Tính giá trí của biểu thức sau theo cách hợp lí nhất.
a) $\mathrm{A}=\dfrac{3}{5} \cdot \dfrac{6}{7}+\dfrac{3}{7}: \dfrac{5}{3}-\dfrac{2}{7}: 1 \dfrac{2}{3}$;
b) $\mathrm{B}=\left(-13 \cdot \dfrac{2}{5}+\dfrac{-2}{9}: 2 \dfrac{1}{2}+\dfrac{2}{5}. \dfrac{11}{9}\right) \cdot 2 \dfrac{1}{2}$;
c) $\mathrm{C}=\left(\dfrac{-4}{5}+\dfrac{5}{7}\right): \dfrac{2}{3}+\left(\dfrac{-1}{5}+\dfrac{2}{7}\right): \dfrac{2}{3}$;
d) $\mathrm{D}=\dfrac{4}{9}:\left(\dfrac{1}{15}-\dfrac{2}{3}\right)+\dfrac{4}{9}:\left(\dfrac{1}{11}-\dfrac{5}{22}\right)$.
A= 3/5.6/7+3/5.3/7-3/5.2/7
A= 3/5. (6/7+3/7-2/7) = 3/5
B= (-13.2/5+-2/9.2/5+2/5.11/9).5/2
B= (-13-2/9+11/9).2/5.5/2
B= -13+(11/9-2/9)= -12
C= (-4/5+5/7).3/2+(-1/5+2/7).3/2
C= (-4/5+5/7+-1/5+2/7).3/2
C= ((-4/5+-1/5)+(5/7+2/7)).3/2
C= 0
D= 4/9.-5/3+4/9.-22/3
D= 4/9.110/9
D= 440/81
A=3/5.6/7+3/7.3/5-2/7.3/5
A=3/5.(6/7+3/7-2/7)
A= 3/5.1
A=3/5
B =(-13.2/5+-2/9.2/5+11/9.2/5).5/2
B = 9-13-2/9+11/9).2/5.5/2
B = -13+(11/9-2/9)
B=-12
C=(-4/5+5/7).3/2+(-1/5+2/7).3/2
C = -4/5+5/7+-1/5+2/7).3/2
C = (-4/5+-1/5)+(5/7+2/7).3/2
C =-1+1.3/2
C =0
D =4/9:(1/15-10/15)+4/9:(2/22-5/22)
D = 4/9:-3/5+4/9:-3/22
D = 4/9.(-5/3+-22/3)
D=4/9.-27/3
D=-4
a) \(A=\dfrac{3}{5}.\dfrac{6}{7}+\dfrac{3}{7}.\dfrac{3}{5}-\dfrac{2}{7}.\dfrac{3}{5}\)
\(A=\dfrac{3}{5}.\dfrac{6}{7}+\dfrac{3}{5}.\dfrac{3}{7}-\dfrac{2}{7}.\dfrac{3}{5}\)
\(A=\dfrac{3}{5}.\left(\dfrac{6}{7}+\dfrac{3}{7}-\dfrac{2}{7}\right)\)
\(A=\dfrac{3}{5}.1\)
\(A=\dfrac{3}{5}\)
b) \(B=\left(-13.\dfrac{2}{5}+\dfrac{-2}{9}:2\dfrac{1}{2}+\dfrac{2}{5}.\dfrac{11}{9}\right).2\dfrac{1}{2}\)
\(B=\left(-13.\dfrac{2}{5}+\dfrac{-2}{9}:\dfrac{5}{2}+\dfrac{2}{5}.\dfrac{11}{9}\right).\dfrac{5}{2}\)
\(B=\left(-13.\dfrac{2}{5}+\dfrac{-2}{9}.\dfrac{5}{2}+\dfrac{2}{5}.\dfrac{11}{9}\right).\dfrac{5}{2}\)
\(B=\left(-13+\dfrac{-2}{9}+\dfrac{11}{9}\right).\dfrac{2}{5}.\dfrac{5}{2}\)
\(B=-13+\left(\dfrac{-2}{9}+\dfrac{11}{9}\right)\)
\(B=-13+1\)
\(B=-12\)
c) \(C=\left(\dfrac{-4}{5}+\dfrac{5}{7}\right):\dfrac{2}{3}+\left(\dfrac{-1}{5}-\dfrac{2}{7}\right):\dfrac{2}{3}\)
