<< Chapter < Page | Chapter >> Page > |
$\begin{array}{cc}7\cdot 6-{4}^{2}+{1}^{5}\hfill & \text{Evaluate the exponential forms, moving left to right.}\hfill \\ 7\cdot 6-\text{16}+1\hfill & \text{Multiply 7 and 6:}\phantom{\rule{8px}{0ex}}7\cdot 6=\text{42}\hfill \\ \text{42}-\text{16}+1\hfill & \text{Subtract 16 from 42:}\phantom{\rule{8px}{0ex}}\text{42}-\text{16}=\text{26}\hfill \\ \text{26}+1\hfill & \text{Add 26 and 1:}\phantom{\rule{8px}{0ex}}\text{26}+1=\text{27}\hfill \\ \mathrm{27}\hfill & \end{array}$
$\begin{array}{cc}6\cdot ({3}^{2}+{2}^{2})+{4}^{2}\hfill & \text{Evaluate the exponential forms in the parentheses:}\phantom{\rule{8px}{0ex}}{3}^{2}=9\text{and}{2}^{2}=4\hfill \\ 6\cdot (9+4)+{4}^{2}\hfill & \text{Add the 9 and 4 in the parentheses:}\phantom{\rule{8px}{0ex}}9+4=\mathrm{13}\hfill \\ 6\cdot (\text{13})+{4}^{2}\hfill & \text{Evaluate the exponential form:}\phantom{\rule{8px}{0ex}}{4}^{2}=\mathrm{16}\hfill \\ 6\cdot \left(\mathrm{13}\right)+\mathrm{16}\hfill & \text{Multiply 6 and 13:}\phantom{\rule{8px}{0ex}}6\cdot \mathrm{13}=\mathrm{78}\hfill \\ \mathrm{78}+\mathrm{16}\hfill & \text{Add 78 and 16:}\phantom{\rule{8px}{0ex}}\mathrm{78}+\mathrm{16}=\mathrm{94}\hfill \\ \mathrm{94}\hfill & \end{array}$
$\begin{array}{cc}\frac{{6}^{2}+{2}^{2}}{{4}^{2}+6\cdot {2}^{2}}+\frac{{1}^{3}+{8}^{2}}{{\text{10}}^{2}-\text{19}\cdot 5}\hfill & \begin{array}{c}\text{Recall that the bar is a grouping symbol.}\hfill \\ \text{The fraction}\frac{{6}^{2}+{2}^{2}}{{4}^{2}+6\cdot {2}^{2}}\text{is equivalent to}({6}^{2}+{2}^{2})\xf7({4}^{2}+6\cdot {2}^{2})\hfill \end{array}\hfill \\ \frac{\text{36}+4}{\text{16}+6\cdot 4}+\frac{1+\text{64}}{\text{100}-\text{19}\cdot 5}\hfill & \hfill \\ \frac{\text{36}+4}{\text{16}+\text{24}}+\frac{1+\text{64}}{\text{100}-\text{95}}\hfill & \hfill \\ \frac{\text{40}}{\text{40}}+\frac{\text{65}}{5}\hfill & \hfill \\ 1+\text{13}\hfill & \hfill \\ \text{14}\hfill & \end{array}$
Determine the value of each of the following.
$8(\text{10})+4(2+3)-(\text{20}+3\cdot \text{15}+\text{40}-5)$
0
$\frac{{3}^{3}+{2}^{3}}{{6}^{2}-\text{29}}+5\left(\frac{{8}^{2}+{2}^{4}}{{7}^{2}-{3}^{2}}\right)\xf7\frac{8\cdot 3+{1}^{8}}{{2}^{3}-3}$
7
Using a calculator is helpful for simplifying computations that involve large numbers.
Use a calculator to determine each value.
$\mathrm{9,}\text{842}+\text{56}\cdot \text{85}$
Key | Display Reads | ||
Perform the multiplication first. | Type | 56 | 56 |
Press | × | 56 | |
Type | 85 | 85 | |
Now perform the addition. | Press | + | 4760 |
Type | 9842 | 9842 | |
Press | = | 14602 |
The display now reads 14,602.
$\text{42}(\text{27}+\text{18})+\text{105}(\text{810}\xf7\text{18})$
Key | Display Reads | ||
Operate inside the parentheses | Type | 27 | 27 |
Press | + | 27 | |
Type | 18 | 18 | |
Press | = | 45 | |
Multiply by 42. | Press | × | 45 |
Type | 42 | 42 | |
Press | = | 1890 |
Place this result into memory by pressing the memory key.
