Week 5 Review Answers and Solutions

This is the full solutions for the problems and exercises about operations on integers, order of operations, and PEMDAS rules.

Practice Exercises 1

a.) 12 + (-4) = 8
b.) (-9) + 3 = – 6
c.) (-7) + (- 5) = -12
d.) 8 + 3 + (-11) = (8+3) + (-11) = (11) + (-11) = 0
e.) 6 + (-10) + (-2) = 6 + (-10 + -2) = 6 + (-12) = -6

Practice Exercises 2

a.) 3 – 5 = (3) + (-5) = -2
b.) -9 – 4 = (-9) + (-4) = -13
c.) (-7) – (- 8) = (-7) + (8) = 1
d.) – 2 – 6 = (-2) + (-6) = -8
e.) 1 – (-10) = (1) + (10) = 11

Practice Exercises 3

a.) 4 × (- 5) = -20
b.) (-2) × (- 4) = 8
c.) 6 × (- 3) = -18
d.) 8 × 2 × (-1) = -16
e.) (-3) × (2) × (-7) = 42

Practice Exercises 4
a.)-20 ÷ 4 = -5
b.) 18 ÷ (- 6) = -3
c.) (-16) ÷ (- 2) = 8
d.) 0 ÷ 8 = 0
e.) 9 ÷ 3 = 3

1.) 2 + 3 × 5

2 + 3 × 5
= 2 + 15
= 17

2.) (2 + 3) × 5

(2 + 3) × 5 = (5) × 5
= 25

3.) 3 × (-3) + 4 × (-2)

= 3× (-3) + 4× (-2)
= (-9) + (-8)
= -17

4.) 3(5^2 – 8)

3(5 × 5 – 8)
= 3(25 – 8)
= 3(17)
= 51

5.)  2(5 – 8)^2
= 2(-3)^2
= 2(-3 × -3)
= 2(9)
= 18

6.) 16 + (-4) + 12 + (-8 x 3)

= 16 + (-4) + 12 + (-24)
= (16 + 12) + (-4 + -24)
= (28) + (-28)
= 0

7.) (3^2 + 2^2)^2 = ?

= (3 × 3 +2× 2)^2
= (9 + 4)^2
= (13)^2
= 13 × 13
= 169

8.) 6 + 3 × 2 – 5 = ?

= 6 + (3 × 2) – 5
= 6 + 6 – 5
= 12 – 5
= 7

9.) 8 – 12(3 – 4) + (-5 × 2)

= 8 – 12(3 – 4) + (-5 × 2)
= 8 – 12(-1) + (-10)
= 8 – (-12) + (-10)
= 20 + (-10)
= 10

10.) 7 + 3 × (-5) – 9 / 3 = ?

= 7 + 3 × (-5) – 9/3
= 7 + (-15) – 3
= 7 + (-18)
= -11

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

  1. How to Add Positive and Negative Integers
  2. How to Subtract Positive and Negative Integers
  3. How to Multiply Positive and Negative Integers
  4. How to Divide Positive and Negative Integers

Videos

  1. How to Add Integers Using the Number Line Part 1
  2. How to Add Integers Using the Number Line Part 2
  3. Addition of Integers Using Chips
  4. How to Subtract Integers Using the Number Line (Part 1)
  5. How to Subtract Integers Using the Number Line (Part 2)
  6. Subtraction of Integers Worked Examples Part 1
  7. Subtraction of Integers Worked Examples Part 2
  8. Subtraction of Integers Using Chips
  9. Addition and Subtraction of Integers Worked Examples
  10. Introduction to Multiplication of Integers
  11. Multiplication of Integers Worked Examples
  12. Division of Integers
  13. Division of Integers Worked Examples

PART 2: PEMDAS

Articles

Videos

  1. PEMDAS Order of Operations Part 1
  2. PEMDAS Order of Operations Part 2
  3. PEMDAS Order of Operations Part 3

More video

Introduction to PEMDAS

PCSR REVIEW SERIES WEEK 4: Multiplication and Division of Fractions

Last week, you have learned about addition and subtraction of fractions. This week, we will be studying about multiplication and division of fractions.

