24/29 + 7/38 + 31/38 + 5/38
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\(\frac{24}{29}+\frac{7}{38}+\frac{31}{38}+\frac{5}{29}=\left(\frac{24}{29}+\frac{5}{29}\right)+\left(\frac{7}{38}+\frac{31}{38}\right)=\frac{29}{29}+\frac{38}{38}=1+1=2\)
A) 7/38 x 9/11 +7/38 x 4/11 -7/38 x 2/11
=7/38.(9/11+4/11-2/11)
=7/38
B) 5/31 x 21/25 + 5/31 x -7/10 - 5/31 x 9/20
=5/31.(21/25-7/10-9/20)
=5/31.(-31/100)
=-1/20
=\(\dfrac{1}{18}-\dfrac{1}{23}+\dfrac{1}{23}-\dfrac{1}{24}+\dfrac{1}{24}-\dfrac{1}{31}+\dfrac{1}{31}-\dfrac{1}{33}+\dfrac{1}{33}-\dfrac{1}{37}+\dfrac{1}{37}-\dfrac{1}{38}\)
=\(\dfrac{1}{18}-\dfrac{1}{38}=\dfrac{19-9}{38x9}=\dfrac{10}{342}=\dfrac{5}{171}\)
\(\dfrac{5}{18\times23}+\dfrac{1}{23\times24}+\dfrac{7}{24\times31}+\dfrac{2}{31\times33}+\dfrac{4}{33\times37}+\dfrac{1}{37\tímes38}\)
\(\dfrac{23-18}{18\times23}+\dfrac{24-23}{23\times24}+\dfrac{31-24}{24\times31}+\dfrac{33-31}{31\times33}+\dfrac{37-33}{33\times37}+\dfrac{38-37}{37\times38}\)
\(\dfrac{23}{18\times23}-\dfrac{18}{18\times23}+\dfrac{24}{23\times24}-\dfrac{23}{23\times24}+\dfrac{31}{24\times31}-\dfrac{24}{24\times31}+\dfrac{33}{31\times33}-\dfrac{31}{31\times33}+\dfrac{37}{33\times37}-\dfrac{33}{33\times37}+\dfrac{38}{37\times38}-\dfrac{37}{37\times38}\)
\(\dfrac{1}{18}-\dfrac{1}{23}+\dfrac{1}{23}-\dfrac{1}{24}+\dfrac{1}{24}-\dfrac{1}{31}+\dfrac{1}{31}-\dfrac{1}{33}+\dfrac{1}{33}-\dfrac{1}{37}+\dfrac{1}{37}-\dfrac{1}{38}\)
\(\dfrac{1}{18}-\dfrac{38}=\dfrac{5}{171}\)
Lời giải:
$\frac{24}{19}+\frac{7}{38}+\frac{31}{38}+\frac{5}{38}$
$=\frac{48}{38}+\frac{7}{38}+\frac{31}{38}+\frac{5}{38}$
$=\frac{48+7+31+5}{38}=\frac{91}{38}$