## Answers to Practice Test on Dividing Integers

Below are the answers and the explanations of the Practice Test on Dividing Integers. Note that as mentioned in the post Dividing Positive and Negative Integers, the rules in dividing integers as well as real numbers are the following:

(1) positive number ÷ positive number = positive number

(2) positive number ÷ negative number = negative number

(3) negative number ÷ positive number = negative number

(4) negative number ÷ negative number = positive number.

1.) -35 ÷ 7 = -5 (by rule 3)

2.) 38 ÷ -19 = -2 (by rule 2) Continue Reading

## Practice Test on Dividing Integers

In the previous post we have discussed how to divide integers. Operations on real numbers, particularly integers, is one of the scopes of the Civil Service Examinations both Professional and Subprofessional.  You must master these operations because you will use them in solving equations and word problems in Algebra.

Test your skill by answering the exercises below. Recall that a divided by b is the same as a times reciprocal of b.

Practice Test on Dividing Integers

1.) -35 ÷ 7

2.) 38 ÷ -19  Continue Reading

## Solutions to Practice Test on Multiplying Integers

Recall the rules on multiplying integers. Multiplying two with the like signs (negative and negative or positive and positive) gives a positive product. Multiplying two numbers with unlike signs gives a negative product.

1. -4 x -8 = 32

2. 3 x -7 = -21

3. -12 x -7 = 84

4. -8 x -1 x -4
Group any two first: -8 x -1 = 8. Then 8 x -4 = -32. Continue Reading

## Practice Test on Multiplying Integers

In the previous post, we have learned the rules in multiplying integers.  Below is a 10-item practice test on multiplying integers. Note that in multiplication, we can use the x and () symbols in multiplying two numbers. This means that 3 x 4 is the same as 3 (4) and (3)(4). We will use both symbols in the practice test below to familiarize yourselves with them.  Any of the two symbols can be used in the Civil Service exams.

##### Practice Test on Multiplying Integers

1. -4 x -8

2. 3 x -7

3. -12 x -7

4.  -8 x -1 x -4 Continue Reading

## Solutions to Subtracting Integers Practice Test

Blow are the solutions to the Civil Service Exam subtracting integers practice test.  As I have mentioned before, you do not have to memorize the rules of subtraction. All you have to do is convert it to addition. We can do this by converting a subtraction of integers problem  to addition of integers by changing the signs: minus “-: to plus negative “+ (-“  and minus negative “– –” or “– (-” to plus “+“. Observe how the subtraction problems are converted into addition problems in the solutions below. If you have any questions, please use the comment box below.

1. 12 23 = 12 + (-23) = -11

2. -21 – (-4) = -21 + 4 = -17

3. 17 – (-36) = 17 + 36 = 53

4. -18 13 = -18 + (-13) =-31

5. 22 35 = 22 + (-35) = -13

6. -34 – (-21) = -34 + 21 = – 13

7. 29 – (-6) = 29 + 6 = 35

8. 98 – 14 = 84 (no need to change signs, this is ordinary subtraction since the minuend is larger than the subtrahend).

9. -87 53 = -87 + (-53) = -140

10. 63 92 = 63 + (-92) = -29

In the next post, we are going to discuss about multiplication and division of integers.

## Solutions to Practice Exercises on Addition of Integers

We have learned how to add integers and in the previous post, I have given you practice exercises that you can use to evaluate your understanding of the topic. Below is the complete solutions to the practice exercises on adding integers. Share to me how many did you get right.

Solutions to Practice Exercises on Addition of Integers

1. 28 + 12 = 40.

2. 14 + 11 = 25

3. 24 + 15 = 9

Solution: We pair 15 and 15  to get 0. We have 9  left. So, the correct answer is 9.

4. –16 + 31 = 15

We pair 16  and 16 to get 0. We are left with positive 15.
5. 23 + 46 + 15 = 54

We add the two positive numbers first: 23 + 46 = 69. Next, we add 69 and 15. We get 15 from 69 and pair it with 15 resulting to 0, so we have 54 left.

6. 45 + 12 + 16 = 17

We add the negative numbers first: 12 + 16 = 28. We add the result to 45. We get 28 from 45 and pair it with  28 to get 0 leaving 17.

7. 12 +15 + 62 =  89

Explanation: They are negative, so we just added them. Of course negative added to negative is always negative.

8. 22 +  36 + 36 = 22

Explanation: 36 + 36 = 0, so we are left with 22.

9. 12 + 18 + 12 + 18 = 0

Explanation: 12 and 12 and 18 and 18 = 0.

10. 31 + 55 + 41 +  32 + 10 = 3

Explanation: Adding the positive integers, we have 31 + 55  = 86. Adding the negative integers, we have  41 +  32 + 10 =83. Now, 86 + 83 = 3

## Practice Exercises on Addition of Integers

In the previous post, we have learned about adding positive and negative integers particularly on how to add integers with different signs. In this post, I am going to give you 10 exercises on adding integers. I will give the answers below for you to be able to check if your answers are correct. Also, I am going to omit the + sign before the positive integers because this is not usually shown in the exam. This means that 3 will automatically mean +3 unless a – sign precedes it.

Exercises on Addition of Integers

1. 28 + 12
2. 14 + 11
3. 24 + 15
4. 16 + 31
5. 23 + 46 + 15
6. 45 + 12 + 16
7.  12 + 15 + 62
8. 22 +  36 + 36
9. 12 + 18 + 12 + 18
10. 31 + 55 + 41 + 32 + 10

See if your answers and solutions are correct.