Below are the articles and videos that you should read and watch. Later, I will post exercises and problems.

Articles

Videos

Enjoy learning!

Week 3 Review: Practice Exercises and Problems

In the last post, we learned about addition and subtraction of mixed fractions.  To test your knowledge about these topics, answer the exercises and word problems below. The answer answers and solutions will be posted soon.

Practice Exercises 1

a.) 2 1/5 + 3 2/5
b.) 8 1/4 + 2 3/4
c.) 5 + 2 1/4
d.) 5 1/2 + 1/5
e.) 3 1/3 + 4 1/4 + 5 1/5

Practice Exercises 2

a.) 4 6/7 – 3/7
b.) 8 – 3/4
c.) 12 – 5 2/9
d.) 7 3/10 – 7/10
e.) 6 1/5 – 3/4
f.) 9 3/8 – 4 5/7

Practice Problems

1.) Leo’s family drank 1 3/5 liters of juice yesterday morning and 4/5 liters of juice yesterday afternoon. How much juice did Leo’s family drank in all yesterday?

2.) A train station is between a school and a clinic. The distance between the school and the clinic is 2 5/8 kilometers and the distance between the train station and the clinic is 1 5/6 kilometers. What is the distance between the school and the train station?

3.) A piece of iron rod weighs 2 5/6 kg and another piece weighs 17/8 kilograms. Which is heavier and by how much?

4.) Gina bought a pizza. She gave 3/8 of it to her kids and 1/4 to her neighbor. What part of the pizza was left?

5.) Jaime’s house is two rides away from school. The jeepney ride is 3 4/15 kilometers and the tricycle ride is 5/8 kilometers. How far is Jaime’s school from his house?

PCSR REVIEW SERIES WEEK 3: Addition and Subtraction of Fractions

Last week, we have learned how to add and subtract fractions. In this post, we are going to learn about addition of mixed fractions.

There are two strategies in addition and subtraction of mixed fractions. The first one is to add or subtract first the whole numbers (if possible), then add or subtract the fraction. The second is to convert the mixed fractions to improper fractions before performing addition or subtraction.

The following are the Youtube videos where you can learn how to add and subtract mixed fractions.

If you have time, I suggest that you watch the complete FRACTION SERIES here (24 videos):

Good luck!

Week 2 Review Answers and Solutions

Below are the solutions and answers to the Practice Exercises and Problems for the Week 2 Review on Addition and Subtraction of Fractions.

Practice Exercises 1 Answers
1.) 3/5
2.) 2/5
3.) 4/7
4.) 2
5) 3/5

Practice Exercises 2
Convert the following improper fractions to mixed form.
1.) 3 3/5
2.) 1 5/7
3.) 4 1/2
4.) 12 3/4
5) 10 1/12

Practice Problems Solutions and Answers

1. The LCM of the denominators 2 and 8 is 8. We convert ½ to a fraction whose denominator is 8 in order for the two fractions to be similar. To do this, we divided 8 by 2 and the multiply by 1. The result will be the numerator of the fraction. That is

\dfrac{8}{2} \times \dfrac{ 1}{8} = \dfrac{4}{8}.

So, \dfrac{4}{8} + \dfrac{9}{8} = \dfrac{13}{8}.

Converting the answer to mixed form, we have 1\dfrac{5}{8}

Answer: 1 5/8

2. The LCM of 5 and 4 is 20. After getting the LCM, we convert 3/5 and 1/4 to their equivalent fractions whose denominator is 20.

The equivalent fraction for 3/5 is 12/20.
The equivalent fraction of 1/4 is 5/20.

12/20 + 5/20 = 17/20

Answer: 17/20

3. The LCM of 2, 3 and 4 is 12. After getting the LCM, we convert 1/2, 1/3, and 1/4 to their respective equivalent fractions whose denominator is 12.

The equivalent fraction for 1/2 is 6/12.
The equivalent fraction of 1/3 is 4/12.
The equivalent fraction of 1/4 is 3/12.

