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?

PCSR REVIEW SERIES WEEK 2: Addition and Subtraction of Fractions

PCSR REVIEW SERIES for October 2016
Week 2: Addition and Subtraction of Fractions

In Week 1 of our PCSR Review Series , we have learned how to get the Least Common Multiple (LCM) and Greatest Common Divisor (GCD) of two or more numbers. The LCM is used to add and subtract dissimilar fractions. To add or subtract fractions, you have to get the LCM of their denominator and convert them to similar fractions.

The GCD is used for converting fractions to lowest terms. In converting fractions to lowest terms, you have to get the GCD of the numerator and denominator of a fraction, and divide both the numerator and the denominator by the GCD.

There are two more skills you need to know: to convert improper fractions to mixed fractions. Most of the time, final answers are required to be in mixed fractions. Links to tutorials on how to do it are included below.

Articles

  1. A Gentle Introduction to Fractions
  2. How to Convert Mixed Fractions to Improper Fractions
  3. How to Convert Improper Fractions to Mixed Fractions
  4. How to Add Fractions
  5. How to Subtract Fractions

Videos

More… 

If you have time and your internet is fast, I suggest that you watch the entire fraction series (21 videos):

Week 1 Review Answers and Solutions

Below are the solutions and answers to the Practice Exercises and Problems for the Week 1 Review on LCM and GCD.

Practice Exercises
I. Find the GCD of each of the following.
a.) 6, 10
Answer: 2

b.) 18, 42
Answer: 6

c.) 12, 48, 60
Answer: 12

d.) 56, 72
Answer: 8

e.) 225, 75
Answer: 75

II. Find the LCM of each of the following.
a.) 3, 4
Answer: 12

b.) 2, 5
Answer: 10

c.) 3, 6, 8
Answer: 24
d.) 3, 4, 5
Answer: 60

e.) 6, 12, 15
Answer: 60

III. Practice Problems Solutions and Answers

1.) 24 (GCD of 3, 4, and 8)

2.) 15 (GCD of 3 and 15)

3.) Solution: GCD of 3, 7, and 21 is 42. They will be seen in the gym on the same day in 42 days. Since June has 30 days, we need an additional 12 days to complete the 42 days. Therefore, they will be seen on the same day on July 12 (of the same year of course).

Answer: July 12

4.) Solution: The LCM of the two sequences is 12 and since we are looking for the tenth common number, we multiply 12 by 10. This gives us 120.
Answer: 120

5.) (a) Solution: LCM of 24 and 30 is 6. That is 6 groups.
(b) Solution: From (a) we can form 6 groups. There are 30 + 24 = 54 students. So in each group, there are 54/6 = 9 members. Since there are 6 groups, we divide each Grade level by 6. That is, 24/6 = 6 Grade 11 and 30/6 = 5 Grade 12 students in each group.
Answer: 4 Grade 11 students and 5 Grade 12 students.

6.) Reduce 42/56 to lowest terms.
Solution: GCD of 42 and 56 is 14. 42 divided by 14 is 3 and 56 divided by 14 is 4. Therefore, the lowest terms is 3/4.
Answer: 3/4

7.) Answer: 24 (LCM of 6 and 8)

8.) Answer: 6 (GCD of 18 and 12)

9.) Solution: The GCD of 21, 35, and 84 is 7. So, the cube has a side length of 7 cm.
Answer: 7 by 7 by 7

10.) Answer: 30 (GCD of 3, 5, and 6).

Week 1 Review: Practice Exercises and Problems

Below are the practice exercises for the Week 1 Review on LCM and GCD. You can read the answers and solutions to these exercises and problems.

Practice Exercises

I. Find the GCD of each of the following.
a.) 6, 10
b.) 18, 42
c.) 12, 48, 60
d.) 56, 72
e.) 225, 75

II. Find the LCM of each of the following.

a.) 3, 4
b.) 2, 5
c.) 3, 6, 8
d.) 3, 4, 5
e.) 6, 12, 15

III. Practice Problems

1.) The fractions 1/3, 1/4 and 1/8 are added. To add them, you need to convert them to similar fractions. What will be the least possible denominator of these similar fractions?

2.) In a disco, the red lights blink every 3 seconds and the blues light blink every 5 seconds. The two lights blink every ___ seconds.

3.) Anna, Karen, and Nina go to the same gym. Anna goes every 2 days, Karen goes every 3 days, and Nina goes every 7 days. On June 1, all of them were seen on the gym. What is the soonest date that they will be seen on the gym on same day?

4.) Consider the following sequences:
Sequence 1: 4, 8, 12, 16, 20, 24, …
Sequence 2: 6, 12, 18, 24, …
Notice that 12 and 24 are the first and second common numbers, respectively, to both sequences.
What is the 10th common number?

5.) In Senior High School athletic meet, there are 24 students from Grade 11 and 30 students from Grade 12. Groups are formed such that in each group should have an equal number students from each Grade level.
(a) If everyone is included, how many of such groups can be formed?
(b) When the largest number of groups is formed, how many students from each Grade level are there in one group?

6.) Reduce 42/56 to lowest terms.

7.) Boxes of chocolates have a height of 6 cm each. Boxes of cookies have a height of 8 cm each. A combination of these boxes will be packed in a large box. What should be the minimum height of the large box so that the smaller boxes would exactly fit?

8.) Square cardboard of the same size are to completely cover a rectangle with dimensions 18 cm by 12 What should be the dimensions of the largest possible squares so that there is no wasted cardboard?

9.) Cubes of the same size are to be placed inside a rectangular box. What is the size of the largest possible cubes that can fit exactly inside the box if its dimensions are 21 cm by 35 cm by 84 cm and no space is to be wasted?

10.) In a flour shop, a cake flour comes in 5-kg packages, a pastry flour comes in 3-kg packages and the bread flour comes in 6 kg packages. If Gina bought the same number of kilograms of these flour, what is the minimum number of kilograms of each she must have bought?

PCSR REVIEW SERIES WEEK 1: LCM and GCD

I have decided to outline a 16-week Philippine Civil Service Review (PCSR) series in mathematics. This way, you will be able to study systematically. In this series, I will post links every week, give exercises, and discuss the solutions of the exercises. Included in the links are articles that I have written and Taglish Youtube videos that I have created.

Let’s start our review in mathematics by learning about GCD and LCM. These two concepts are very important since you will use them in solving problems involving fractions. Fractions appear everywhere in the Civil Service exams. Be sure that you master these concepts before we proceed to our Week 2 review.

LEAST COMMON MULTIPLE

Least Common Multiple (LCM) is used when adding, subtracting, comparing and ordering, fractions. Here are the links with examples.

Articles

Youtube Videos

GREATEST COMMON DIVISOR
Greatest Common Divisor (GCD) is used in factoring and reducing fractions to lowest terms. GCD is also called Greatest Common Factor (GCF)

Articles

Youtube Videos

Enjoy!

If you have questions about the articles and the videos just post them below.

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