\(C=\left(\dfrac{-4}{5}+\dfrac{5}{7}\right).\dfrac{3}{2}+\left(\dfrac{-1}{5}-\dfrac{2}{7}\right).\dfrac{3}{2}\)
\(C=\left(\dfrac{-4}{5}+\dfrac{5}{7}+\dfrac{-1}{5}-\dfrac{2}{7}\right).\dfrac{3}{2}\)
\(C=\left(\dfrac{-4}{5}+\dfrac{-1}{5}+\dfrac{5}{7}+\dfrac{2}{7}\right).\dfrac{3}{2}\)
\(C=\left(-1+1\right).\dfrac{3}{2}\)
\(C=0\)
d) \(D=\dfrac{4}{9}:\left(\dfrac{1}{15}-\dfrac{2}{3}\right)+\dfrac{4}{9}:\left(\dfrac{1}{11}-\dfrac{5}{22}\right)\)
\(D=\dfrac{4}{9}:\left(\dfrac{1}{15}-\dfrac{10}{15}\right)+\dfrac{4}{9}:\left(\dfrac{2}{22}-\dfrac{5}{22}\right)\)
\(D=\dfrac{4}{9}:\dfrac{-3}{5}+\dfrac{4}{9}:\dfrac{-3}{22}\)
\(D=\dfrac{4}{9}.\dfrac{-5}{3}+\dfrac{4}{9}.\dfrac{-22}{3}\)
\(D=\dfrac{4}{9}.\left(\dfrac{-5}{3}+\dfrac{-22}{3}\right)\)
\(D=\dfrac{4}{9}.\left(-9\right)\)
\(D=-4\)
a) \(A=\dfrac{3}{5}.\dfrac{6}{7}+\dfrac{3}{7}.\dfrac{3}{5}-\dfrac{2}{7}.\dfrac{3}{5}\)
\(A=\dfrac{3}{5}.\dfrac{6}{7}+\dfrac{3}{5}.\dfrac{3}{7}-\dfrac{2}{7}.\dfrac{3}{5}\)
\(A=\dfrac{3}{5}.\left(\dfrac{6}{7}+\dfrac{3}{7}-\dfrac{2}{7}\right)\)
\(A=\dfrac{3}{5}.1\)
\(A=\dfrac{3}{5}\)
b) \(B=\left(-13.\dfrac{2}{5}+\dfrac{-2}{9}:2\dfrac{1}{2}+\dfrac{2}{5}.\dfrac{11}{9}\right).2\dfrac{1}{2}\)
\(B=\left(-13.\dfrac{2}{5}+\dfrac{-2}{9}:\dfrac{5}{2}+\dfrac{2}{5}.\dfrac{11}{9}\right).\dfrac{5}{2}\)
\(B=\left(-13.\dfrac{2}{5}+\dfrac{-2}{9}.\dfrac{5}{2}+\dfrac{2}{5}.\dfrac{11}{9}\right).\dfrac{5}{2}\)
\(B=\left(-13+\dfrac{-2}{9}+\dfrac{11}{9}\right).\dfrac{2}{5}.\dfrac{5}{2}\)
\(B=-13+\left(\dfrac{-2}{9}+\dfrac{11}{9}\right)\)
\(B=-13+1\)
\(B=-12\)
c) \(C=\left(\dfrac{-4}{5}+\dfrac{5}{7}\right):\dfrac{2}{3}+\left(\dfrac{-1}{5}-\dfrac{2}{7}\right):\dfrac{2}{3}\)
\(C=\left(\dfrac{-4}{5}+\dfrac{5}{7}\right).\dfrac{3}{2}+\left(\dfrac{-1}{5}-\dfrac{2}{7}\right).\dfrac{3}{2}\)
\(C=\left(\dfrac{-4}{5}+\dfrac{5}{7}+\dfrac{-1}{5}-\dfrac{2}{7}\right).\dfrac{3}{2}\)
\(C=\left(\dfrac{-4}{5}+\dfrac{-1}{5}+\dfrac{5}{7}+\dfrac{2}{7}\right).\dfrac{3}{2}\)
\(C=\left(-1+1\right).\dfrac{3}{2}\)
\(C=0.\dfrac{3}{2}\)
\(C=0\)
d) \(D=\dfrac{4}{9}:\left(\dfrac{1}{15}-\dfrac{2}{3}\right)+\dfrac{4}{9}:\left(\dfrac{1}{11}-\dfrac{5}{22}\right)\)
