## Week 5 Review: Practice Exercises and Problems

In the previous post, we learned about operations on integers, order of operations, and PEMDAS rules. Below are the exercises and problems about these topics.

PCSR WEEK 5 Review: Operations on Integers

Practice Exercises 1

a.) 12 + (-4)
b.) (-9) + 3
c.) (-7) + (- 5)
d.) 8 + 3 + (-11)
e.) 6 + (-10) + (-2)

Practice Exercises 2

a.) 3 – 5
b.) -9 – 4
c.) (-7) – (- 8)
d.) – 2 – 6
e.) 1 – (-10)

Practice Exercises 3

a.) 4 × (- 5)
b.) (-2) × (- 4)
c.) (6) × (- 3)
d.) 8 × 2 × (-1)
e.) (-3) × (2) × (-7)

Practice Exercises 4
a.)-20 ÷ 4
b.) 18 ÷ (- 6)
c.) (-16) ÷ (- 2)
d.) 0 ÷ 8
e.) 9 ÷ 3

Practice Problems

1.) 2 + 3 × 5
2.) (2 + 3) × 5
3.) 3 x (-3) + 4 ×(-2)
4.) $3(5^2 - 8)$
5.) $2(5 - 8)^2$
6.) 16 + (-4) + 12 + (-8 × 3)
7.) $(3^2 + 2^2)^2$
8.) 6 + 3 × 2 – 5
9.) 8 – 12(3 – 4) + (-5 × 2)
10.) 7 + 3 × (-5) – 9 / 3

## PCSR REVIEW SERIES WEEK 5: Operations on Integers and PEMDAS

Below are the articles and videos that you should read and watch about operations on integers, order of operations, and PEMDAS. Exercises and problems will be posted soon.

PART 1: OPERATIONS ON INTEGERS

Articles

Videos

PART 2: PEMDAS

Articles

Videos

More video

Introduction to PEMDAS

## Practice Exercises on Subtraction of Integers

In subtraction of integers, we have learned two rules:

(1) a – b = a + (-b)
(2) a – (-b) = a + b

We will use these rules in answering the exersises below.

Exercises

1. 2 – 5
2. 18 – ( – 2)
3. 16 – 7
4. -17 – 3
5. -9 – (-3)
6. 0 – (-11)
7. -18 – (-25)
8. -10 – 9
9. 12 – (-9)
10. -6 – 3

1. 2 – 5

Solution 1: 5 is greater than 2. If you subtract two numbers, if the subtrahend is larger than the minuend, the answer will be negative. So, the answer is -3.

Solution 2: From rule 1, a – b = a + (-b), so 2 + 5 = 2 + (-5) = -3

2. 18 – ( – 2)

Solution: From rule 2, a – (-b) = a + b, so 18 + 2 = 20.

3. 16 – 7

4. -17 – 3

Solution: From rule 1, -17 – 3 = -17 + (- 3) = -20. Recall that in adding two negative numbers, we just add the numbers and then the answer will be negative.

5. -9 – (-3)

Solution: From rule 2, -9 – (-3) = -9 + 3 = -6.

6. 0 – (-11)

Solution: From rule 2, 0 – (-11) = 0 + 11 = 11.

7. -18 – (-25)

Solution: From rule 2, a –(-b) = a + b. So, -18 + 25 = 7.

8. -10 – 9

Solution: From rule 1, a – b = a + (-b), so -10 + (- 9) = – 19.

9. 12 – (-9)

Solution: From rule 2, a –(-b) = a + b, so 12 + 9 = 21.

10.- 6 – 3

Solution: From rule 1, a – b = a + (-b) = -6 + -3 = -9.

## Four Effective Techniques in Adding Integers

We have already discussed addition of integers. In this post, I am going to discuss four different techniques in adding integers.

Adding Numbers with the Same Sign

In adding integers with the same sign, we just add them and then copy the sign. For example, in adding 2 + 8, 2 and 8 are positive integers, so we just add them, and the answer will be positive. So, 2 + 8 = 10. On the other hand, if both integers are negative we also do the same: add them, then copy the sign. For example, -9 + -3 = -12 since both of them are negative integers.

The techniques below are for adding integers with different signs. These strategies are important because you can visualize addition even without memorizing the rules.

Techniques in Adding Integers with Different Signs

Technique 1: Using Positive and Negative Chips

You can imagine integers as positive and negative chips. Since +1 + -1 = 0, a pair of positive and negative chips will give a sum of 0. So, 3 means 3 positive chips and -4 means 4 negative chips. Since each pair of positive and negative chip cancels out each other (their sum is 0), then the remaining chips after the pairing will be the answer. So, 3 + (-4) as represented below is -1 since only one negative chip remains.

Another example is -4 + 6 = 2.

Technique 2: Decomposing the Numbers

This strategy uses the fact that a + (-a) = 0. Using this strategy, we can split one of the addends. For example, in 8 + (-5), we split 8 to 3 + 5 so that 5 and -5 will become 0. So,

8 + (-5) = 3 + 5 + (-5)

=3 + (5 + -5)= 3 + 0 = 3.

In -11 + 3, we can split -11 to -8 + -3. So,

-11 + 3 = -8 + (-3 + 3) = -8 + 0 = -8.

Technique 3: Using the Number Line

Integers can also be represented as movement on the number line. A positive integer is a movement to the right of 0 and a negative integer is a movement to the left. Positive 3 and -2 can be represented as shown below.

So, 3 + (-5) can be represented as a movement of 3 units to the right of 0, then a movement of 5 units to the left. As we can see in the next diagarm, it the movement stopped at -2. So, 3 + (-5) = -2.

Also, -2 + 3 can be represented as a movement 2 units to the left of 0 and then a movement of 3 units to the right. The movement stopped at 1, so -2 + 3 = 1.

Technique 4: Grouping Numbers with Similar Signs

In adding more than 2 addends with different signs, group the numbers with the same signs. For example, 9 + (-2) + 4 + (-1), we can do the following:

(1) add the positive integers first: 9 + 4 = 13
(2) add the negative integers (-2 + -1 = -3)
(3): finally, add the two sums: 13 + (-3) = 10.

Try using the techniques above by answering the following and share to us which technique do you like most.

1.) 5 + (-10)
2.) -3 + 8
3.) 12 + – 10 + 7
4.) -10 + -3 + 4

## The Operations on Integers Series

In the previous post, I have mentioned that it is important for you to master basic mathematics. One of the basic skills that you should master is operations on integers. Luckily, I have finished writing all the tutorials and reviewers for all the operations on integers.  They are listed below.

Good luck and have fun. I will be posting the quizzes and PDF exercises soon, so keep posted.

## Subtraction of Integers Quiz 1

Now that you have learned how to add and subtract integers, test your skills in this 10-item quiz. Items 1-8 are worth 2 points each and items 9-10 are worth 3 points each. In case you get a low score, please read How to Add Positive Integers and How to Subtract Positive and Negative Integers.

Note that in the solutions shown below, each subtraction was converted in addition. This way, you will only have to master addition of fractions.

Subtraction of Integers Quiz 1. Let’s begin!

A 10-item easy quiz on subtraction of integers.

## Addition of Integers Quiz 1

We have already learned how to operate with integers (addition, subtraction, multiplication, and division) as well as its order of operation. Test your skills in addition of fraction in this quiz below. Fill in the blanks with the correct answer. Good luck!

## Addition of Integers Quiz 1

A quiz on addition of integers.

## 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.