SUBTRACTING NEGATIVE RATIONAL NUMBERS

We can use number line to subtract negative rational numbers.

If we subtract a negative rational number, we have to move in the positive direction on the number line.

For example, if we want to subtract -0.5 from 5, we have to move 0.5 units from 5 in the positive direction.   

Example 1 : 

Subtract -1.5 from 2.5. 

Solution : 

Step 1 : 

Since we subtract the negative rational number -1.5 from 2.5, we have to move 1.5 units from 2.5 in the positive direction on the number line.  

It has been illustrated in the picture given below.

Step 2 :

After having moved 1.5 units in the positive direction from 2.5, we are in the position of 4.

So,

2.5 - (-1.5)  =  4

Example 2 : 

Subtract -2.5 from -2. 

Solution : 

Step 1 : 

Since we subtract the negative rational number -2.5 from -2, we have to move 2.5 units from -2 in the positive direction on the number line.  

It has been illustrated in the picture given below.

Step 2 :

After having moved 2.5 units in the positive direction from -2, we are in the position of 0.5

So,

-2 - (-2.5)  =  0.5

Example 3 : 

During the hottest week of the summer, the water level of the Muskrat River was 5/6 foot below normal. The following week, the level was 1/3 foot below normal. What is the overall change in the water level ?

Solution :

Subtract to find the difference in water levels. That is, we have to find -1/3 - (-5/6)

Step 1 : 

Since we subtract the negative rational number -5/6 from -1/3, we have to move 5/6 units from -1/3 in the positive direction on the number line.  

It has been illustrated in the picture given below.

Step 2 :

After having moved 5/6 units in the positive direction from -1/3, we are in the position of 1/2.

So, the water level changed 1/2 foot.

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