ADDING THREE OR MORE NUMBERS

Recall that the Associative Property of Addition states that if we are adding more than two numbers, we can group any of the numbers together. This property can help us to add numbers with different signs.

Example 1 : 

Add :  -1.5 + 3.5 + 2

Solution : 

Step 1 :

According to the associative property of addition, we can add any two numbers among the given three numbers. 

Then, we have 

-1.5 + 3.5 + 2  =  (-1.5 + 3.5) + 2  ------(1)

Step 2 : 

In (-1.5 + 3.5), the two numbers have different signs. 

So, find the absolute difference of them without the actual signs. 

|1.5 - 3.5|  =  |-2|  =  2

Step 3 : 

In the two numbers 1.5 and 3.5, the sign of the bigger number is positive. So, we have to take positive sign to the result. 

(1) ----->  -1.5 + 3.5 + 2  =  (+2) + 2

-1.5 + 3.5 + 2  =  4

Example 2 : 

Add :  5 + (-3) + 7

Solution : 

Step 1 :

According to the associative property of addition, we can add any two numbers among the given three numbers. 

Then, we have 

5 + (-3) + 7  =  [(5 + (-3)] + 2  ------(1)

Step 2 : 

In [(5 + (-3)], the two numbers have different signs. 

So, find the absolute difference of them without the actual signs. 

|5 - 3|  =  |2|  =  2

Step 3 : 

In the two numbers 5 and 3, the sign of the bigger number is positive. So, we have to take positive sign to the result. 

(1) ----->  5 + (-3) + 7  =  [+2] + 2

5 + (-3) + 7  =  4

Example 3 : 

Tina spent $5.25 on craft supplies to make friendship bracelets. She made $6.75 and spent an additional $3.25 for supplies on Monday. On Tuesday, she sold an additional $4.50 worth of bracelets. What was Tina’s overall profit or loss?

Solution : 

Step 1 :

Use negative numbers to represent the amount Tina spent and positive numbers to represent the money Tina earned.

Step 2 : 

Find -5.25 + 6.75 + (-3.25) + 4.50.

Step 3 : 

Group numbers with the same sign.

-5.25 + (-3.25) + 6.75 + 4.50 ----> Commutative property

(-5.25 + (-3.25)) + (6.75 + 4.50) ----> Associative property

Step 4 : 

Add the numbers inside the parentheses.

-8.50 + 11.25

Find the difference of the absolute values :

|11.25 - 8.50|  =  |2.75|  =  2.75 

In 8.50 and 11.25, the sign of the greater number is positive. So, the result also must be positive and it is 2.75.

So, Tina earned a profit of $2.75.

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