Integer

1. For a horizontal number line, the direction from left

to right indicates the positive direction while the

direction from right to left indicates the negative direction.

For example :- 
   

2. For a vertical number line, and upward direction

indicates the positive direction indicates the negative

direction.

For example :

    

3. We can add two or more integers using a number line.

(a) When adding a positive integer, we move in the

positive direction on the number line.

(b) When adding a negative integer, we move in the

negative direction on the number line.

(c) Zero is usually taken as the starting point.

Worked Example 10

Solve the following by using the number lines.

(a) 3 + (+5)       (c) – 2+ (- 5)

(b) – 6 + 4         (d) 3 + (- 5)+(+8)

Solution: 

Worked Example 11

Solve each of the following.

(a) – 9 + (+5)         (c) – 6 + (- 2)

(b) + 7 + (- 5)


Solution:

B) Problem Solving involving Addition of Integers

Worked Example 12

A submarine which is 9 km below sea level

moves up 3 km. What is the position of the

submarine now ?


Solution:

1. Understand the problem

Given information :

The submarine is 9 km below sea level.

It moves up 3 km.

Find : Final position of the submarine

2. Devise a plan

Use addition.

3. Carry out the plan

– 9 + 4 = – 5

Therefore, the submarine is 5 km below sea

level now.

4. Check 
            



C) Subtraction of Integers

1. Subtraction of integers is to find the difference

between two integers.

2. We can use a number line to find the difference

between two integers.

3. The difference can be determined by counting the

number of units to be moved from the second integer

to the first integer. The direction of the movement will

determine the ‘+’ or ‘_’ sign in the answer.

Worked Example 13

Solve the following by using number line.

(a) 3 – 5            (c) – 2 – 4

(b) 8 – (+4)        (d) 0 – (- 7)

Solution: 

Worked Example 14

Find the value of each of the following.

(a) 8 – (+5)

(b) 6 – (- 3)

(c) – 9 – (- 9)


Solution:

Worked Example 15

Find the value of each of the following.

(a) 30 – (+18) – (- 6)

(b) – 21 – (- 7) – (- 13)

Solution:

(a) 30 – (+18) – (- 6) = 30 – 18 + 6

= 12 + 6

= 18

(b) – 21 – (- 7) – ( – 13) = – 21 + 7 + 13

= – 14 + 13

= -1



D) Problem Solving involving Subtraction of Integers

A submarine is 8 m below sea level. An eagle is 3 m

above sea level directly above the submarine. What 

is the distance between the submarine and the eagle?


Solution :


1. Understand the problem

Given information :

A submarine is 8 m below sea level.

An eagle is 3 m above sea level.

Find : Distance between the submarine

and the eagle

2. Devise a plan

Use subtraction.

3. Carry out the plan

3 – (- 8) = 3 + 8 = 11

Therefore, the distance between the submarine

and the eagle is 11 m.

4. Check

    



E) Combined Operations of Addition and Subtraction of Integers 

Worked Example 17

Find the value of each of the following.

(a) 25 – (+30) + (- 12)

(b) – 12 – (- 26) + (- 15)

Solution:

(a) 25 – (+30) + (- 12)

= 25 – 30 – 12

= – 5 – 12

= – 17

(b) – 12 – (- 26) + (- 15)

= – 12 + 26 – 15

= 14 – 15

= – 1



F) Problem Solving involving Addition and Subtraction of Integers

Worked Example 18

A diver at 7 m below sea level swam up 3 m. A

turtle at that moment was 2 m below sea level.

What was the distance between them when the

turtle was directly above the diver? 


Solution:

1. Understand the problem

Given information :

The diver was 7 m below sea level at first.

He swam up 3 m.

The turtle is 2 m below sea level.

Find : Distance between the diver and the turtle.

2. Devise a plan

Use addition and subtraction.

3. Carry out the plan

(- 7 + 3) – (-5) = (- 7 + 3) + 5

= – 4 + 5

= 1

Therefore, the distance between the diver and

the turtle was 1 m.

4. Check 
    


GLOSSARY

  1. Integers- integer
  2. Positive Integers- integer positif
  3. Negative Integers- integer negatif
  4. Positive Number- nombor positif
  5. Negative Number- nombor negatif
  6. Inverse- songsangan
  7. Like signs- tanda serupa
  8. Unlike signs- tanda tak serupa
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