a: \(\dfrac{13}{21}+\dfrac{-17}{14}=\dfrac{26}{42}-\dfrac{51}{42}=\dfrac{-25}{42}\)
b: \(\dfrac{29}{48}-\dfrac{31}{36}=\dfrac{87}{144}-\dfrac{124}{144}=-\dfrac{37}{144}\)
c: \(-\dfrac{53}{84}+\dfrac{-19}{63}=\dfrac{-53\cdot3+\left(-19\right)\cdot4}{252}\)
\(=\dfrac{-159-76}{252}=-\dfrac{235}{252}\)
d: \(\dfrac{59}{72}-\dfrac{-73}{108}=\dfrac{177}{216}+\dfrac{146}{216}=\dfrac{323}{216}\)
e: \(\dfrac{31}{56}+\dfrac{-39}{84}\)
\(=\dfrac{31}{56}+\dfrac{-26}{56}=\dfrac{5}{56}\)
f: \(\dfrac{43}{48}-\dfrac{31}{36}=1-\dfrac{5}{48}-\left(1-\dfrac{5}{36}\right)\)
\(=-\dfrac{5}{48}+\dfrac{5}{36}=\dfrac{-5\cdot3+5\cdot4}{144}=\dfrac{5}{144}\)
g: \(\dfrac{-97}{96}+\dfrac{-53}{64}=\dfrac{-97\cdot2+\left(-53\right)\cdot3}{192}\)
\(=\dfrac{-194-159}{192}=-\dfrac{353}{192}\)
h: \(\dfrac{23}{32}-\dfrac{-47}{48}=\dfrac{23}{32}+\dfrac{47}{48}\)
\(=\dfrac{69}{96}+\dfrac{94}{96}=\dfrac{163}{96}\)
`a, 13/21 + (-17)/14`
`= 13/21 - 17/14`
`= 26/42 - 51/42`
`=-25/42`
`b, 29/48 - 31/36`
`= 87/144 - 124/144`
`= -37/144`
`c, -53/84 + (-19)/63`
`= -53/84 - 19/63`
`= -159/252 - 76/252`
`= -235/252`
`d, 59/72 - (-73)/108`
`= 59/72 + 73/108`
`= 177/216 + 146/216`
`= 323/216`
\(a,\dfrac{13}{21}+\dfrac{-17}{14}\)
\(=\dfrac{13}{21}-\dfrac{17}{14}\)
\(=\dfrac{26}{42}-\dfrac{51}{42}\)
\(=\dfrac{-25}{42}\)
\(b,\dfrac{29}{48}-\dfrac{31}{36}\)
\(=\dfrac{87}{144}-\dfrac{124}{144}\)
\(=\dfrac{-37}{144}\)
\(c,\dfrac{-53}{84}+\dfrac{-19}{63}\)
\(=\dfrac{-53}{84}-\dfrac{19}{63}\)
\(=\dfrac{-159}{252}-\dfrac{76}{252}\)
\(=\dfrac{-235}{252}\)
\(d,\dfrac{59}{72}-\dfrac{-73}{108}\)
\(=\dfrac{59}{72}+\dfrac{73}{108}\)
\(=\dfrac{177}{216}+\dfrac{146}{216}\)
\(=\dfrac{323}{216}\)
\(e,\dfrac{31}{56}+\dfrac{-39}{84}=\dfrac{31}{56}-\dfrac{39}{84}=\dfrac{93}{168}-\dfrac{78}{168}=\dfrac{15}{168}=\dfrac{5}{56}\)
\(f,\dfrac{43}{48}-\dfrac{31}{36}=\dfrac{129}{144}-\dfrac{124}{144}=\dfrac{5}{144}\)
\(g,\dfrac{-97}{96}+\dfrac{-53}{64}=\dfrac{-97}{96}-\dfrac{53}{64}=\dfrac{-194}{192}-\dfrac{159}{192}=\dfrac{-353}{192}\)
\(h,\dfrac{23}{32}-\dfrac{-47}{48}=\dfrac{23}{32}+\dfrac{47}{48}=\dfrac{69}{96}+\dfrac{94}{96}=\dfrac{163}{96}\)
