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

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

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 $1\dfrac{5}{8}$

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

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.

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.

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

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

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

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.

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.

## 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