Đáp án: $a.\dfrac{1}{43}$
$b.\dfrac{179}{468}$
$c.-21$
Giải thích các bước giải:
a.Ta có:
$\dfrac{-1}{3}-\dfrac{-3}{5}-\dfrac{1}{6}+\dfrac{1}{43}-\dfrac{-3}{7}+\dfrac{-1}{2}-\dfrac{1}{35}$
$=-\dfrac{1}{3}+\dfrac{3}{5}-\dfrac{1}{6}+\dfrac{1}{43}+\dfrac{3}{7}-\dfrac{1}{2}-\dfrac{1}{35}$
$=(-\dfrac{1}{3}-\dfrac{1}{6}-\dfrac12)+(\dfrac{3}{5}+\dfrac{3}{7}-\dfrac{1}{35})+\dfrac{1}{43}$
$=-(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac12)+(\dfrac{21}{35}+\dfrac{15}{7}-\dfrac{1}{35})+\dfrac{1}{43}$
$=-(\dfrac{2}{6}+\dfrac{1}{6}+\dfrac36)+(\dfrac{21}{35}+\dfrac{15}{35}-\dfrac{1}{35})+\dfrac{1}{43}$
$=-\dfrac{2+1+3}{6}+\dfrac{21+15-1}{35}+\dfrac{1}{43}$
$=-\dfrac{6}{6}+\dfrac{35}{35}+\dfrac{1}{43}$
$=-1+1+\dfrac{1}{43}$
$=\dfrac{1}{43}$
b.Ta có:
$\dfrac12-\dfrac14+\dfrac1{13}+\dfrac{1}{18}$
$=\dfrac24-\dfrac14+\dfrac1{13}+\dfrac{1}{18}$
$=\dfrac{2-1}4+\dfrac1{13}+\dfrac{1}{18}$
$=\dfrac{1}4+\dfrac1{13}+\dfrac{1}{18}$
$=\dfrac{117}{468}+\dfrac{36}{468}+\dfrac{26}{468}$
$=\dfrac{117+36+26}{468}$
$=\dfrac{179}{468}$
c.Ta có:
$\dfrac34\cdot 15\dfrac13-\dfrac34\cdot 43\dfrac13$
$=\dfrac34\cdot (15\dfrac13 -43\dfrac13)$
$=\dfrac34\cdot (15+\dfrac13 -(43+\dfrac13))$
$=\dfrac34\cdot (15+\dfrac13 -43-\dfrac13)$
$=\dfrac34\cdot (-28)$
$=-21$
