, 6, 9, -1.5, 0, -6

Solution

The whole numbers are -3,3, 102, 6, 9, -6 and 0

b). Identify the integers represented by the letters a, b, c and d




 

Solution

a is 3, b is -1, c is -2, d is -4

Note: On the number line, numbers are marked at unit integers, that is, equal single steps increasing from zero (0) to the right.

The arrow head shows the direction in which the numbers increase or decrease.

The left of zero (0) on a number line are negative numbers.
If the two numbers on a number line are taken, the one to the right is the greater one.
Note: -3 is less that -2 and 5 is less than 6

1.Choose the greater number in each of the following pairs:

a) -7,-2

b) -1, 4

c) 0, -3

d) 3, 8

Solutions

a) -2

b) 4

c) 0

d) 8

2. Addition and subtraction of whole numbers

 Practice Exercise worked out examples

Observe carefully how these are worked out

Work out the following using a number line

 

a). (+2) + (+5)

  

b). (+2) + (+2) + (+1)

  

  d). (-5) + (+2) 

    

e). (-6) + (+2) + (+4)

 

Lesson objective

By the end of this lesson you should be able to

:

add integers using numberline correctly

subtract integers using number line correctly

Addition of Integers

Brackets

Brackets should be used around negative numbers to separate the minus sign attached to the number from the arithmetic operation symbol.for example, 5 - -3 should be written as 5 -(-3) and 7 x -2 should be written as 7 x (-2).

Note :Never write two arithmetic operations symbols together without using brackets.

 

N.B

When adding a positive number to an integer

using a number line start from the first number

and move right a number of steps equal to the

integer being added.

INTRODUCTION

 

Work out the following using a number line:

a). (+6) + (-4)  

b). (+7) + (-2) + (-1)

c). (-4) + (-3) 

d). (-3) + (-2) + (-1)

 

Exercise

Work out the following using the number line:

a). (+3) - (-4)

  

 

 b). (-5) - (-2) - (-3)

 

 

 c). (-7) - (-4)

 

 

 

d). (+2) - (-3) - (-1)

 

 

 

 

INTEGERS

In our daily lives we always deal with integers .

Discover how useful they are

In our daily we always deals

discover how useful they are

b) Work out (-2) + (-5) using a number line

When adding a negative integers start from the

first number and move left a number of steps

equal to the integers being added
 

SUBTRACTION OF INTEGERS

When subtracting a positive number from an integer using a number line, start from the first number and move left a number of steps equal to the integer being subtracted.

Case3 Example 1 Work out (+4) - (+7) using number line

   

 

When subtracting a positive number from an integer  using a number line, start from the first number and move left a number of steps equal to the integer being subtracted.   Work out the following using the number line

a). (+10) - (+3)

                  

            b). (+ 9) - (+2) - (+1)

   

  c). (- 6)- (+ 3)

   

     

  Case 4

Subtraction of negative integers

Work out (+5) - (-3) using a number line

 

 

      Work out (-4) - (-5) using a number line

 

   

When subtracting a negative number from an

 integer using the number line start from the

 first number and move right to a number of

 steps equal to the integer being subtracted.

 

NB. When subtracting an integer from another

 using the number line, the following steps can

be followed:

1.Find the difference between the two numbers

2.Determine the direction you move from the

 second number to first. 

3.If to the right the answer is positive and if to the left the answer is negative

REMEMBER

That subtracting a negative integer from any number is the   

same as adding an equivalent positive integer.    e.g (-7) - (- 4) = (-7 ) + (+4) = -3.

Subtracting a positive number from any number is the same

as adding an equivalent negative integer.  e.g (+3) - (+4) = (+3) + (-4) = -1

SUBTRACTION OF INTEGERS

When subtracting a positive number from an integer using a number line, start from the first number and move left a number of steps equal to the integer being subtracted.

Case3 Example

Work out (+4) - (+7) using number line

 

When subtracting a positive number from an integer using a number line, start from the first number and move left a number of steps equal to the integer being subtracted.Work out the following using the number line.

 

Subtraction of negative integers

Work out (+5) - (-3) using a number line

Work out (-4) - (-5) using a number line

 

 



 Integers 

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 Integers  

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 Integers 




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