ADDING RATIONAL NUMBERS WITH DIFFERENT SIGNS WORKSHEET

Problem 1 : 

Add (-4/5) and (+7/5). 

Problem 2 : 

Add (+5/9) and (-8/9).

Problem 3 : 

Add (+2.03) and (-2.3). 

Problem 4 :

Add 3 and -2 using a number line.

Problem 5 :

During the day, the temperature increases by 4.5 degrees. At night, the temperature decreases by 7.5 degrees. What is the overall change in temperature ?

Problem 6 :

Ernesto writes a check for $2.50. Then he deposits $6 in his checking account. What is the overall increase or decrease in the account balance ?

Detailed Answer Key

Problem 1 : 

Add (-4/5) and (+7/5). 

Solution : 

Step 1 : 

Find the absolute difference of the rational numbers without the actual signs. 

|4/5 - 7/5|  =  |-3/5|  =  3/5

Step 2 : 

In the given two rational numbers 4/5 and 7/5, the sign of the bigger number is positive. So, we have to take positive sign to the answer. 

So,

(-4/5) + (+7/5)  =  +3/5

Problem 2 : 

Add (+5/9) and (-8/9).

Solution : 

Step 1 : 

Find the absolute difference of the rational numbers without the actual signs. 

|5/9 - 8/9|  =  |-3/9|  =  3/9  =  1/3

Step 2 : 

In the given rational numbers 5 and 8, the sign of the bigger number is negative. So, we have to take negative sign to the answer. 

So, 

(+5/9) + (-8/9)  =  -1/3

Problem 3 : 

Add (+2.03) and (-2.3). 

Solution : 

Step 1 : 

Find the absolute difference of the rational numbers without the actual signs. 

|2.03 - 2.3|  =  |-0.27|  =  0.27

Step 2 : 

In the given rational numbers 2.03 and 2.3, the sign of the bigger number is negative. So, we have to take negative sign to the answer. 

So,

(+2.03) + (-2.3)  =  -0.27

Problem 4 :

Add 3 and -2 using a number line.

Solution :

Here, the rational numbers "3" and "-2" are having different signs. 

To find the sum of rational numbers 3 and -2, we have to start at 3 

Since the second number "-2" is negative, we have to move 2 units in the negative  direction as given in the picture below.

After having move 2 units in the negative direction, we are in the position of "1"

So,

3 + (-2)  =  1

Problem 5 :

During the day, the temperature increases by 4.5 degrees. At night, the temperature decreases by 7.5 degrees. What is the overall change in temperature ?

Solution :

Step 1 :

Use a positive number to represent the increase in temperature and a negative number to represent a decrease in temperature.

Step 2 : 

Find 4.5 + (-7.5).

Let us use the real number line to add 4.5 and (-7.5).

Step 3 : 

Start at 4.5.

Step 4 :

Move | -7.5 | = 7.5 units to the left because the second addend is negative.

The result is -3.

The temperature decreased by 3 degrees overall.

Problem 6 :

Ernesto writes a check for $2.50. Then he deposits $6 in his checking account. What is the overall increase or decrease in the account balance ?

Solution :

Step 1 :

Use a positive number to represent a deposit and a negative number to represent a withdrawal or a check.

Step 2 : 

Find -2.5 + 6.

Let us use the real number line to add -2.5 and 6.

Step 3 : 

Start at -2.5.

Step 4 :

Move | 6 | = 6 units to the right because the second addend is positive .

The result is 3.5.

So, the account balance will increase by $3.50.

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