Chapter Two — Rational Numbers
The Humongous Book of Algebra Problems
In this case, the repeated string is consists of one digit (5). To convert into a
fraction, divide the repeated string by 9.
The rationale behind this shortcut is omitted here, as it is based on skills
not discussed until Chapter 4. This technique, in its more rigorous form, is
explained in greater detail in Problems 4.26–4.28.
2.21 Express as a fraction.
The repeated string of 0.727272 … consists of two digits, so divide the repeated
string (72) by two nines (99) and reduce the fraction to lowest terms.
Remember that this technique applies only when the repeated string of digits
begins immediately to the left of the decimal point. If the repeated string
begins farther left in the decimal, you should apply the technique described in
Add, subtract, multiply, and divide fractions
2.22 Explain what is meant by a least common denominator.
Equivalent fractions might have different denominators. For instance, Problem
2.13 demonstrated that and have the same value, as is expressed
in lowest terms. It is often useful to rewrite one or more fractions so that their
denominators are equal. Usually, there are numerous options from which you
can choose a common denominator, and the least common denominator is the
smallest of those options.
Note: Problems 2.23–2.25 refer to the fractions and .
2.23 Identify the least common denominator of the fractions.
Begin by identifying the largest of the given denominators; here, the largest
denominator is 10. Because the other denominator (2) is a factor of 10,
then 10 is the least common denominator (LCD). The LCD is never
smaller than the largest denominator.
is two digits long,
divide by 99. If it’s
three digits long,
divide by 999.