Math Refresher - CSEA Tax Local 690

[Pages:46]Math Refresher

Book #2

Workers ?Opportunities ?Resources ?Knowledge

Contents

Introduction ..................................................................................1 Basic Math Concepts ...................................................................2

1. Fractions..........................................................................2 2. Decimals........................................................................11 3. Percentages..................................................................15 4. Ratios............................................................................17 Sample Questions ......................................................................18 Answer Key ................................................................................28 Answers and Explanations .........................................................29

Math Refresher

This booklet is designed to refresh your understanding of basic math operations involving fractions, decimals, percents, and ratios. The first part of this booklet contains explanations of some basic math concepts. The second part contains practice questions that will test your ability to apply these concepts to a variety of math problems. Answers and explanations for all of the problems are included in the back of the book.

The best way to master this material is to work with the practice questions. Some of these questions may seem very difficult at first, especially if it has been years since you've worked with math problems. But if you study the explanations in the back of the book, you will learn how to approach these problems and you will gain a better understanding of the basic math concepts they involve.

Good luck!

Basic Math Concepts

1. Fractions

A fraction represents part of a whole. For example, if you divided a pie into four equal pieces, each piece would be 1 of the whole.

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The top number in a fraction is called the numerator. The bottom number is called the denominator.

In the fraction 1 the numerator is 1 and the denominator is 2. 2

Any whole number (1, 2, 3, etc) can be written as a fraction with a denominator of 1.

Adding Fractions

2 =2 1 50 = 50 1

It is easy to add fractions that have the same denominator. You simply add the numerators and keep the denominators the same. For example:

1+1 =2 333 Adding fractions becomes a little more complicated when the denominators are different. For example:

1+1 =? 24 In these cases, you need to find a common denominator, that is, a denominator that you can use for both fractions.

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One way to find a common denominator is to multiply the denominators together.

To find a common denominator for 1 and 1 , you could multiply 2 times 4.

2

4

2?4=8 So you know that these two fractions have a common denominator of 8.

When you convert the original fractions into fractions with a common denominator, you have to be sure to keep the values of the fractions the same. You can do this by multiplying both the numerator and the denominator of the fractions by the same number.

To convert 1 to a fraction with a denominator of 8, you would have to multiply 2

both the numerator and the denominator by 4

1?4=4 248

To convert 1 to a fraction with a denominator of 8, you would have to multiply 4

both the numerator and the denominator by 2

1?2=2 428

So now the two fractions have the same denominator, and to add them you can simply add the numerators:

4+2 =6 88 8

When you come up with an answer like 6 , you should simplify the answer. To 8

simplify a fraction, you look for the largest number that you can divide evenly into both the numerator and the denominator. In the fraction 6 , you can divide both

8 the numerator and the denominator by 2.

6?2=3 8?2=4

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So you can simplify 6 to 3 . 8 4

You can also find a common denominator by mentally reviewing your multiplication tables. Look for the smallest number that can be divided evenly by both denominators. For example:

1+3 =? 68 Both 6 and 8 will divide evenly into 24: 24 ? 6 = 4 24 ? 8 = 3 To convert the denominators of these two fractions to 24, multiply both the numerators and denominators by the same number. To convert 1 to a fraction with a denominator of 24, multiply both the numerator 6 and the denominator by 4: 1?4= 4 6 4 24 To convert 3 to a fraction with a denominator of 24, multiply both the numerator 8 and the denominator by 3: 3?3= 9 8 3 24 So now the two fractions have the same denominator, and to add them you can simply add the numerators: 4 + 9 = 13 24 24 24

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Subtracting Fractions You can use the same basic procedure for subtracting fractions. If the denominators are the same, subtract the numerators and leave the denominators the same. For example:

2-1 =1 333 If the denominators are different, you will have to find a common denominator: 1 - 1=? 24 If you use a common denominator, you come up with: 2-1=1 444

Multiplying Fractions To multiply fractions, you simply multiply the numerators together and multiply the denominators together. For example:

1?3=3 248

In this example, you multiply the numerators (1? 3 = 3) and the denominators (2 ? 4 = 8). You would follow the same process to multiply three or more fractions. For example:

1?3?2 = 6 2 4 3 24

When you come up with an answer like 6 , you should simplify the answer to 1 .

24

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Dividing Fractions In a division problem, the divisor is the number we are dividing by. In the problem

2 ? 1=? 34 the divisor is 1 . 4 To divide fractions, invert the divisor and then multiply. In the problem 2 ? 1=? 34 Invert 1 to 4 and multiply. 4 1 2?4=8 313 Remember: to multiply fractions, multiply the numerators together and multiply the denominators together. In this problem, multiply the numerators (2 ? 4 = 8) and the denominators (3 ?1 = 3).

Mixed Numbers A mixed number is a whole number and a fraction, for example 2 1 . To work with

3 mixed numbers, you often need to convert them to fractions. To do this, you need to perform two steps.

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