\(D=\dfrac{4}{9}:\left(\dfrac{1}{15}-\dfrac{10}{15}\right)+\dfrac{4}{9}:\left(\dfrac{2}{22}-\dfrac{5}{22}\right)\)
\(D=\dfrac{4}{9}:\dfrac{-3}{5}+\dfrac{4}{9}:\dfrac{-3}{22}\)
\(D=\dfrac{4}{9}.\dfrac{-5}{3}+\dfrac{4}{9}.\dfrac{-22}{3}\)
\(D=\dfrac{4}{9}.\left(\dfrac{-5}{3}+\dfrac{-22}{3}\right)\)
\(D=\dfrac{4}{9}.\left(-9\right)\)
\(D=-4\)
a) \(A=\dfrac{3}{5}.\dfrac{6}{7}+\dfrac{3}{7}:\dfrac{5}{3}-\dfrac{2}{7}:1\dfrac{2}{3}\)
\(A=\dfrac{3}{5}.\dfrac{6}{7}+\dfrac{3}{7}:\dfrac{5}{3}-\dfrac{2}{7}:\dfrac{5}{3}\)
\(A=\left(\dfrac{3}{5}.\dfrac{5}{3}:\dfrac{5}{3}\right):\left(\dfrac{6}{7}+\dfrac{3}{7}-\dfrac{2}{7}\right)\)
\(A=\left(1.\dfrac{3}{5}\right):1\)
\(A=\dfrac{3}{5}:1\)
\(A=\dfrac{3}{5}\)
c) \(C=\left(\dfrac{-4}{5}+\dfrac{5}{7}\right):\dfrac{2}{3}+\left(\dfrac{-1}{5}+\dfrac{2}{7}\right):\dfrac{2}{3}\)
\(C=\dfrac{-4}{5}+\dfrac{5}{7}:\dfrac{2}{3}+\dfrac{-1}{5}+\dfrac{2}{7}:\dfrac{2}{3}\)
\(C=\left[\left(\dfrac{-4}{5}\right)+\left(\dfrac{-1}{5}\right)\right]:\left(\dfrac{2}{3}:\dfrac{2}{3}\right)+\left(\dfrac{5}{7}+\dfrac{2}{7}\right)\)
\(C=\left(-1\right):1+1\)
\(C=0\)
\(a,A=\dfrac{3}{5}.\dfrac{6}{7}+\dfrac{3}{7}:\dfrac{5}{3}-\dfrac{2}{7}:1\dfrac{2}{3}\)
\(=\dfrac{3}{5}.\left(\dfrac{6}{7}+\dfrac{3}{7}-\dfrac{2}{7}\right)\)
\(=\dfrac{3}{5}\)
\(b,B=(-13.\dfrac{2}{5}+\dfrac{-2}{9}.\dfrac{2}{5}+\dfrac{2}{5}.\dfrac{11}{9}).\dfrac{5}{2}\)
\(=(-13-\dfrac{2}{9}+\dfrac{11}{9}).\dfrac{2}{5}.\dfrac{5}{2}\)
\(=-13+(\dfrac{11}{9}-\dfrac{2}{9})\)
\(=-13+(\dfrac{11}{9}-\dfrac{2}{9})\)
\(=-12\)
\(c,C=(\dfrac{-4}{5}+\dfrac{5}{7}).\dfrac{3}{2}+(\dfrac{-1}{5}+\dfrac{2}{7}).\dfrac{3}{2}\)
\(=(\dfrac{-4}{5}+\dfrac{5}{7}+\dfrac{-1}{5}+\dfrac{2}{7}).\dfrac{3}{2}\)
\(=[(\dfrac{-4}{5}+\dfrac{-1}{5})+(\dfrac{5}{7}+\dfrac{2}{7})].\dfrac{3}{2}\)
\(=0\)
\(d,D=\dfrac{4}{9}:(\dfrac{1}{15}-\dfrac{10}{15})+\dfrac{4}{9}:(\dfrac{2}{22}-\dfrac{5}{22})\)
\(=\dfrac{4}{9}:\dfrac{-3}{5}+\dfrac{4}{9}:\dfrac{-3}{22}\)
\(=\dfrac{4}{9}.\dfrac{-5}{3}+\dfrac{4}{9}.\dfrac{-22}{3}\)
\(=\dfrac{4}{9}.(\dfrac{-5}{3}+\dfrac{-22}{3})\)
\(=\dfrac{4}{9}.\dfrac{-27}{3}\)
\(=-4\)