6/12 + 4/12 + 3/12 = 13/12

Converting 13/12 to mixed fractions, we get 1 1/12.

Answer: 1 1/12

4. The LCM of 12, 2 and 3 is 12. After getting the LCM, we convert 5/12, 1/2, and 2/3 to their respective equivalent fractions whose denominator is 12.

The equivalent fraction for 5/12 is still 5/12.
The equivalent fraction of 1/2 is 6/12.
The equivalent fraction of 2/3 is 8/12.

5/12 + 6/12 + 8/12 = 19/12

Converting 19/12 to mixed fractions, we get 1 7/12.

Answer: 1 7/12

5. The LCM of 4 and 6 is 12. Therefore, we convert 3/4 and 1/6 to their respective equivalent fractions whose denominator is 12.

The equivalent fraction for 3/4 is still 9/12.
The equivalent fraction of 1/6 is 2/12.

9/12 – 2/12 = 7/12

Answer: 7/12

6. The LCM of 15 and 30 is 30. Therefore, we convert 13/15 and 7/30 to their respective equivalent fractions whose denominator is 30.

The equivalent fraction for 13/15 is still 26/30.
The equivalent fraction of 15/30 is 15/30.

26/30 – 7/30 = 19/30

Answer: 19/30

7. In this problem, we can just add the fractions first. We add ¾ and ½ which is equal to 1 ¼ kg. We now add the 4 and 1 which is 5 ¼ kg.

8.  We need to add 1/8 and 1/2.
The LCM of 8 and 2 is 8. Therefore, we convert 1/2 to a fraction whose denominator is 8.

The equivalent fraction of 1/2 is 4/8.

1/8 + 4/8 = 5/8

Answer: 5/8

9. We need to add 1 1/2 and 3/4. We just add the fractions and then add the whole numbers later. We first add ½ and ¾.

The LCM of 2 and 4 is 4. Therefore, we convert 1/2 to a fraction whose denominator is 4.

The equivalent fraction of 1/2 is 3/4.

2/4 + 3/4 = 5/4

Converting 5/4 to mixed fractions, we have 1 ¼.

We add 1 ¼ to 1 from the original given. The answer 2 ¼.

Answer: 2 1/4

10. We need to add ¼, 1/5, and 3/10.

The LCM of 4, 5 and 10 is 20. Therefore, we convert 1/4, 1/5, and 3/10 to their respective equivalent fractions whose denominator is 20.

The equivalent fraction for 1/4 is still 5/20.
The equivalent fraction of 1/5 is 4/20.
The equivalent fraction of 3/10 is 6/20.

5/20 + 4/20 + 6/20 = 15/20

Changing 15/20 to lowest terms, we have ¾.

Week 2 Review: Practice Exercises and Problems

Below are the practice exercises for the Week 2 Review on Addition and Subtraction of Fractions. I will post the solutions and answers soon.

Practice Exercises 1

Add/Subtract the following fractions.

1.) 1/5 + 2/5
2.) 1/10 + 3/10
3.) 6/7 – 3/7
4.) 5/6 + 3/6 + 4/6
5) 12/5 – 9/5

Practice Exercises 2
Convert the following improper fractions to mixed form.
1.) 18/5
2.) 12/7
3.) 9/2
4.) 51/4
5) 121/12

Practice Problems

1. 1/2 + 9/8

2. 3/5 + 1/4

3. 1/2 + 1/3 + 1/4

4. 5/12 + 1/2 + 2/3

5. 3/4 – 1/6

6. 13/15 – 7/30

7. A 4 1/2 kg of rice placed inside a container weighing 3/4 kg. What is the total weight of the rice and the container?

8. Alfie bought a cake. He gave 1/8 of the cake to his wife and 1/2 of the cake to his children. What part of the cake was left?
Solution

9. Revie spend 1 1/2 hours studying here homework, 3/4 hours watching the television before sleeping. How much time did she spend studying and watching TV?

10. Ria drinks 1/4 L of milk everyday. Her son drinks 1/5 L of milk everyday. Her husband drinks 3/10 L of milk everyday. How much milk do the three of them drink everyday?

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