Addition of Fractions Exercises – Set 2

Add the following fractions.

1.) \dfrac{1}{7} + \dfrac{2}{7}

2.) \dfrac{1}{12} + \dfrac{5}{12}

3.) \dfrac{7}{15} + \dfrac{2}{15} + \dfrac{6}{15}

4.) \dfrac{1}{3} + \dfrac{1}{4}

5.) \dfrac{2}{9} + \dfrac{1}{3}

6.) \dfrac{3}{8} + \dfrac{1}{4}

7.) 8 \dfrac{2}{3} + \dfrac{3}{2}

8.) \dfrac{1}{2} + \dfrac{2}{3} + \dfrac{3}{4}

9.) 7 \dfrac{2}{7} + 6 \dfrac{3}{14}

10.) 3 \dfrac{1}{4} + 2 \dfrac{1}{8}

Answer key and solution:

1.) \dfrac{3}{7}

2.) \dfrac{6}{12} = \dfrac{1}{2}

3.) \dfrac{15}{15} = 1

4.) \dfrac{7}{12}
Solution:
LCD: 12
\dfrac{4}{12} + \dfrac{3}{12} = \dfrac{7}{12}

5.) \dfrac{5}{9}
Solution:
LCD: 9
\dfrac{2}{9} + \dfrac{3}{9} = \dfrac{5}{9}

6.) \dfrac{5}{8}
Solution:
LCD: 8
\dfrac{3}{8} + \dfrac{2}{8} = \dfrac{5}{8}

7.) 10 \dfrac{1}{6}
Solution:
LCD: 6

8 \dfrac{4}{6} + \dfrac{9}{6} = 8 \dfrac{13}{6} = 10 \dfrac{1}{6}

8.) 1 \dfrac{11}{12}
Solution:
LCD: 12

\dfrac{6}{12} + \dfrac{8}{12} + \dfrac{9}{12} = \dfrac{23}{12} = 1 \dfrac{11}{12}

9.) 13 \dfrac{1}{2}

Solution:
LCD: 14

7 \dfrac{4}{14} + 6 \dfrac{3}{14} = 13 \dfrac{7}{14} = 13 \dfrac{1}{2}

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

Solution:
LCD: 8

3 \dfrac{2}{8} + 2 \dfrac{1}{8} = 5 \dfrac{3}{8}

LCM and GCD Exercises Set 2

Here are some Civil Service exam exercises on GCD and LCM.

1.) What is the GCD of 8, 20, and 28?

2.) What is the GCD of 21, 35, and 56?

3.) What is 18/54 in lowest terms?

4.) What is 38/95 in lowest terms?

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

6.) What is the LCM of 5, 6, and 12?

7.) What is the product of the LCM and the GCD of 4, 8, and 20?

8.) There are 18 red marbles and 27 blue marbles to be distributed among children. What is the maximum number of children that can receive the marbles if each kid receives the same number of marbles for each color and no marble is to be left over?

9.) In a school sportsfest, there are 60 Grade 4 pupils, 48 Grade 5 pupils and 36 Grade 6 pupils. What is the largest number of teams that can be formed if the pupils in each Grade level are equally distributed and no pupil is left without a team?

10.) In a disco, the red lights blink every 3 seconds and the blue lights blink every 5 seconds. If the two colored lights blink at the same time if you turn them on, they will blink at the same time every ___ seconds.

Answers:

1.) Answer: 4
Solution:
Divisors of 8 – 1, 2, 4, 8
Divisors of 20 – 1, 2, 4, 5, 10, 20
Divisors of 28 – 1, 2, 4, 7, 14, 28

2.) Answer: 7
Solution:
Divisors of 21 – 1, 3, 7, 21
Divisors of 35 -1, 3, 5, 7, 35
Divisors of 56 -1, 2, 7, 8, 14, 28, 56

3.) Answer: 1/3
Note: Reducing fractions to lowest terms is one of the applications of GCD.
Solution:
Divisors of 18 – 1, 2, 6, 9, 18
Divisors of 54 – 1, 2, 3, 9, 18, 27, 54
Numerator = 18 divided by 18 (GCD) = 1
Denominator = 54 divided by 18 (GCD) = 3
Final answer: 1/3

4.) Answer: 2/5
Solution:
Divisors of 38 – 1, 2, 19, 38
Divisors of 95 – 1, 2, 3, 19, 95

5.) Answer: 24.
Solution:
Multiples of 6 – 6, 12, 18, 24
Multiples of 8 – 8, 16, 24

6.) Answer: 60.
Solution:
Multiples of 5 – 5, 10, 15, 20, 25, 30 … 55, 60
Multiples of 6 – 6, 12, 18, 24, 30, 36, 42, 48, 54, 60
Multiples of 12 – 12, 24, 36, 48, 60

7.) Answer: 160.
Solution
GCD of 4, 6, and 20 is 4.
LCM of 4, 6, and 20 is 40.
4 x 40 = 160.

