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\begin{document}

\noindent
{\Large 
Rational Numbers Worksheet \hfill Name:\underline{\hspace{2.8in}}\\ \\
MA~201}
\vspace{.25in}


\be 
\item Which of the following are true?
	\be
	\item The rational numbers are commutative under addition.
	\item The rational numbers are commutative under subtraction.
	\item The rational numbers are commutative under multiplication.
	\item The rational numbers are commutative under division.
	\item The rational numbers are associative under addition.
	\item The rational numbers are associative under subtraction.
	\item The rational numbers are associative under multiplication.
	\item The rational numbers are associative under division.
	\item The rational numbers are closed under addition.
	\item The rational numbers are closed under subtraction.
	\item The rational numbers are closed under multiplication.
	\item The rational numbers are closed under division.
	\item Every rational number has an additive inverse.
	\item Every rational number has an multiplicative inverse.
	\item Every rational number has a unique additive inverse.
	\item Every nonzero rational number has a unique multiplicative inverse.
	\item One is the multiplicative identity for the set of rational
	numbers.
	\item Zero is the additive identity for the set of rational
	numbers.
	\item If $\frac{a}{b}$ and $\frac {c}{d}$ are distinct rational
	numbers with $\frac{a}{b} < \frac{c}{d}$,
	then there is a rational number $\frac{e}{f}$ such that
	$\frac{a}{b} < \frac{e}{f} < \frac{c}{d}$.
	\item (problem 21 from section 6.1)
	There are infinitely many rational numbers between $0$ and
	$1$.
	\item (problem 21 from section 6.1)
	There are infinitely many ways to replace two fractions with two
	equivalent fractions that have a common denominator.
	\item (problem 21 from section 6.1)
	There is a unique least common denominator for a given pair of
	fractions.
	\item (problem 21 from section 6.1)
	There is a least common fraction.
	\ee

\item Find the additive inverse. 
	\be
	\item $\frac{3}{5}$
	\item $2\frac{1}{3}$
	\item $-\frac{3}{5}$
	\item $0$
	\ee
\item Find the multiplicative inverse, if possible. 
	\be
	\item $\frac{3}{5}$
	\item $2\frac{1}{3}$
	\item $-\frac{3}{5}$
	\item $0$
	\ee
\item Find a rational number that is
between the two rational numbers you are given. 
	\be
	\item $0$; $1$
	\item $\frac{2}{3}$; $\frac{4}{5}$
	\item $2 \frac{1}{3}$; $\frac{5}{7}$
	\item $2 \frac{1}{3}$; $3\frac{5}{7}$
	\ee
\item Explain why we define $a^0 = 1$ and $a^{-n} = \frac{1}{a^n}$ when $a
\neq 0$ and $n$ is a positive integer.  (See the discussion on pages
415--416.)
\item Write each decimals in expanded form. 
	\be
	\item $456.6787$
	\item $0.7856$
	\item $123.6712143$
	\ee
\item Quickly multiply.
	\be
	\item $10,123.67 \times 100$
	\item $10,123.67 \times 1000$
	\item $10,123.67 \times 10000$
	\item $10,123.67 \times 10$
	\item $10,123.67 \times 10^6$
	\item $10,123.67 \times 10^7$
	\item $10,123.67 \times 10^2$
	\item $10,123.67 \times 10^3$
	\item $10,123.67 \times 10^{12}$
	\item $10,123.67 \times \frac{1}{100}$
	\item $10,123.67 \times \frac{1}{10}$
	\item $10,123.67 \times \frac{1}{10000}$
	\item $10,123.67 \times 10^{-6}$
	\item $10,123.67 \times 10^{-10}$
	\item $10,123.67 \times 10^{-2}$
	\item $10,123.67 \times 10^{-1}$
	\ee
\item Quickly multiply.
	\be
	\item $10,123.67 \div 100$
	\item $10,123.67 \div 1000$
	\item $10,123.67 \div 10000$
	\item $10,123.67 \div 10$
	\item $10,123.67 \div 10^6$
	\item $10,123.67 \div 10^7$
	\item $10,123.67 \div 10^2$
	\item $10,123.67 \div 10^3$
	\item $10,123.67 \div 10^{12}$
	\item $10,123.67 \div \frac{1}{100}$
	\item $10,123.67 \div \frac{1}{10}$
	\item $10,123.67 \div \frac{1}{10000}$
	\item $10,123.67 \div 10^{-6}$
	\item $10,123.67 \div 10^{-10}$
	\item $10,123.67 \div 10^{-2}$
	\item $10,123.67 \div 10^{-1}$
	\ee

\ee
\end {document}
