## Week 3 Review: Practice Exercises and Problems

Practice Exercises 1

a.) 2 1/5 + 3 2/5
b.) 8 1/4 + 2 3/4
c.) 5 + 2 1/4
d.) 5 1/2 + 1/5
e.) 3 1/3 + 4 1/4 + 5 1/5

Practice Exercises 2

a.) 4 6/7 – 3/7
b.) 8 – 3/4
c.) 12 – 5 2/9
d.) 7 3/10 – 7/10
e.) 6 1/5 – 3/4
f.) 9 3/8 – 4 5/7

Practice Problems

1.) Leo’s family drank 1 3/5 liters of juice yesterday morning and 4/5 liters of juice yesterday afternoon. How much juice did Leo’s family drank in all yesterday?

2.) A train station is between a school and a clinic. The distance between the school and the clinic is 2 5/8 kilometers and the distance between the train station and the clinic is 1 5/6 kilometers. What is the distance between the school and the train station?

3.) A piece of iron rod weighs 2 5/6 kg and another piece weighs 17/8 kilograms. Which is heavier and by how much?

4.) Gina bought a pizza. She gave 3/8 of it to her kids and 1/4 to her neighbor. What part of the pizza was left?

5.) Jaime’s house is two rides away from school. The jeepney ride is 3 4/15 kilometers and the tricycle ride is 5/8 kilometers. How far is Jaime’s school from his house?

## Division of Fraction Practice Test Solutions and Answers

This is the complete solutions and answers to the Practice Test on Division of Fractions. If you are not familiar with the method, or you have forgotten how to do it, please read “How to Divide Fractions.

In dividing fractions, you must convert all mixed fractions to improper fractions before performing the division. The division involves getting the reciprocal (multiplicative inverse) of the divisor, and then multiplying both fractions instead of dividing them.

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

Solution

We get the reciprocal of $\frac{2}{3}$  and multiply it to $\frac{4}{5}$. The reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$. So,  Continue Reading

## How to Convert Mixed Fractions to Improper Fractions

We have already learned how to convert improper fractions to mixed fractions.  In this post, we are going to learn how to convert mixed fractions to improper fractions.  In converting mixed fractions to improper fractions, the denominator stays as it is. You only have to calculate for the numerator.  To get the numerator of the improper fraction, multiply the denominator to the whole number and then add the numerator of the mixed fraction.

Let’s have three examples.

Example 1

Convert $6 \displaystyle \frac{2}{5}$ to improper fraction. Continue Reading

## Answers to Practice Test on Converting Improper Fraction to Mixed Number

This is the complete solutions and answers to the Practice Test on Converting Improper Fraction to Mixed Number. As illustrated in the image below, the quotient in the division becomes the whole number in the mixed fraction, the remainder in the division becomes the numerator of the fraction part of mixed fraction, and the denominator from the improper fraction becomes  the denominator of the fractional part of the mixed fraction.

In the solutions below, all answers were also reduced to lowest terms.

## How to Convert Improper Fractions to Mixed Forms

In Introduction to Functions, we have learned about proper and improper fractions. A fraction whose numerator (the number above the fraction bar) is less than its denominator (the number below the fraction bar) is called a proper fraction. Therefore, $\frac{1}{3}$, $\frac{2}{5}$ and $\frac{11}{20}$ are proper fractions.

On the other hand,  a fraction whose numerator is greater than its denominator is called an improper fraction. Therefore the fractions $\frac{21}{7}$, $\frac{8}{3}$ and $\frac{67}{5}$ are improper fractions.

In the Civil Service Examinations, some fractions need to be converted from one form to another. For example, in answering a number series test, you might need to convert an improper fraction to mixed form in order to compare it to other fractions in mixed form. In this post, we learn this method: how to convert an improper fraction to mixed form.

In converting improper fractions to mixed form you will just have to divide the fraction, find its quotient and its remainder. Remember that the fraction $\frac{34}{5}$ also means 34 divided by 5. Continue Reading

## Exercises on Converting Fractions to Lowest Terms

In the previous post, we learned how to convert fractions to lowest terms. In this post, I have created 15 exercises for you to practice.

Convert the following fractions to lowest terms. In case the fraction is improper, convert it to mixed form. Be sure that the fraction part is in lowest terms.

1. $\displaystyle \frac{12}{15}$

2. $\displaystyle \frac{18}{24}$

3. $\displaystyle \frac{21}{49}$ Continue Reading

## How to Convert Fractions to Lowest Terms

In the Civil Service Examination and in many mathematics examinations, results that are fractions are usually required to be converted to their lowest terms.  The numerator and the denominator of a fraction in lowest terms cannot be divided by any  similar integer. Knowledge of divisibility rules can be helpful in this process.

Example 1: Convert $\frac{6}{9}$ to lowest terms.

In the first example, we can see that the numerator and the denominator are both divisible by 3. Dividing both the numerator and the denominator by 3 gives us 2/3.

$\displaystyle \frac{6 \div 3}{9 \div 3} = \frac{2}{3}$

Note that dividing both the numerator and the denominator by the same integer does not change the value of the fraction. Continue Reading

## 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.  Continue Reading