8.) Answer: 9
Solution:
Divisors of 18 – 1, 2, 3, 6, 9, 18
Divisors of 27 – 1, 2, 3, 9, 27

9.) Answer: 12.
Solution:
Divisors of 60 – 1, 2, 3, 4, 5, 6, 10, 12, 20, 30, 60
Divisors of 36 – 1, 2, 3, 4, 6, 9, 12, 18, 36
Divisors of 48 – 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

10.) Answer: 15 seconds.
Solution
LCM of 3 and 5 is 15

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Civil Service Exam Correct Usage Reviewer

Here are some multiple-choice Civil Service exam reviewers on Correct Usage.

Instruction: Choose the letter that corresponds to the word or phrase that will correctly complete each sentence.

1.) The musical play _______ we saw last night was fascinating.
A.) whose
B.) whom
C.) that
D.) since

2.) _______ the four candidates, Margot was chosen to become the school representative.
A.) Between
B.) Among
C.) Meanwhile
D.) Already

3.) I noticed that you don’t look too well. What is it that _______ you?
A.) ails
B.) ales
C.) aisles
D.) isles

4.) My teacher _______ I was absent last time when she _______ the lesson on Tirad Pass.
A.) taught, thought
B.) tot, thawed
C.) thought, taught
D.) thought, teached

5.) The envoy from Latvia handled the affair in a _______ fashion.
A.) discreet
B.) discrete
C.) discretely
D.) discreetly

6.) My friends and I have known each other _______ 1990.
A.) after
B.) since
C.) mean while
D.) because of

7.) Jasper, a known rebel, _______ the speed limit by doing 170 on the road.
A.) flaunted
B.) flouted
C.) flagged
D.) flippant

8.) Martin speaks French. _______ you?
A.) Should
B.) Can
C.) May
D.) How

9.) Policies in society that do not work for the people should be _______ so that they serve the common good.
A.) praised
B.) undermined
C.) ameliorated
D.) metabolized

10.) _______ are fourteen volunteers in _______ group. _______ waiting for you.
A.) Their, they’re, There
B.) There, they’re, Their
C.) There, their, They’re
D.) They’re, there, Their

11.) Cheating on you is the _______ thing in my mind right now.
A.) furthest
B.) farther
C.) farthest
D.) further

12.) After playing three soccer games, Diego left _______.
A.) burned out
B.) burned in
C.) burned over
D.) burned up

13.) Please do not _______ the volume of the radio as I am studying for my exams.
A.) turn over
B.) turn out
C.) turn up
D.) turn with

14.) They were playing in the yard when the balloons _______.
A.) pooped
B.) plooped
C.) bursted
D.) burst

15.) People of different religions should _______ with each other despite their creeds and beliefs.
A.) get around
B.) get along
C.) get over
D.) get with

16.) _______ are my students you are scolding.
A.) That
B.) Than
C.) This
D.) These

17.) There is _______ that I can do to help you at this point.
A.) little
B.) more
C.) somehow
D.) few

18.) The fifth grade children of Mrs. Santos are _______. They ignored their teacher’s reminders.
A.) uninteresting
B.) disinterested
C.) disinteresting
D.) interested

19.) The sheriff _______ the bank robbers last Sunday.
A.) hung
B.) hanging
C.) hanged
D.) hunging

20.) The _______ at work is that of gravity.
A.) participle
B.) particle
C.) principal
D.) principle

Answers:

1.) C.) that. The relative pronoun used here (“here”) applies to any object that is concrete or tangible.
2.) B.) among. The proper word should be “among” as there are several choices given. “Between” applies only when two choices are provided.
3.) A.) ails. The correct word is “ails” which means “makes one feel sick”.
4.) C.) thought, taught. “Thought” as the past tense of “think, and “taught” as the past tense of “teach”
5.) A.) discreet. “Discreet” means in a secret manner while “discrete” means separate unit.
6.) B.) since. The adverb of time “since” is the correct choice to suggest that the speaker in the sentence and his peers have known each other sometime in the past.
7.) B.) flouted. The word “flaunt” means to be overly expressive so as to boast while “flout” means to disregard rules or conventions. The correct answer is therefore flouted.
8.) B.) can. The correct choice is “can” making the reader ask if it is possible for him to do what is suggested.
9.) C.) ameliorated. Policies that don’t work need to be improved. “Ameliorate” means to change something for the better.
10.) C.) There, their, they’re. The use of “there” indicates an assertion of some quality or trait, or even to point at a direction. “Their” is a pronoun used to show possession, while “they’re” is a contraction (short-cut) for “they are”.
11.) A.) furthest. The rule on the use of “farther” applies to physical distance in space, while “further” implies mental distance/degree.
12.) A.) burned out. The expression “burn out” means to reach a point of exhaustion.
13.) C.) turn up. To “turn up” something means to increase the sound or volume.
14.) D.) burst. The verb “burst” is an irregular verb and its past tense is also “burst” not bursted.
15.) B.) get along. The phrasal verb “get along” means to cooperate with each other.
16.) D.) these. The correct answer is “these” as it agrees with the referent, children (plural form).
17.) A.) little. The tone of the sentence suggests not much can be done. The appropriate answer is “little” not “few” because the idea is something that is not quantifiable.
18.) B.) disinterested. “Disinterested” means indifferent, impartial or unconcerned.
19.) C.) hanged. The verb hang has two meanings but both mean to suspend something. The past tense for hanging “people” as a form of punishment in some societies is “hanged” while “hung” suggests the past of objects being suspended like clothes.
20.) D.) principle. “Principle” names a fundamental belief, rule or idea.