a) A = \(\dfrac{3}{5}\) . \(\dfrac{6}{7}\) + \(\dfrac{3}{7}\) : \(\dfrac{5}{3}\) - \(\dfrac{2}{7}\) : 1\(\dfrac{2}{3}\) = \(\dfrac{3}{5}\) . \(\dfrac{6}{7}\) + \(\dfrac{3}{7}\) . \(\dfrac{3}{5}\) - \(\dfrac{2}{7}\) . \(\dfrac{3}{5}\)
= \(\dfrac{3}{5}\) . ( \(\dfrac{6}{7}\) + \(\dfrac{3}{7}-\dfrac{2}{7}\) ) = \(\dfrac{3}{5}\)
b) B = ( \(-13.\dfrac{2}{5}\) + \(\dfrac{-2}{9}\) : 2\(\dfrac{1}{2}\) + \(\dfrac{2}{5}\) . \(\dfrac{11}{9}\) ) . 2\(\dfrac{1}{2}\)
a, A = \(\dfrac{3}{5}.\dfrac{6}{7}+\dfrac{3}{7}.\dfrac{3}{5}-\dfrac{2}{7}.\dfrac{3}{5}\)
= \(\dfrac{3}{5}.\left(\dfrac{6}{7}+\dfrac{3}{7}-\dfrac{2}{7}\right)\)
= \(\dfrac{3}{5}\)
b, B = ( - 13 . \(\dfrac{2}{5}+\dfrac{-2}{9}.\dfrac{2}{5}+\dfrac{2}{5}.\dfrac{11}{9}\) ) . \(\dfrac{5}{2}\)
= ( - 13 - \(\dfrac{2}{9}\) + \(\dfrac{11}{9}\) ) . \(\dfrac{2}{5}.\dfrac{5}{2}\)
= - 13 + \(\left(\dfrac{11}{9}-\dfrac{2}{9}\right)\)
= - 12
c, \(\left(\dfrac{-4}{5}+\dfrac{5}{7}\right).\dfrac{3}{2}+\left(\dfrac{-1}{5}+\dfrac{2}{7}\right).\dfrac{3}{2}\)
= \(\left(\dfrac{-4}{5}+\dfrac{5}{7}+\dfrac{-1}{5}+\dfrac{2}{7}\right).\dfrac{3}{2}\)
= \(\left(\left(\dfrac{-4}{5}+\dfrac{-1}{5}\right)+\left(\dfrac{5}{7}+\dfrac{2}{7}\right)\right)\) . \(\dfrac{3}{2}\)
= 0
d, D = \(\dfrac{4}{9}:\left(\dfrac{1}{15}-\dfrac{10}{15}\right)+\dfrac{4}{9}:\left(\dfrac{2}{22}-\dfrac{5}{22}\right)\)
= \(\dfrac{4}{9}:\dfrac{-3}{5}+\dfrac{4}{9}:\dfrac{-3}{22}=\dfrac{4}{9}.\dfrac{-5}{3}+\dfrac{4}{9}.\dfrac{-22}{3}\)
= \(\dfrac{4}{9}.\left(\dfrac{-5}{3}+\dfrac{-22}{3}\right)=\dfrac{4}{9}.\dfrac{-27}{3}=-4\)
A = 3/5 . 6/7 + 3/7 : 5/3 - 2/7 : 1(2/3)
A = 3/5 . ( 6/7 + 3/7 - 2/7 ) : ( 5/3 : 5/3 )
A = 3/5 . 1 : 1
A = 3/5
B = ( -13 . 2/5 + -2/9 : 2(1/2) + 2/5 . 11/9 ). 2(1/2)
B = -13 . ( 2/5 : 2/5 ) + ( -2/9 + 11/9 ) . ( 5/2 . 5/2 )
B = -13 . 1 + 1 . 5
B = -13 + 5
B = -8
C = ( -4/5 + 5/7 ) : 2/3 + ( -1/5 + 2/7 ) : 2/3
C = 3/2 . [( -4/5 + -1/5 )+( 5/7 + 2/7 )]
C = 3/2 . [ (-1) + 1 ]
C = 3/2 . 0
C = 0
D = 4/9 : ( 1/15 - 2/3 ) + 4/9 : ( 1/11 - 5/22 )
D = 4/9 . ( -5/3 + -22/3 )
D = 4/9 . (-9)
D = -4
Bước làm:
Bước 1: Đưa số hữu tỉ về dạng phân số.
