## Practice Test on Dividing Fractions

Divide the following fractions and reduce your answers to lowest terms. Convert all answers that are improper fractions to mixed fractions.

1.) $\frac{4}{5} \div \frac{2}{3}$.

2.) $\frac{2}{7} \div \frac{5}{21}$

3.) $8 \div \frac{4}{5}$

4.) $\frac{3}{5} \div 12$

5.) $15 \frac{2}{3}$

6.) $3 \frac{2}{5} \div \frac{3}{4}$ » Read more

## 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. » Read more

## Practice Test on Multiplying Fractions

In the previous post, we have learned how to multiply fractions. We have learned that it is the easiest operation on fractions. To multiply fraction, we just have to multiply the numerators and then the denominators. That is a fraction $\frac{a}{b}$ multiplied by $\frac{c}{d}$ is equal to $\frac{a \times c}{b \times d}$.

Practice Test on Multiplying Fractions

Below are the exercises on multiplying fractions.  Multiply the fractions and reduce your answers to the lowest terms. If the answer is an improper fraction, convert the improper fraction to mixed fraction.

1. $\displaystyle \frac{2}{3} \times \frac{4}{5}$ » Read more

## Practice Test on Converting Improper Fractions to Mixed Number

In the previous post, we have learned how to convert improper fractions to mixed number . Now, try the following exercises. All the answers must also be reduced to lowest terms. Good luck.

1.) 22/7

2.) 81/6

3.) 55/10

## Solution to the Exercises on Reducing Fractions to Lowest Terms

Below are the complete solutions and answers to the exercises on reducing fractions to lowest terms. I will not give any tips or methods of shortcuts on doing this because teaching you shortcuts will give you problems in case you forget them. The best thing that you can do is to solve as many related problems as you can and develop shortcuts that work for you. Each person has his own preference in solving procedural problems such as these, so it is important that you discover what’s best for you.

For converting improper fractions to mixed form, I will discuss it in a separate post. Try to see the solutions below and see if you can use these solutions to develop your own method. Honestly, the three examples below on converting improper fractions to mixed form should be enough to teach you how to do it yourself. 🙂 » Read more

## Grammar and Correct Usage Practice 2 Answers and Explanations

Below are the answers and the explanations to the Grammar and Correct Usage Practice Test 2. The incorrect word or phrase in the sentence is highlighted red, while the correct word or phrase is highlighted green.

1. Paul Erdos was a mathematician who writes a lot of research papers in collaboration with other mathematicians.

Correct Sentence: Paul Erdos was a mathematician who wrote a lot of research papers in collaboration with other mathematicians

Explanation: The tense of the verbs in a sentence must be consistent unless there is a reason to change. The verb was is past tense, so the verb writes must be changed to wrote» Read more

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

## Fraction Addition Practice Test 1

In the previous post, we have learned how to add fractions both similar and dissimilar. We have discussed that that in adding similar fractions, we just add the numerator of the addends and copy the denominator. On the other hand, in adding dissimilar fractions, we need to get the least common multiple of the denominator or the least common denominator to be able to convert them to similar fractions.

Below is a practice test on on adding similar and dissimilar fractions.  If you already know how, convert your answers to lowest terms or mixed form.

1. $\displaystyle \frac{2}{7} + \frac{3}{7}$  » Read more