ADDING RATIONAL NUMBERS WITH THE SAME SIGN

Example 1 : 

Add (-2/3) and (-1/3).

Solution : 

Step 1 : 

Find the absolute values.

|-2/3|  =  2/3 and  |-1/3|  =  1/3

Step 2 : 

Find the sum of the absolute values :

 2/3 + 1/3  =  (2+1) / 3

2/3 + 1/3  =  3/3

2/3 + 1/3  =  1

Step 3 : 

Use the sign of the rational numbers to write the sum.

(-2/3) + (-1/3)  =  -1

Example 2 : 

Add (+2/5) and (+1/5).

Solution : 

Step 1 : 

Find the absolute values.

|+2/5|  =  2/5 and  |+1/5|  =  1/5

Step 2 : 

Find the sum of the absolute values :

 2/5 + 1/5  =  (2+1)/5

 2/5 + 1/5  =  3/5

Step 3 : 

Use the sign of the rational numbers to write the sum.

(+2/5) + (+1/5)  =  +3/5

Example 3 : 

Malachi hikes for 2.5 miles and stops for lunch. Then he hikes for 1.5 more miles. How many miles did he hike altogether?

Solution : 

Step 1 : 

Use positive numbers to represent the distance Malachi hiked. 

Step 2 : 

Find 2.5 + 1.5.

Let us use the real number line to add 2.5 and 1.5.

Step 3 : 

Start at 2.5.

Step 4 : 

Move 1.5 units to the right because the second addend is positive.

The result is 4.

So, Malachi hiked 4 miles.

Example 4 : 

Kyle pours out 3/4 liter of liquid from a beaker. Then he pours out another 1/2 liter of liquid. What is the overall change in the amount of liquid in the beaker?

Solution : 

Step 1 : 

Use negative numbers to represent amounts the change each time Kyle pours liquid from the beaker.

Step 2 : 

Find -3/4 + (-1/2).

Let us use the real number line to add -3/4 and -1/2.

Step 3 : 

Start at -3/4.

Step 4 : 

Move | -1/2 | = 1/2 unit to the left because the second addend is negative.

The result is -1 1/4.

So, the amount of liquid in the beaker has decreased by 1 1/4 liters.

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