Fractions and Decimals

This chapter reviews fractions and decimals and how to order real numbers. Fractions and decimals are the most common ways that numbers are represented. An understanding of these representations, and how to perform operations on these types of numbers is essential to your success at math. Before you study the lessons in this chapter, take a few minutes to take the following ten-question Benchmark Quiz. These questions are similar to the type of questions that you will find on important tests. When you are finished, check the answer key carefully to assess your results. The quiz will help you assess your prior knowledge of fractions and decimals. You may find that you are successful with one type and need additional help with another. You can then proceed to the lessons with focus. 

How did you do on the Benchmark Quiz Check your success in working with fractions and decimals here, and then analyze your results to figure out your plan of attack to master these topics. The answer explanations will give you an indication of what is required to solve these types of problems. 

If you answered 8-10 questions correctly, you most likely have a solid understanding of performing basic arithmetic with fractions and decimals. Read over the chapter there may be alternative ways you can learn to work with decimals and fractions, and the shortcuts and sidebar information may... 

If you answered 1-3 questions correcdy, you need extended clarification on the topics in this section. A solid understanding of fractions and decimals is crucial to your success in any type of mathematics test. First, carefully read this chapter and concentrate on the sidebars and visual aids that will help with comprehension. Perhaps you learned this information and forgot take the time now to refresh your skills and improve your knowledge. Go to the suggested website in the Extra Help sidebar in this chapter, and do extended practice. You may also want to refer to Practical Math Success in 20 Minutes a Day, Lessons 1-8, published by LearningExpress. This book provides more extensive lessons on fractions and decimals. 

Do you feel more confident about fractions and decimals Take the following quiz to see if you have mastered these concepts. 

Distributing the 2.70 and simplifying don t make for very pretty computations, but a calculator makes short work of all the operations. I choose to find a common denominator to combine the fractions and decimals, because the decimal you get with a denominator of 19 just keeps repeating. Then you solve for p by multiplying each side of the equation by the reciprocal of its coefficient. 

You can fill in whole numbers, fractions, and decimals on the grids. Examples follow. 

Rational numbers are numbers that can be written as fractions (and decimals and repeating decimals). Similarly, numbers raised to rational exponents are numbers raised to fractional powers ... 

A PERCENT IS a ratio that represents a part-to-a-whole as a number out of 100. Fractions are used to represent a part-to-a-whole, but fractions can have many different denominators. A percent is like a fraction whose denominator is always 100. The relationship 50 out of 100 is written as 50%. The relationship 1 out of 2 can also be written as 50%. That is because the fraction is equal to Fractions and decimals can be written as percents, and vice versa, as we ll see in Chapter 11. 

Real Numbers Include fractions and decimals in addition to the integers. Some examples of real numbers are -j, -8.5, 3, y, -9. 

Stumped If you don t know the answer to a question, chances are Dr. Math (www.mathforum.com/dr.math) will. The "Dr. Math" column is a question-and-answer service that examines classic math problems. The Frequently Asked Questions area covers topics ranging from basic (order of operations, fractions, and decimals) to advanced (imaginary numbers and two-column proofs). If you don t see what you re looking for, you can even e-mail Dr. Math for help. 

Let s look at 25%. Put 25 over 100 to get y y. Notice that reduces to. It is good to be familiar with some of the common fraction and decimal equivalents of percentages. Some are listed in the chart below. 

Real numbers Include fractions and decimals in addition to integers. 

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