a: \(1\frac{4}{23}+\frac{5}{21}-\frac{4}{23}+0,5+\frac{16}{21}\)
\(=\left(1+\frac{4}{23}-\frac{4}{23}\right)+\left(\frac{5}{21}+\frac{16}{21}\right)+0,5\)
=1+1+0,5
=2,5
b: \(\frac{21}{47}+\frac{9}{45}+\frac{26}{47}+\frac45\)
\(=\left(\frac{21}{47}+\frac{26}{47}\right)+\left(\frac15+\frac45\right)\)
=1+1
=2
c: \(\frac{13}{25}+\frac{6}{41}-\frac{38}{25}+\frac{35}{41}-\frac12\)
\(=\left(\frac{13}{25}-\frac{38}{25}\right)+\left(\frac{6}{41}+\frac{35}{41}\right)-\frac12\)
\(=-\frac{25}{25}+\frac{41}{41}-\frac12=-\frac12\)
d: \(12\cdot\left(-\frac23\right)^2+\frac43=12\cdot\frac49+\frac43=\frac{48}{9}+\frac{12}{9}=\frac{60}{9}=\frac{20}{3}\)
e: \(12,5\cdot\left(-\frac57\right)+1,5\cdot\left(-\frac57\right)\)
\(=-\frac57\left(12,5+1,5\right)=-\frac57\cdot14=-10\)
f: \(\frac{5^4\cdot20^4}{25^5\cdot4^5}=\frac{\left(5\cdot20\right)^4}{\left(25\cdot4\right)^5}=\frac{100^4}{100^5}=\frac{1}{100}\)
g: \(\left(\frac53-\frac37+9\right)-\left(2+\frac57-\frac23\right)+\left(\frac87-\frac43-10\right)\)
\(=\frac53-\frac37+9-2-\frac57+\frac23+\frac87-\frac43-10\)
\(=\left(\frac87-\frac37-\frac57\right)+\left(\frac53+\frac23-\frac43\right)+\left(9-2-10\right)\)
=1+7-10
=8-10
=-2
