Algebra Know-It-ALL

Fraction or ratio? Sometimes a fraction is called a ratio. These two terms are almost synonymous, but not quite. The term “fract ...

86 Fractions Built of Integers Here’s a challenge! Suppose a car dealer tells you that a certain sports car has a top speed that ...

go 150 miles per hour under the same conditions. You can then write the ratio of the car’s top speed to the truck’s top speed as ...

88 Fractions Built of Integers Getting the lowest form Even after we have reduced a fraction to a lower form, we might not have ...

Here’s a challenge! Suppose that a, b, c, d, e, and f are all primes, and no two of them are the same. Reduce the following rati ...

90 Fractions Built of Integers Once you’ve “prepped” the fractions and you want to multiply them together, multiply the individu ...

Are you confused? Any ratio of two integers, where the denominator is nonzero, is known as a rational number. The set of rationa ...

92 Fractions Built of Integers Now multiply a/b by d/d, which is equal to 1. Then multiply c/d by b/b, which is also equal to 1. ...

Suppose you want to describe how many people in Country X have green eyes, per 100,000 popula- tion. You might discover that one ...

94 Fractions Built of Integers Practice Exercises This is an open-book quiz. You may (and should) refer to the text as you solve ...

Now that you know how a rational number can be expressed as a ratio of two integers, let’s look at the other common way these nu ...

96 Decimal Fractions Start at the decimal point The “cornerstone” on which any decimal numeral is “built” is the decimal point. ...

105 100,000 (^104) 10,000 103 1,000 102 100 10 1 10 100 1 1/10 1/100 1/1,000 1/10,000 1/100,000 10 –1 10 –2 10 –3 10 –4 10 –5 Co ...

98 Decimal Fractions Starting at the decimal point and working toward the right: (7 × 10 −^1 )+ (7 × 10 −^2 )+ (3 × 10 −^3 )+ (5 ...

The string of numerals to the right of the point represents the sum SB= (b 1 × 10 −^1 )+ (b 2 × 10 −^2 )+ (b 3 × 10 −^3 )+ ··· + ...

100 Decimal Fractions Don’t be fooled here! These examples don’t represent changes in the order of magnitude. Instead, they all ...

Are you confused? Numbers such as 4,580,103.7864892022 can be hard to read, especially when you see them on a calcula- tor displ ...

102 Decimal Fractions A good way to see the difference between a terminating decimal and an endless repeating decimal is to use ...

were able to prove that this number, which can be so easily defined in terms of geometry, can- not be defined as a ratio between ...

104 Decimal Fractions Therefore, 1,000m= ### +m Subtract m from the expressions on both sides of the equals sign, obtaining 1,00 ...