## SAT SUBJECT TEST MATH LEVEL 1

## TOPICS IN ARITHMETIC

**CHAPTER 3**

**Fractions, Decimals, and Percents**

• Fractions

• Arithmetic Operations with Fractions

• Arithmetic Operations with Mixed Numbers

• Complex Fractions

• Percents

• Percent Increase and Decrease

• Exercises

• Answers Explained

**N**umbers such as , , and in which one integer is written over a second integer are called ** fractions**. The center line is called the fraction bar. The integer above the fraction bar is called the

**, and the integer below the fraction bar is called the**

*numerator***.**

*denominator***FRACTIONS**

Most of the numbers that we deal with in life are fractions—or can be expressed in fractions. The correct mathematical term for such a number is a ** rational number**. A rational number is any number that can be written in the form, where

*a*and

*b*are integers. When a number is actually written as , we call it a fraction. For example, of 4, 0.7, , 20%, and , only is a fraction. However, all of them are rational numbers because they can be expressed as fractions: , , , and .

Numbers that cannot be expressed as fractions are called ** irrational numbers**. Any nonterminating, nonrepeating decimal is an irrational number. For the Math 1 test, it is sufficient to know that π is irrational, as is , unless

*a*=

*b*

*where*

^{n }*b*is rational. For example, is rational because 8 = 2

^{3}and 2 is rational, but is irrational because there is no rational number whose square is 8.

A fraction is in ** lowest terms** if no single positive integer greater than 1 is a factor of both the numerator and denominator. For example, is in lowest terms since no integer greater than 1 is a factor of both 8 and 15; but is not in lowest terms since 2 is a factor of both 8 and 18.

**Key Fact B1**

**Every fraction can be reduced**

**to lowest terms by dividing the numerator and the denominator by their greatest common factor (GCF). If the GCF is 1, the fraction is already in lowest terms.**

**Smart Strategy**

You can always use your calculator to reduce a fraction to lowest terms.

For example, by dividing 8 and 18 by 2, their GCF, we can reduce to . Since the GCF of 4 and 9 is 1, is in lowest terms.

**Key Fact B2**

**Every fraction can be expressed as a decimal (or a whole number) by dividing the numerator by the denominator.**

• **If a fraction is written in lowest terms and if the only prime factors of the denominator are 2 or 5, the decimal terminates.**

• **If a fraction is written in lowest terms and if the denominator has any prime factor other than 2 or 5, the decimal repeats.**

**EXAMPLE 1:** Since 4, 5, 8, 10, 16, 20, 25, and 40 have no prime factors other than 2 and 5, the decimal equivalents of each of the following fractions terminate:

**EXAMPLE 2:** Since 6, 7, 9, 12, and 22 all have prime factors other than 2 and 5 (6, 9, and 12 are multiples of 3; 7 is a multiple of 7, and 22 is a multiple of 11), the decimal equivalents of each of the following fractions repeat:

To determine if two fractions are ** equivalent** (have the same value) or if one is greater than the other, cross multiply.

**Key Fact B3**

**To compare** **and** , **cross multiply.**

• **If ad** =

*bc*, then• **If ad** >

*bc*, then• **If ad** <

*bc*, then**EXAMPLE 3:** because . Although KEY FACT B3 is useful, remember that you can always compare fractions by using your calculator to convert them to decimals.

**EXAMPLE 4:** because and , and 0.666 > 0.625.