Civil Service Exam Synonyms Reviewer

Here are some multiple-choice Civil Service exam reviewers on synonyms.

Choose the letter that corresponds to the word closest in meaning to the bold and italicized word in the sentence.

1.) It is paradoxical to say that one can be patriotic and not patriotic at the same time.

A.) supportive
B.) contradictory
C.) energizing
D.) truthful

2.) Many false stories surfaced the author’s death but only those which are widely popular remained canonical.

A.) valuable
B.) meaningful
C.) engaging
D.) acceptable

3.) The five star general remained composed in his behaviour although a lot of logistical problems continued to fill his ranks.

A.) serene
B.) inspired
C.) thoughtful
D.) focused

4.) The football team remained enervated after the particularly difficult final match with the defending champions from Barotac.

A.) exhausted
B.) motivated
C.) calculating
D.) noisy

5.) The chief operating officer suggested a more pragmatic approach in dealing with the situation, relying more on results and outcomes.

A.) planned
B.) practical
C.) polite
D.) purposeful

6.) Between rumors of a tryst with a government official and allegations of drug dependency, the student athlete decided to disappear from the public eye.

A.) flight
B.) love affair
C.) secret meet
D.) corruption

7.) Doctors recommend that people should drink more water when they are working out strenuously.

A.) consistently
B.) thoroughly
C.) vigorously
D.) slowly

8.) The Harry Potter books have become ubiquitous in bookstores around the English-speaking world.

A.) amazing
B.) widespread
C.) annoying
D.) entertaining

9.) Batman defeated Gotham’s mob bosses and ended their nefarious activities that took advantage on the weak and the poor.

A.) questionable
B.) hidden
C.) altruistic
D.) wicked

10.) Because of his flippant remarks, Quentin’s friends never took him seriously.

A.) light-hearted
B.) profound
C.) demeaning
D.) wise

11.) The old professor’s lectures were soporific in their effect as seen from the immediate results in the lecture hall.

A.) enlightening
B.) merciful
C.) sleep-inducing
D.) engaging

12.) The young lady was often lachrymose whenever she reads books that lead to tragic ends.

A.) silly
B.) preoccupied
C.) lazy
D.) tear-filled

13.) Many civic minded members of society decry government policies that continue to ignore the concerns of the poor.

A.) condemn
B.) express
C.) support
D.) lessen

14.) Many college textbooks, despite the appeal of their subject matter, remain stodgy in their discussion and presentation of topics.

A.) limited
B.) short-sighted
C.) boring
D.) erroneous

15.) Because of his warm attitude and scholarly erudition, the class admired Mr. Pelaez and ignored his minor weaknesses.

A.) positivity
B.) intelligence
C.) virtue
D.) religiousness

Answer key:

1.) B.) contradictory
2.) D.) acceptable
3.) A.) serene
4.) A.) exhausted
5.) B.) practical
6.) C.) secret meet
7.) C.) vigorously
8.) B.) widespread
9.) D.) wicked
10.) A. ) light-hearted
11.) C.) sleep-inducing
12.) D.) tear-filled
13.) A.) condemn
14.) C.) boring
15.) B.) intelligence

PDF Download: Integer Addition Practice Sheet

I have many requests to create downloadable files, so, I will be publishing downloadable files in PDF starting with the Integer Addition Practice Sheet below. You are allowed to print and share the file below (and future PDF files) via hard copy or email. However, you are not allowed to sell or publish them in print or upload them on websites of any kind (e.g. blogs).

In each worksheet, I will recommend the time limit to answer the questions. This way, you should be conscious of the time since the Civil Service Exam or any other exam is usually under time pressure.

I have also placed the answer key on a different page, so you don’t have to see it when answering the practice sheet on your computer.

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