## PCSR Civil Service Exam Review Guide 4

After learning how to subtract fractions, in this review guide we will be learning about multiplication and division of fractions. Watch the video below and read the articles.

PART I: MATHEMATICS

Videos

A. Multiplication of Fractions

B. Division of Fractions

More videos (Taglish videos from Youtube)

Articles

Multiplication of Fractions

Division of Fractions

PART II: ENGLISH

A. Vocabulary

Civil Service Exam Vocabulary Review Part 4
Tip: Try to memorize the words and use it in your own words.

B. Grammar – The Progressive Tenses

Below are the solutions and answers to the Week 4 Practice Problems and Solutions.

Practice Exercises 1

Note: In multiplying fractions, we multiply the numerator by the numerator of the other fraction, and then multiply the denominator by the denominator of the other fraction. For whole numbers, we can put 1 as the denominator. All fractions must be in lowest terms.

A. 1/2 × 1/3 = 1/6
B. 2/3 × 4/5 = 8/15
C. 8/1 × 5/6 = 40/6 = 6 4/6 or 6 2/3
D. 2 5/8 × 3 = 21/8 × 3/1 = 63/8 = 7 7/8
E. 3 1/8 × 4/5 = 25/8 × 4/5 = 100/40 = 2 20/40 or 2 1/2
F. 1 2/3 × 2 3/4 = 5/3 × 11/4 = 55/12 = 4 7/12

Practice Exercises 2

A. When dividing fractions you get the reciprocal of the divisor, and then multiply. In 1/5÷ 3/10, the divisor 3/10 and the reciprocal of 3/10 is 10/3. So, 1/5 × 10/3 = 10/15 or 2/3

B. 1/2 ÷ 3/8 = 1/2 × 8/3 = 8/6 = 1 2/6 or 1 1/3

C. 9 ÷ 3/7 = 9 × 7/3 = 63/3 or 21

D. 2 5/8 ÷ 2

First, we convert 2 5/8 to improper fraction as follows. That is $2\frac{5}{8} = \frac{8 \times 2 + 5}{8} = \frac{21}{8}$. Don’t forget that the denominator of the mixed fraction is the same as the denominator of the improper fractions.

Here, the reciprocal of 2 is 1/2. So, 21/8 × 1/2 = 21/16 = 1 5/16

E. 3 1/8 ÷ 3/5 = 25/8 × 5/3 = 125/24 = 5 5/24

F. 2 3/4 ÷ 1 1/8 = 11/4 ÷ 9/8 = 11/4 × 8/9 = 88/36 = 2 16/36 or 2 4/9

Practice Problems

Note: In multiplication and division of fractions, all mixed fractions must be converted to improper fractions (see Practice Problem 2D above).

1.) 2/3 × 1/4 = 2/12 or 1/6

2.) 3/5 × 35/1=105/5 = 21 (women)
2/5 × 35/1 = 70/5 = 14 (men)

3.) 2 3/4 × 7 = (11/4) ×  7 = 77/4 = 19 1/4

4.) A = L × W
A = (35 1/4) × (20 1/2) = (141/4) × (41/2)
= 5781/8= 722 5/8

5.) 2 4/5 × 5/1= 14/5 × 5/1 = 14

6.) 1 1/2 L juice is to be shared equally by 6 friends, so 1 1/2 ÷ 6.

The mixed fraction  1 1/2 is 3/2 in improper form.

Dividing by 6 is the same as multiplying by 1/6, so 3/2 × 1/6 = 3/12

3/12 is not yet in its lowest term. So get its lowest term, divide the numerator and denominator by their GCF which is 3.  So, 3/12 will become 1/4.

The final answer is 1/4 L.

7.) 8 ÷ 2/5 = 8 × 5/2 = 8/1 × 5/2 = 40/2 = 20.

8.) Bookshelf length divided by book’s thickness = number of books that will fit in the bookshelf

5 1/4 feet ÷ 1 1/2 inches = ?

Notice that the units are in feet and inches. We cannot proceed until the units are the same, so we need  to convert feet into inches. (1 ft = 12 in) So 5 ft × 12 in per ft = 60 in. We still have 1/4 ft, so 1/4 of 12 which is 3 in. All in all, we have 63 in. Now our equation is

63  ÷ 3/2 = 63/1 × 2/3

= 126/3 = 42.

9.) 5 pumpkin pies are to be shared equally among 12 persons, equals 5/12.

10.) We have 8 3/4 hectares ÷ 4 children

35/4 ÷ 4 =35/4 × 1/4 = 35/16

Converting 35/16 to mixed fraction, we have 2 3/16.

## Week 4 Review: Practice Exercises and Problems

In the previous post, you have learned about multiplication and division of fractions. Now, let’s solve some exercises and problems.

Practice Exercises 1

a.) 1/2 × 1/3
b.) 2/3 × 4/5
c.) 8 × 5/6
d.) 2 5/8 × 3
e.) 3 1/8 × 4/5
f.) 1 2/3 × 2 3/4

Practice Exercises 2
a.) 1/5 ÷ 3/10
b.) 1/2 ÷ 3/8
c.) 9 ÷ 3/7
d.) 2 5/8 ÷ 2
e.) 3 1/8 ÷ 3/5
f.) 2 3/4 ÷ 1 1/8

Practice Problems

1.) What is 2/3 of 1/4?

2.) In a dance studio, 3/5 are women and 2/5 are men. If there are 35 persons in the dance studio, how many are men? How many are women?

3.) 2 3/4 liters of water is needed to water a flower bed. How many liters is needed to water 7 flower beds?

4.) A rectangular fish pond is 35 1/4 feet long and 20 1/2 wide. What is its area?

5.) 2 4/5 deciliters or soda is needed to make a punch. How many deciliters of soda is needed to make 5 punches?

6.) A 1 1/2 L juice is to be shared equally by 6 friends. How many L of soda is the share of each person?

7.) Two-fifth cup of oil is needed to make a birthday cake. How many birthday cakes can be made using 8 cups?

8.) The length of a bookshelf is 5 1/4 feet long. Each book on the shelf is 1 1/2 inches thick. How many books will fit on the shelf?

9.) Five pumpkin pies are to be shared equally among 12 persons. How much pumpkin pie does each person get?

10.) Jessie has 8 3/4 hectares of land. He decided to divide it equally among his four children. How many hectares of land will each receive?

## PCSR REVIEW SERIES WEEK 4: Multiplication and Division of Fractions

Last week, you have learned about addition and subtraction of fractions. This week, we will be studying about multiplication and division of fractions.

Below are the articles and videos that you should read and watch. Later, I will post exercises and problems.

Articles

Videos

Enjoy learning!

## 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.

## Answers to the Multiplying Fractions Practice Test

In the previous post, we have learned how to multiply fractions. We have learned that it is Below are the solutions and answers to the Practice Test on Multiplying Fractions.  If you have forgotten the methods of calculation, you can read How to Multiply Fractions.

The methods shown in some of the solutions below is only one among the many. I have mentioned some tips, but I don’t want to fill the solution with short cuts because there are times that when you forget the shortcut, you are not able to solve the problem. My advice if you want to pass the Civil Service Examination for Numerical Literacy is to master the basics, practice a lot, and develop your own shortcuts. Continue Reading