Thực hiện phép tính ( tính nhanh nếu có thể )
a, 3+1/7 + (-5) *1/5 -(-7+3/4)
b,-1/2-(-3/5)+(-1/9)+1/27+7/18+4/35-(-2/7)
c,4/17-4/49+4/31 phần 3/17-3/49+3/31
Thực hiện phép tính ( tính nhanh nếu có thể )
a, 3+1/7 + (-5) *1/5 -(-7+3/4)
b,-1/2-(-3/5)+(-1/9)+1/27+7/18+4/35-(-2/7)
c,4/17-4/49+4/31 phần 3/17-3/49+3/31
Đáp án:
$a)
\dfrac{235}{28}\\
b)
\dfrac{22}{27}\\
c)
\dfrac{4}{3}$
Giải thích các bước giải:
$a)
3+\dfrac{1}{7}+(-5).\dfrac{1}{5}-(-7+\dfrac{3}{4})\\
=3+\dfrac{1}{7}-1+7-\dfrac{3}{4}\\
=9+\dfrac{1}{7}-\dfrac{3}{4}\\
=\dfrac{252}{28}+\dfrac{4}{28}-\dfrac{21}{28}\\
=\dfrac{235}{28}\\
b)
\dfrac{-1}{2}-\left ( -\dfrac{3}{5} \right )+\left ( -\dfrac{1}{9} \right )+\dfrac{1}{27}+\dfrac{7}{18}+\dfrac{4}{35}-\left ( -\dfrac{2}{7} \right )\\
=\dfrac{-1}{2}+\dfrac{3}{5}-\dfrac{1}{9}+\dfrac{1}{27}+\dfrac{7}{18}+\dfrac{4}{35}+\dfrac{2}{7}\\
=\left (\dfrac{-1}{2}-\dfrac{1}{9} +\dfrac{7}{18} \right )+\left (\dfrac{3}{5} +\dfrac{4}{35} \right )+\left ( \dfrac{1}{27} +\dfrac{2}{7}\right )\\
=\left (\dfrac{-9}{18}-\dfrac{2}{18} +\dfrac{7}{18} \right )+\left (\dfrac{21}{35} +\dfrac{4}{35} \right )+\left ( \dfrac{1}{27} +\dfrac{2}{7}\right )\\
=\dfrac{-4}{18}+\dfrac{25}{35}+\dfrac{1}{27}+\dfrac{2}{7}\\
=\dfrac{-2}{9}+\dfrac{5}{7}+\dfrac{1}{27}+\dfrac{2}{7}\\
=\dfrac{-2}{9}+1+\dfrac{1}{27}\\
=\dfrac{-6}{27}+\dfrac{27}{27}+\dfrac{1}{27}\\
=\dfrac{22}{27}\\
c)
\dfrac{\dfrac{4}{17}-\dfrac{4}{49}+\dfrac{4}{31}}{\dfrac{3}{17}-\dfrac{3}{49}+\dfrac{3}{31}}\\
=\dfrac{4\left ( \dfrac{1}{17}-\dfrac{1}{49}+\dfrac{1}{31} \right )}{3.\left ( \dfrac{1}{17}-\dfrac{1}{49}+\dfrac{1}{31} \right )}\\
=\dfrac{4}{3}$