Chapter 4
Thinking Mathematically · 185 exercises
Problem 1
Add in the indicated base. $$ \begin{array}{r} 23_{\text {four }} \\ +13_{\text {four }} \\ \hline \end{array} $$
4 step solution
Problem 1
Convert the numeral to a numeral in base ten. \(43_{\text {five }}\)
3 step solution
Problem 1
Evaluate the expression. \(5^{2}\)
2 step solution
Problem 2
Add in the indicated base. $$ \begin{array}{r} 31_{\text {four }} \\ +22_{\text {four }} \\ \hline \end{array} $$
4 step solution
Problem 2
Convert the numeral to a numeral in base ten. \(34_{\text {five }}\)
3 step solution
Problem 2
Evaluate the expression. \(6^{2}\)
3 step solution
Problem 3
Add in the indicated base. $$ \begin{array}{r} 11_{\text {two }} \\ +11_{\text {two }} \\ \hline \end{array} $$
4 step solution
Problem 3
Convert the numeral to a numeral in base ten. \(52_{\text {eight }}\)
3 step solution
Problem 3
Evaluate the expression. \(2^{3}\)
2 step solution
Problem 4
Add in the indicated base. $$ \begin{array}{r} 101_{\text {two }} \\ +\quad 11_{\text {two }} \\ \hline \end{array} $$
4 step solution
Problem 4
Convert the numeral to a numeral in base ten. 67 eight
3 step solution
Problem 4
Evaluate the expression. \(4^{3}\)
2 step solution
Problem 5
Add in the indicated base. $$ \begin{array}{r} 342_{\text {five }} \\ +413_{\text {five }} \\ \hline \end{array} $$
3 step solution
Problem 5
Convert the numeral to a numeral in base ten. \(132_{\text {four }}\)
3 step solution
Problem 5
Evaluate the expression. \(3^{4}\)
3 step solution
Problem 6
Add in the indicated base. $$ \begin{array}{r} 323_{\text {five }} \\ +421_{\text {five }} \\ \hline \end{array} $$
5 step solution
Problem 6
Convert the numeral to a numeral in base ten. \(321_{\text {four }}\)
3 step solution
Problem 6
Evaluate the expression. \(2^{4}\)
4 step solution
Problem 7
Add in the indicated base. $$ \begin{array}{r} 645_{\text {seven }} \\ +324_{\text {seven }} \\ \hline \end{array} $$
4 step solution
Problem 7
Convert the numeral to a numeral in base ten. \(1011_{\text {two }}\)
3 step solution
Problem 7
Evaluate the expression. \(10^{5}\)
2 step solution
Problem 8
Add in the indicated base. $$ \begin{array}{r} 632_{\text {seven }} \\ +564_{\text {seven }} \\ \hline \end{array} $$
4 step solution
Problem 8
Convert the numeral to a numeral in base ten. \(1101_{\text {two }}\)
3 step solution
Problem 8
Evaluate the expression. \(10^{6}\)
3 step solution
Problem 9
Add in the indicated base. $$ \begin{array}{r} 6784_{\text {nine }} \\ +7865_{\text {nine }} \\ \hline \end{array} $$
4 step solution
Problem 9
Convert the numeral to a numeral in base ten. \(2035_{\text {six }}\)
3 step solution
Problem 9
Write each Hindu-Arabic numeral in expanded form. 36
2 step solution
Problem 10
Add in the indicated base. $$ \begin{array}{r} 1021_{\text {three }} \\ +2011_{\text {three }} \\ \hline \end{array} $$
3 step solution
Problem 10
Convert the numeral to a numeral in base ten. 2073 nine
3 step solution
Problem 10
Write each Hindu-Arabic numeral in expanded form. 65
3 step solution
Problem 11
Add in the indicated base. $$ \begin{array}{r} 14632_{\text {seven }} \\ +\quad 5604_{\text {seven }} \\ \hline \end{array} $$
6 step solution
Problem 11
Convert the numeral to a numeral in base ten. \(70355_{\text {eight }}\)
3 step solution
Problem 11
Write each Hindu-Arabic numeral in expanded form. 249
3 step solution
Problem 12
Add in the indicated base. $$ \begin{array}{r} 53 \mathrm{~B}_{\text {sixteen }} \\ +694_{\text {sixteen }} \\ \hline \end{array} $$
3 step solution
Problem 12
Convert the numeral to a numeral in base ten. \(41502_{\text {six }}\)
3 step solution
Problem 12
Write each Hindu-Arabic numeral in expanded form. 698
3 step solution
Problem 13
Subtract in the indicated base. $$ \begin{array}{r} 32_{\text {four }} \\ -13_{\text {four }} \\ \hline \end{array} $$
4 step solution
Problem 13
Convert the numeral to a numeral in base ten. \(2096_{\text {sixteen }}\)
3 step solution
Problem 13
Write each Hindu-Arabic numeral in expanded form. 703
3 step solution
Problem 14
Subtract in the indicated base. $$ \begin{array}{r} 21_{\text {four }} \\ -12_{\text {four }} \\ \hline \end{array} $$
4 step solution
Problem 14
Convert the numeral to a numeral in base ten. \(3104_{\text {fifteen }}\)
3 step solution
Problem 14
Write each Hindu-Arabic numeral in expanded form. 902
3 step solution
Problem 15
Subtract in the indicated base. $$ \begin{array}{r} 23_{\text {five }} \\ -14_{\text {five }} \\ \hline \end{array} $$
4 step solution
Problem 15
Convert the numeral to a numeral in base ten. \(110101_{\text {two }}\)
3 step solution
Problem 15
Write each Hindu-Arabic numeral in expanded form. 4856
3 step solution
Problem 16
Subtract in the indicated base. $$ \begin{array}{r} 32_{\text {seven }} \\ -16_{\text {seven }} \\ \hline \end{array} $$
5 step solution
Problem 16
Convert the numeral to a numeral in base ten. \(101101_{\text {two }}\)
3 step solution
Problem 16
Write each Hindu-Arabic numeral in expanded form. 5749
4 step solution
Problem 17
Subtract in the indicated base. $$ \begin{array}{r} 475_{\text {eight }} \\ -267_{\text {eight }} \\ \hline \end{array} $$
3 step solution
Problem 17
Convert the numeral to a numeral in base ten. \(\mathrm{ACE} 5_{\text {sixteen }}\)
4 step solution