## 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

## Grammar and Correct Usage Practice Test 2

This is the second part of the Grammar and Correct Usage practice tests series. In each sentence, identify the error in punctuation, grammar, and usage.

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

2. Anna lay her books on the table before opening her laptop.

3. Please seat here, Mr. Reyes. I’ll just call the doctor.

4. Which constellation do you see most often, Leo Minor or Pegasus?

5. He is the one which called earlier.

6. I am taking japanese class next semester. » 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

Fractions whose denominators are the same are called similar fractions. Fractions that are not similar are called dissimilar fractions. Hence, the fractions $\frac{1}{8}$, $\frac{3}{8}$, and $\frac{5}{8}$ are similar fractions, while the fractions $\frac{2}{3}$ and $\frac{1}{2}$ are dissimilar fractions. In this post, we are going to learn how to add fractions.

Adding similar fractions is very easy.  In adding similar fractions, you just add the numerator and copy the denominator.  Here are a few examples.

Example 1

$\displaystyle \frac{1}{5} + \frac{2}{5} = \frac{1 + 2}{5} = \frac{3}{5}$

Example 2

$\displaystyle \frac{1}{8} + \frac{2}{8} + \frac{4}{8} = \frac{1 + 2 + 4}{8} = \frac{7}{8}$ » Read more

## 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. » Read more

## A Gentle Introduction to Fractions

Fractions is one of the mathematics topics that many people have difficulty with. However, unfortunately, it is also one of the most important topics that must be mastered. This is because examination questions in mathematics always include fractions. For example, in the Civil Service Review Numerical Reasoning tests, fractions appear in almost every test: basic arithmetic, number sequences, equations and problem solving.

In this post, we are going to discuss the basics about fractions particularly about the terminologies used. Of course, you don’t really have to memorize them now, but you can refer to this post in the following discussions. In the future discussions, you will use the vocabulary that you have learned here.  » Read more

## PEMDAS Rules Practice 1 Solutions

Below are the solutions and answers to the problems in PEMDAS Rules Practice 1. Notice that I have color coded the solution to guide you which operation results to which answer. I have also varied the notations like / and ÷ to familiarize you with both of them. In addition, I have also included operations on fractions with expressions in the numerator and the denominator. In a fraction whose numerator and/or denominator contains one or more operations , you have to simplify first both the numerator and the denominator before dividing. The methods in calculating fractions are shown in numbers 7, 9 and 10.

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