Subtraction of Fractions Exercises – Set 1

Find the difference of the following:

1.) \dfrac{8}{11} - \dfrac{3}{11}

2.) \dfrac{7}{16} - \dfrac{3}{16}

3.) \dfrac{4}{5} - \dfrac{3}{4}

4.) 7 - \dfrac{4}{9}

5.) 8 \dfrac{9}{10} - \dfrac{3}{10}

6.) 6 \dfrac{2}{7} - \dfrac{5}{7}

7.) 4 \dfrac{1}{3} - \dfrac{1}{6}

8.) 6 \dfrac{3}{5} - 2 \dfrac{3}{4}

9.) 11 \dfrac{2}{3} - 7

10.) 9 \dfrac{2}{5} - \dfrac{11}{9}

Answers:

1.) \dfrac{5}{11}

2.) \dfrac{1}{4}

Solution
\dfrac{7}{16} - \dfrac{3}{6} = \dfrac{4}{16} = \dfrac{1}{4}

3.) \dfrac{1}{20}

Solution
LCD: 20
\dfrac{4}{5} - \dfrac{3}{4} = \dfrac{16}{20} - \dfrac{15}{20} = \dfrac{1}{20}

4.) 6 \dfrac{5}{9}

Solution

We can decompose 7 into 6 and 9/9.

6 \dfrac{9}{9} - \dfrac{4}{9} = 6 \dfrac{5}{9}

5.) 8 \dfrac{3}{5}

Solution
8 \dfrac{9}{10} - \dfrac{3}{10} = 8 \dfrac{6}{10} = 8 \dfrac{3}{5}

6.) 5 \dfrac{4}{7}

Solution
5 \dfrac{9}{7} - \dfrac{5}{7} = 5 \dfrac{4}{7}

7.) 4 \dfrac{1}{6}

Solution
LCD: 6
4 \dfrac{1}{3} - \dfrac{1}{6} = 4 \dfrac{2}{6} - \dfrac{1}{6} = 4 \dfrac{1}{6}

8.) 3 \dfrac{17}{20}

Solution
LCD: 20
5 \dfrac{8}{5} - 2 \dfrac{3}{4} = 5 \dfrac{32}{20} - 2 \dfrac{15}{20} = 3 \dfrac{17}{20}

9.) 4 \dfrac{2}{3}

Solution
11 \dfrac{2}{3} - 7 = 4 \dfrac{2}{3}

10.) 8 \dfrac{8}{45}

Solution
9 \dfrac{2}{5} - \dfrac{11}{9} = 8 \dfrac{7}{5} - \dfrac{11}{9}

LCD: 45
8 \dfrac{63}{45} - \dfrac{55}{45} = 8 \dfrac{8}{45}

 

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Addition of Fractions Exercises – Set 1

Find the sum of the following.

  1. 1/8 + 2/8 + 3/8
  2. 2/5 + 1/4
  3. 5/8 + 7/12
  4. 1/15 + 3/5 + 1/3
  5. 4 + 3/5
  6. 2 1/3 + 1/2
  7. 3 3/4 + 7/10
  8. 6 1/5 + 2 7/15 + 1/3
  9. 3 + 7 1/8 + 4/5
  10. 9 1/2 + 11/3

Solution and Answers

1. 3/4

2. 13/20
LCD: 20
8/20 + 5/20 = 13/20

3. 1 1/6
LCD: 24
15/24 + 14/24 = 29/24 = 1 5/24

4. 1
LCD: 15
1/15 + 9/15 + 5/15 = 15/15 = 1

5. 4 3/5
4 3/5

6. 2 5/6
LCD: 6
2 2/6 + 3/6 = 2 5/6

7. 4 9/20
LCD: 20
3 15/20 + 14/20
= 3 29/20 = 4 9/20

8. 9
LCD: 15
6 3/15 + 2 7/15 + 5/15
= 8 15/15 = 9

9. 10 37/40
LCD: 40
3 + 7 5/40 + 32/40
= 10 37/40

10. 13 1/6
LCD: 6
9 3/6 + 22/6
= 9 25/6 or 13 1/6

 

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Civil Service Exam Vocabulary Review 15

This is the PCSR 15th vocabulary reviewer.

1. Abridge – verb
Shorten, diminish, curtail

Because my time was limited, I just watched the abridged version of the movie.

2. Blunder – noun
Error, careless mistake, blooper

The criminal’s blunder led to his capture.

3. Cacophonous- adjective
Discordant, loud noise

I did not sleep well last night because of the cacophonous sound upstairs.

