Week 1 Review: Practice Exercises and Problems

Below are the practice exercises for the Week 1 Review on LCM and GCD. You can read the answers and solutions to these exercises and problems. Practice Exercises I. Find the GCD of each of the following. a.) 6, 10 b.) 18, 42 c.) 12, 48, 60 d.) 56, 72 e.) 225, 75 II. Find the… Read More »


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… Read More »

Solving Ratio and Proportion Problems Part 2

In the previous post, we have learned the meaning and notation of ratio. We can write the ratio of 8 girls and 12 boys as 8:12 or as 8/12. However, if we represent this as fraction, we can also reduce the fraction to its lowest terms which is equal to 2/3. Converting to lowest term is dividing… Read More »

Solving Ratio and Proportion Problems Part 1

One of the key concepts tested in the Civil Service Exam is ratio and proportion. In this series, we are going to discuss how to solve problems involving ratio and proportion. We first begin below by explaining the meaning and concept of ratio and how to represent it. Suppose we are cooking, and for every… Read More »

Practice Exercises on Subtraction of Integers

To answer the exercises below, it is assumed that you have already finished reading addition of integers and subtraction of integers. In subtraction of integers, we have learned two rules: (1) a – b = a + (-b) (2) a – (-b) = a + b We will use these rules in answering the exersises… Read More »

Four Effective Techniques in Adding Integers

We have already discussed addition of integers. In this post, I am going to discuss four different techniques in adding integers. Adding Numbers with the Same Sign In adding integers with the same sign, we just add them and then copy the sign. For example, in adding 2 + 8, 2 and 8 are positive integers,… Read More »

Solving Word Problems by Working Backwards: Summary

In the previous posts, I have shown to you a series on how to solve word problems by working backward.  Although I recommend that you learn this method, it is also very important to learn algebraic methods and others since some problems are difficult to solve by working backward. Below are the posts in this series. How… Read More »

How to Solve Word Problems by Working Backwards Part 3

In part 1 and part 2 of this series, we have learned how to solve number age problems by working backward. In this post, we are going to learn how to solve backward using inverse operations. Recall that multiplication and division are inverse operations and addition and subtraction are inverse operations. Example 5 A number is… Read More »

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