Key | Display Reads | ||
Now operate in the other parentheses. | Type | 810 | 810 |
Press | ÷ | 810 | |
Type | 18 | 18 | |
Press | = | 45 | |
Now multiply by 105. | Press | × | 45 |
Type | 105 | 105 | |
Press | = | 4725 | |
We are now ready to add these two quantities together. | Press | + | 4725 |
Press the memory recall key. | 1890 | ||
Press | = | 6615 |
Thus, $\text{42}(\text{27}+\text{18})+\text{105}(\text{810}\xf7\text{18})=\mathrm{6,}\text{615}$
${\text{16}}^{4}+{\text{37}}^{3}$
Nonscientific Calculators | ||
Key | Display Reads | |
Type | 16 | 16 |
Press | × | 16 |
Type | 16 | 16 |
Press | × | 256 |
Type | 16 | 16 |
Press | × | 4096 |
Type | 16 | 16 |
Press | = | 65536 |
Press the memory key | ||
Type | 37 | 37 |
Press | × | 37 |
Type | 37 | 37 |
Press | × | 1396 |
Type | 37 | 37 |
Press | × | 50653 |
Press | + | 50653 |
Press memory recall key | 65536 | |
Press | = | 116189 |
Calculators with ${\mathrm{y}}^{\mathrm{x}}$ Key | ||
Key | Display Reads | |
Type | 16 | 16 |
Press | ${y}^{x}$ | 16 |
Type | 4 | 4 |
Press | = | 4096 |
Press | + | 4096 |
Type | 37 | 37 |
Press | ${y}^{x}$ | 37 |
Type | 3 | 3 |
Press | = | 116189 |
Thus, ${\text{16}}^{4}+{\text{37}}^{3}=\text{116},\text{189}$
We can certainly see that the more powerful calculator simplifies computations.
Nonscientific calculators are unable to handle calculations involving very large numbers.
$\text{85612}\cdot \text{21065}$
Key | Display Reads | |
Type | 85612 | 85612 |
Press | × | 85612 |
Type | 21065 | 21065 |
Press | = |
This number is too big for the display of some calculators and we'll probably get some kind of error message. On some scientific calculators such large numbers are coped with by placing them in a form called "scientific notation." Others can do the multiplication directly. (1803416780)
Use a calculator to find each value.
$\text{55}(\text{84}-\text{26})+\text{120}(\text{512}-\text{488})$
6,070
$\mathrm{6,}{\text{053}}^{3}$
This number is too big for a nonscientific calculator. A scientific calculator will probably give you $2\text{.}\text{217747109}\times {\text{10}}^{\text{11}}$
For the following problems, find each value. Check each result with a calculator.
$\text{18}+7\cdot (4-1)$
$1-5\cdot (8-8)$
$\text{98}\xf72\xf7{7}^{2}$
$\sqrt{9}+\text{14}$
$\sqrt[3]{8}+8-2\cdot 5$
$\text{61}-\text{22}+4[3\cdot (\text{10})+\text{11}]$
$\text{121}-4\cdot [(4)\cdot (5)-\text{12}]+\frac{\text{16}}{2}$
97
$\frac{(1+\text{16})-3}{7}+5\cdot (\text{12})$
$\frac{8\cdot (6+\text{20})}{8}+\frac{3\cdot (6+\text{16})}{\text{22}}$
29
$\text{10}\cdot [8+2\cdot (6+7)]$
${\text{10}}^{2}\cdot 3\xf7{5}^{2}\cdot 3-2\cdot 3$
$\frac{\text{51}}{\text{17}}+7-2\cdot 5\cdot \left(\frac{\text{12}}{3}\right)$
${2}^{2}\cdot 3+{2}^{3}\cdot (6-2)-(3+\text{17})+\text{11}(6)$
90
$\text{26}-2\cdot \left\{\frac{6+\text{20}}{\text{13}}\right\}$
$0+\text{10}(0)+\text{15}\cdot \{4\cdot 3+1\}$
$(4+7)\cdot (8-3)$
$(\text{21}-3)\cdot (6-1)\cdot (7)+4(6+3)$
$6\cdot \left\{2\cdot 8+3\right\}-(5)\cdot (2)+\frac{8}{4}+(1+8)\cdot (1+\text{11})$
${3}^{4}+{2}^{4}\cdot (1+5)$
$(7)\cdot (\text{16})-{3}^{4}+{2}^{2}\cdot ({1}^{7}+{3}^{2})$
$\frac{{\left(1+6\right)}^{2}+2}{3\cdot 6+1}$
$\frac{{6}^{2}-1}{{2}^{3}-3}+\frac{{4}^{3}+2\cdot 3}{2\cdot 5}$
14
$\frac{5\left({8}^{2}-9\cdot 6\right)}{{2}^{5}-7}+\frac{{7}^{2}-{4}^{2}}{{2}^{4}-5}$
$\frac{(2+1{)}^{3}+{2}^{3}+{1}^{\text{10}}}{{6}^{2}}-\frac{{\text{15}}^{2}-{\left[2\cdot 5\right]}^{2}}{5\cdot {5}^{2}}$
0
$\frac{{6}^{3}-2\cdot {\text{10}}^{2}}{{2}^{2}}+\frac{\text{18}({2}^{3}+{7}^{2})}{2(\text{19})-{3}^{3}}$
$2\cdot \left\{6+\left[{\text{10}}^{2}-6\sqrt{\text{25}}\right]\right\}$
152
$\text{181}-3\cdot \left(2\sqrt{\text{36}}+3\sqrt[3]{\text{64}}\right)$
$\frac{2\cdot \left(\sqrt{\text{81}}-\sqrt[3]{\text{125}}\right)}{{4}^{2}-\text{10}+{2}^{2}}$
$\frac{4}{5}$
( [link] ) The fact that 0 + any whole number = that particular whole number is an example of which property of addition?
( [link] ) Find the product. $\mathrm{4,}\text{271}\times \text{630}$ .
2,690,730
( [link] ) In the statement $\text{27}\xf73=9$ , what name is given to the result 9?
( [link] ) Find the value of ${2}^{4}$ .
Notification Switch
Would you like to follow the 'Fundamentals of mathematics' conversation and receive update notifications?