Bước 2: Đưa phép chia về dạng phép nhân các phân số.
Bước 3: Áp dụng tính chất của phép nhân các phân số: Bao gồm giao hoán, kết hợp, phân phối với phép cộng (trừ).
a) A = 3/5 . 6/7 + 3/7 : 5/3 - 2/7 : 1/ 2/3
=3/5.(6/7+3/7-2/7)=3/5
b,B=(-13.2/5+-2/9.2/5+2/5.11/9).5/2
=(-13.2/5+11/9).2/5.5/2
=-13+(11/9-2/9)
=-12
c,C=(-4/5+5/7).3/2+(-1/5+2/7).3/2
=(-4/5+5/7+-1/5+2/7).3/2
=(-4/5+-1/5)+(5/7+2/7).3/2=0
3/5.6/7+3/7:5/3-2/7:1.2/3
=3/5.6/7+3/7.3/5-2/7:5/3
=3/5.6/7+3/7-3/5-2/7.3/5
3/5(6/7+3/7-2/7)
=3/5.1=3/5
B=(-13.2/5+-2/9:2.1/2+2/5.11/9).2.1/2
=(-13.2/5+-2/9:5/2+2/5.11/9).5/2
(2/5(-13-2/9+11/9)).5/2
2/5.(-12).5/2
=-12
C=(-4/5+5/7):2/3+(-1/5+2/7);2/3
=(-4/5+5/7-1/5+2/7):2/3
=((-4/5-1/5)+(5/7+2/7));2/3
=(-1+1):2/3
=0:2/3
=0
D=4/9:(1/15-2/3)+4/9:(1/11-5/22)
=4/9:(1/15-10/15)+4/9:(2/22-5/22)
=4/9.(15/-9)+4/9:(-3/22)
=4/9.(15/-9)+4/9.(22/-3)
=-20/27+(88/27)=-4
A= 3/5 . 6/7 + 3/7 : 5/3 - 2/7 : 1 2/3 = 3/5 . (6/7 + 3/7 - 2/7) = 3/5
B=( -13 . 2/5 + -2/9 : 2 1/2 + 2/5 .11/9) . 2 1/2=(-13 -2/9 + 11/9) . 2/5 . 5/2=-13 + (11/9 - 2/9)= -12
C=(-4/5 + 5/7) : 2/3 + (-1/5 + 2/7) : 2/3 = -4/5 + 5/7. 3/2 + -1/5 + 2/7.3/2 = 3/2 . (-4/5 + -1/5) + (5/7 + 2/7)= 3/2 :(-1) + 1 = -2/3 + 1 = -1/2
D=4/9 : (1/15 - 2/3) + 4/9 : (1/11 - 5/22) = 4/9 : -3/5 + 4/9 : -3/22 = 4/9 . -5/3 + 4/9 . -22/3 = 4/9 . -5/3 + -22/3 = 4/9 . (-5/3 + -22/3) = 4/9 . -27/3 = -4
A=3/3 , B=-216/87 , C=1/2 , D =-399/440
a)A= \(\dfrac{3}{5}\)
b)B=-14
c) C = 0
d) D = \(\dfrac{440}{729}\)