Addition and Subtraction of Directed Numbers

In a horizontal number line:

1. When adding, start from the first number, count right along the number line.

2. When subtracting, start from the first number, count left alone the number line.

Note: In a horizontal number line, numbers to the right of zero are positive, and numbers to the left are negative.

Worked Example 10.2.1:

Use number line to find the value of:

i. 0 +  6
ii. 2 + 7
iii. -6  –  4
iv. -8  +  11
v. -5   +  4
vi. -3  –  5

i. 0   +   6

Solution

 *Start at 0, count 6 places to the right to end up at 6.

So,   0  +  6   =  6

ii. 2   +   7  

Solution

 *Start at 2, count 7 places to the right to end up at 9.

 So,  2  +  7  =  9.

 iii. -6  –  4

Solution

*Start at -6, count 4 places to the left to end up at -10.

So, -6  -4     =   -10.

iv. -8   +  11

Solution

*Start at -8, count 11 places to the right to end up at 3.

v. -5    +     4

Solution

*Start at -5, count 4 places to the right to end up at -1.

vi.  -3  –  5

Solution

*Start at -3, count -5 places to the left to end up at -8.

So,   -3   – 5   =   -8

Note:  The -ve sign directs the number to the left while the +ve directs the number to the right.