## 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

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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## 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!

## Addition of Fractions Online Quiz 2

To those who want to test their skills on addition of fractions, you can take the online quiz below. This is a 10-item test with no time limit. You can immediately check if your answer is correct or not.

If the result of your score is not very good, you might want to read How to Add Fractions  and take the Practice Exercise with complete solutions. You might also check out the first online quiz on addition of fractions. It is slightly easier.

Rules: All answers must be in lowest terms and/or mixed fractions.

[WpProQuiz 6]

## Addition of Fractions Quiz 1

Operations on fractions is one of the concepts that you should master if you want to take the Civil Service Examination.  Although it maybe an elementary concept, but problems in Number Series as well as  in Algebra (such as Word Problems) usually involve fractions. Take your first quiz on Addition of Fractions and see how much you have learned.

Note that more quizzes will come. All the Quiz 1’s in this blog are appetizers — they are the easiest quizzes and they are not as hard are those in actual Civil Service Exams. Quiz 2 and Quiz 3 on every topic will be likely as hard as the actual exams.

[WpProQuiz 5]

## A Summary of the Operations on Fractions Series

Fractions is one of the concepts that you should master if you want to pass the Civil Service Examination. Although fraction seems like a simple context, most of the time it is used in higher mathematics such as algebraic manipulation as well as in problem solving. We have discussed all the operations in fractions, but notice that I first discussed multiplication and division before addition and subtraction. This is because the first two operations are easier. I recommend that you read the series the order that I have written it.

Operations on Fractions Series

In addition, I am also planning to write 3 to 4 more articles to discuss more complex problems, but not immediately. I will be switching my discussions on decimals and percents and then proceed to Algebra and word problem solving soon. I will also be discussing other types of exams in English.

The next Civil Service Examination is in April 2014. I strongly suggest that you start reviewing now if you are planning to take the test.

## Tagalog Video: The Concept of Least Common Multiple

I am planning to include videos of explanation of mathematical concepts in this blog and below is my first trial video. The explanation in the video is mostly Filipino (Tagalog) and sometimes English. This video discusses the concept of least common multiple which is used in addition of fractions.

I hope you learn something from here. Please feel free to use the comment box.  🙂

Note: In 4:49, I said that the fraction will become larger. Actually, the value of the fraction does not change. It is the number in the numerator and the denominator that becomes larger.

The idea of getting the least common multiple of the denominator in adding dissimilar fractions is to convert them into similar fractions or fractions whose denominators are the same. Once the fractions are similar, you only need to add the numerator and  copy the denominator.

The solutions to Fraction Addition Practice Test 1 below is divided into three parts: (1) getting the least common multiple of the denominator, (2) converting the given fractions to their equivalent fractions whose denominator is the LCM and (3) adding the converted fractions. Of course, in solving this types of problem the Civil Service Exam, you don’t need to go through all the steps. You should try developing your own short cuts to make solving faster.

Solution to Number 1

Given: $\displaystyle \frac{2}{7} + \frac{3}{7}$

$\displaystyle \frac{2}{7} + \frac{3}{7} = \frac{2 + 3}{7} = \frac{5}{7}$

Answer: $\displaystyle \frac{5}{7}$

## How to Get the Least Common Multiple of Numbers

In mathematics, a multiple is a product of any number and an integer. The numbers 16, -48 and 72 are multiples of 8 because 8 x 2 = 16, 8 x -3 = -48 and 8 x 9 = 72. Similarly, the first five positive  multiples of 7 are the following:

7, 14, 21, 28, 35.

In this post, we will particularly talk about positive integers and positive multiples.  This is in preparation for the discussions on addition and subtraction of fractions.

We can always find a common multiple given two or more numbers. For example, if we list all the positive multiples of 2 and 3, we have

2, 4, 6, 8, 10, 12, 14, 16, 18, 20

and

3, 6, 9, 12, 15, 18, 21, 24, 27, 30. Continue Reading