4. Deadlock-noun
Standstill, dead end, stalemate

Because the negotiations had reached a deadlock, the team leader decided to take a recess.

5. Ensconce-verb
Settle, establish

After her retirement, the old maid ensconced on her rest house by the beach.

6. Fervent-adjective
Ardent, hot

After attending a retreat, Allison suddenly felt a fervent desire to change herself.

7. Gibe-verb
Mock, jibe, slam, taunt

The mean girls at school consistently gibed at Minna, teasing her about her old clothes.

8. Heinous-adjective
Atrocious, hatefully bad

Most of the senators voted to bring back the death penalty, but for heinous crimes only.

9. Incorrigible-adjective
not correctable

The effect of the drugs on the youth makes them incorrigible; they will just keep on justifying their wrongdoings.

10. Insipid-adjective
Lack of flavor, dull

Grandma prepared us an insipid cookie. We pretend that it was sweet so that grandma’s feelings won’t get hurt.

Rules in Alphabetic Filing Part 3

This the third post in the Alphabetic Filing series. In this post, we are going to discuss the rules when confusion arises in distinguishing first names and last names.

Rule 3

When it is impossible to distinguish which is the first name or the last name, or if there is confusion in the arrangement of the names, file in alphabetically as written. Consider the following examples.

Carlo Bernardo
Jose Mario
Guillermo Mateo
Rosario Leopoldo
Magno Roberto

In the listed names above, it is difficult to distinguish what which are the first names and the surnames. Therefore, we can assume that the second names are the surnames. Thus, when they are alphabetized, they are arranged as follows.

Bernardo, Carlo
Leopoldo, Rosario
Mario, Jose
Mateo, Guillermo
Roberto, Magno

Exercise 1

Leon Rodrigo
Bianca Victoria
Nicolas Romeo
Benedicto Pedro
Jaime Lee

Exercise 2

Marcos Angelo
Felix Patricio
Alberto Rico
Jericho Rodolfo
Camille Maria

Exercise 3

Jorge Enrique
Luis Nico
Angela Gabriella
Daniel Magnus
Jeffrey Lester

Answer to Exercise 1

Lee, Jaime
Pedro, Benedicto
Rodrigo, Leon
Romeo, Nicolas
Victoria, Bianca

Answer to Exercise 2

Angelo, Marcos
Maria, Camille
Patricio, Felix
Rico, Alberto
Rodolfo, Jericho

Answer to Exercise 3

Enrique, Jorge
Gabriella, Angela
Lester, Jeffrey
Magnus, Daniel
Nico, Luis

That’s it for the third rule in alphabetizing. In the next post, we will learn how to file compound and hyphenated names.

LCM and GCD Exercises Set 1

After learning about LCM and GCD in our PCSR Review Guide 1, let’s practice what we have learned by answering the exercises below.

1.) What is the LCM of 6 and 8?

2.) What is the LCM of 3, 4, and 9?

3.) Consider the following sequences:
Sequence 1: 4, 8, 12, 16, 20, 24, 28, …
Sequence 2: 5, 10, 15, 20, 25, 30, …
As we can see, 20 is common to both sequences. What is the 10th common number?

4.) Gina goes to BODY SLIM gym every 3 days, while Sam goes to the same gym every 4 days. If they were in the same gym on a February 12, what’s the nearest date that they will be both in the gym?

5.) In a decoration LED light, the green lights blink every 400 milliseconds, the blue light every 500 milliseconds, and the red light every 750 milliseconds. If the three lights all blinked at the same time, in how many milliseconds will they again blink at the same time?

6.) What is the LCD of 1/3, 1/4, and 1/6?

7.) What is the GCD of 28 and 35?

8.) What is the GCD of 39, 65, and 91?

9.) A rectangular paper with dimensions 12 inches by 18 inches is to be cut into largest possible squares of equal sizes. If no paper is to be wasted, what should be the dimensions of the squares?

Q10.) A rectangular prism piece of wood with dimensions 16 inches by 20 inches by 32 is to be cut into cubes of the same size.

A. If we want to minimize the wasted wood while cutting, what should be the dimensions of the cubes?

B. How many cubes can we make given the above conditions?

Solutions and Answers

1.) 24

2.) 36

3.)  200

4.) LCM of 3 and 4 is 12. Twelve days after February 12 is February 24.

5.) 6000 milliseconds

6.) 12

7.) 7

8.) 13

9.) Side of the square should be GCD of 12 and 18 which is 6 inches.

10.) A. Side of the cube should be GCD of 16, 20, and 32 which is equal to 4 inches.

B. 16/4 × 20/4× 32/4 = 4 × 5 × 8 = 160 cubes

 

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