Bài 23. Thực hiện phép tính (tính hợp lí nếu có thể):
a) $\dfrac{1}{15}$ + $\dfrac{2}{3}$ + $\dfrac{-3}{5}$
= $\dfrac{1}{15}$ + $\dfrac{10}{15}$ + $\dfrac{-9}{15}$
= $\dfrac{2}{15}$
b) $\dfrac{-1}{2}$ + $\dfrac{2}{5}$ - $\dfrac{3}{10}$
= $\dfrac{-5}{10}$ + $\dfrac{4}{10}$ - $\dfrac{3}{10}$
= $\dfrac{-2}{5}$
c) $\dfrac{1}{4}$ + $\dfrac{-9}{11}$ + $\dfrac{7}{4}$ + $\dfrac{-2}{11}$
= ( $\dfrac{1}{4}$ + $\dfrac{7}{4}$ ) + ( $\dfrac{-9}{11}$ + $\dfrac{-2}{11}$ )
= $\dfrac{8}{4}$ + $\dfrac{-11}{11}$
= 2 + (-1)
= 1
d) $\dfrac{-9}{8}$ + $\dfrac{4}{7}$ + $\dfrac{1}{8}$ + $\dfrac{10}{7}$
= ( $\dfrac{-9}{8}$ + $\dfrac{1}{8}$ ) + ( $\dfrac{4}{7}$ + $\dfrac{10}{7}$ )
= $\dfrac{-8}{8}$ + $\dfrac{14}{7}$
= (-1) + 2
= 1
e) $\dfrac{-6}{11}$ + ( $\dfrac{-2}{3}$ + $\dfrac{-5}{11}$ )
= ( $\dfrac{-6}{11}$ + $\dfrac{-5}{11}$ ) + $\dfrac{-2}{3}$
= $\dfrac{-11}{11}$ + $\dfrac{-2}{3}$
= $\dfrac{-33}{33}$ + $\dfrac{-22}{33}$
= $\dfrac{-55}{33}$
= $\dfrac{-5}{3}$
f) $\dfrac{5}{15}$ + $\dfrac{-11}{4}$ - ( $\dfrac{1}{3}$ - $\dfrac{11}{4}$ )
= $\dfrac{1}{3}$ + $\dfrac{-11}{4}$ - $\dfrac{1}{3}$ + $\dfrac{11}{4}$
= ( $\dfrac{1}{3}$ - $\dfrac{1}{3}$ ) + ( $\dfrac{-11}{4}$ + $\dfrac{11}{4}$ )
= 0
g) ( 9 $\dfrac{2}{9}$ + $\dfrac{3}{5}$ ) - 7 $\dfrac{2}{9}$
= 9 $\dfrac{2}{9}$ + $\dfrac{3}{5}$ - 7 $\dfrac{2}{9}$
= ( 9 $\dfrac{2}{9}$ - 7 $\dfrac{2}{9}$ ) + $\dfrac{3}{5}$
= ( $\dfrac{83}{9}$ - $\dfrac{65}{9}$ ) + $\dfrac{3}{5}$
= $\dfrac{18}{9}$ + $\dfrac{3}{5}$
= $\dfrac{90}{45}$ + $\dfrac{27}{45}$
= $\dfrac{117}{45}$
= $\dfrac{13}{5}$
h) ( $\dfrac{55}{6}$ - 2 $\dfrac{4}{7}$ ) - ( 5 $\dfrac{1}{6}$ + $\dfrac{3}{7}$ )
= ( $\dfrac{55}{6}$ - $\dfrac{18}{7}$ ) - ( $\dfrac{31}{6}$ + $\dfrac{3}{7}$ )
= $\dfrac{55}{6}$ - $\dfrac{18}{7}$ - $\dfrac{31}{6}$ - $\dfrac{3}{7}$
= ( $\dfrac{55}{6}$ - $\dfrac{31}{6}$ ) - ( $\dfrac{18}{7}$ - $\dfrac{3}{7}$ )
= $\dfrac{24}{6}$ - $\dfrac{15}{7}$
= $\dfrac{168}{42}$ - $\dfrac{90}{42}$
= $\dfrac{78}{42}$
= $\dfrac{13}{7}$
Bài 23. Thực hiện phép tính:
a) ( $\dfrac{3}{5}$ + $\dfrac{-3}{4}$ + $\dfrac{1}{20}$ ) : $\dfrac{1}{2}$ - $\dfrac{1}{2}$
= ( $\dfrac{12}{20}$ + $\dfrac{-15}{20}$ + $\dfrac{1}{20}$ ) : $\dfrac{1}{2}$ - $\dfrac{1}{2}$
= $\dfrac{-2}{20}$ . 2 - $\dfrac{1}{2}$
= $\dfrac{-1}{5}$ - $\dfrac{1}{2}$
= $\dfrac{-2}{10}$ - $\dfrac{5}{10}$
= $\dfrac{-7}{10}$
b) 1 $\dfrac{2}{3}$ : $\dfrac{1}{6}$ + 1 $\dfrac{1}{4}$ . ( $\dfrac{1}{2}$ - $\dfrac{1}{5}$ )
= $\dfrac{5}{3}$ . 6 + $\dfrac{5}{4}$ . ( $\dfrac{5}{10}$ - $\dfrac{2}{10}$ )
= 10 + $\dfrac{5}{4}$ . $\dfrac{3}{10}$
= 10 + $\dfrac{3}{8}$
= $\dfrac{83}{8}$
c) 0,75 - ( $\dfrac{13}{11}$ - 50% ) : $\dfrac{5}{11}$
= $\dfrac{3}{4}$ - ( $\dfrac{13}{11}$ - $\dfrac{1}{2}$ ) . $\dfrac{11}{5}$
= $\dfrac{3}{4}$ - $\dfrac{13}{11}$ + $\dfrac{1}{2}$ . $\dfrac{11}{5}$
= $\dfrac{3}{4}$ - $\dfrac{13}{11}$ + $\dfrac{11}{10}$
= $\dfrac{147}{220}$
d) $\dfrac{1}{27}$ : ( $\dfrac{-1}{3}$ )^2 + 75% . ( -2 $\dfrac{2}{3}$ ).
= $\dfrac{1}{27}$ : $\dfrac{1}{9}$ + $\dfrac{3}{4}$ . $\dfrac{-8}{3}$
= $\dfrac{1}{27}$ . 9 + $\dfrac{3}{4}$ . $\dfrac{-8}{3}$
= $\dfrac{1}{3}$ + (-2)
= $\dfrac{-5}{3}$
