\(\begin{array}{l}a)\left| { - 3,5} \right| = 3,5;\\b)\left| {\frac{{ - 4}}{9}} \right| = \frac{4}{9};\\c)\left| 0 \right| = 0;\\d)\left| {2,0(3)} \right| = 2,0(3)\end{array}\)

Chú ý:

Nếu \(a \ge 0\) thì \(\left| a \right| = a\)

Nếu \(a < 0\) thì \(\left| a \right| =  - a\)

a) \(\left( {\frac{7}{3} + 3,5} \right):\left( { - \frac{{25}}{6} + \frac{{22}}{7}} \right) + 0,5\)

\(\begin{array}{l} = \left( {\frac{7}{3} + \frac{7}{2}} \right):\left( { - \frac{{25}}{6} + \frac{{22}}{7}} \right) + \frac{1}{2}\\ = \frac{{35}}{6}:\frac{{ - 25.7 + 22.6}}{{6.7}} + \frac{1}{2}\\ = \frac{{35}}{6}:\frac{{ - 43}}{{7.6}} + \frac{1}{2} = \frac{{35}}{6}.\frac{{7.6}}{{ - 43}} + \frac{1}{2}\\ = \frac{{ - 245}}{{43}} + \frac{1}{2} = \frac{{ - 245.2 + 43}}{{43.2}} = \frac{{ - 447}}{{86}}\end{array}\)

b) \(\frac{{38}}{7} + \left( { - 3,25} \right) - \frac{{17}}{7} + 4,55\)

\(\begin{array}{l} = \left( {\frac{{38}}{7} - \frac{{17}}{7}} \right) + \left( {4,55 - 3,25} \right)\\ = \frac{{38 - 17}}{7} + 1,3 = \frac{{21}}{7} +1,3\\ = 3 + 1,3 =  4,3\end{array}\)

\(=1+1.79^3-1.71^3=1.735128\)

Tính bằng máy tính cầm tay

mình cần tính nhanh cơ hoặc tính ra đày đủ đó

\(a,A=\left|3,4-x\right|+1,7\ge1,7\)

Dấu \("="\Leftrightarrow3,4-x=0\Leftrightarrow x=3,4\)

\(c,C=\left|4x-3\right|+\left|5y+7,5\right|+17,5\ge17,5\)

Dấu \("="\Leftrightarrow\left\{{}\begin{matrix}4x-3=0\\5y+7,5=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{3}{4}\\y=-\dfrac{3}{2}\end{matrix}\right.\)

\(M=\left(2\frac{1}{3}+3,5\right):\left(-4\frac{1}{6}+3\frac{1}{7}\right)+7,5\)

\(=\left(\frac{7}{3}+\frac{7}{2}\right):\left(\frac{-25}{6}+\frac{22}{7}\right)+\frac{15}{2}\)

\(=\left(\frac{14}{6}+\frac{21}{6}\right):\left(\frac{-175}{42}+\frac{132}{42}\right)+\frac{15}{2}\)

\(=\frac{14+21}{6}:\frac{-175+132}{42}+\frac{15}{2}\)

\(=\frac{35}{6}:\frac{-43}{42}+\frac{15}{2}=\frac{35}{6}.\frac{-42}{43}+\frac{15}{2}\)

\(=\frac{-245}{43}+\frac{15}{2}=\frac{-490}{86}+\frac{645}{86}\)

\(=\frac{-490+645}{86}=\frac{155}{86}\)

= -\(\frac{55}{58}\)