a. 2/7-2/7 . 7/12
b. -11/12. 18/25+ -11/12.7/25+5/12
c. x- 3/5= 2/3
d. [ x- 1/3] ; 1/2 + 3/7 = 5 và 3/7
e. -2/3x + 1/5x = -14/15
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Số cây nhãn trong vườn là: 160.3/8=60(cây)
Số cây vải trong vườn là: 60.80/100=48(cây)
Trong vườn có số cây xoài là: 160-60-48=52(cây)
\(\dfrac{1}{2^2}>\dfrac{1}{2\cdot3}=\dfrac{1}{2}-\dfrac{1}{3}\)
\(\dfrac{1}{3^2}>\dfrac{1}{3\cdot4}=\dfrac{1}{3}-\dfrac{1}{4}\)
...
\(\dfrac{1}{63^2}>\dfrac{1}{63\cdot64}=\dfrac{1}{63}-\dfrac{1}{64}\)
Do đó: \(A=\dfrac{1}{2^2}+\dfrac{1}{3^2}+...+\dfrac{1}{63^2}>\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{63}-\dfrac{1}{64}\)
=>\(A>\dfrac{1}{2}-\dfrac{1}{64}>\dfrac{1}{2}\)
-\(\dfrac{8}{5}\).(\(\dfrac{1}{8}\)+\(\dfrac{7}{8}\))+\(\dfrac{2}{5}\)
=-\(\dfrac{8}{5}\)+\(\dfrac{2}{5}\)
=-\(\dfrac{6}{5}\)
a/12,567+5,67=18,237~18,24
b/-12,3+345,68=333,38
c/0,8-3,1651=-2,3651~2,37
d/-5,5+9,007=3,507~3,51
e/0,008-3,9999=-3,9919~3,99
f/125:0,25=500=500,00
g/20,24.0,125=2,53
h/12,75:(-2,125)=-6=-6,00
i/(-14,3).(-2,5)=35,75
k/-9,66:3,22=3=3,00
l/4,38-1,9+0,623=2,48+0,623=3,103~3,10
n/100.(2,01+3,99)=100.6=600=600,00
có rất nhiều PS bằng \(\dfrac{5}{8}\) ví dụ:\(\dfrac{10}{16},\dfrac{15}{24},\dfrac{20}{32},\dfrac{25}{40},...\)chúc học tốt
\(\dfrac{5}{8}\) là phân số tối giản nên những phân số bằng phân số \(\dfrac{5}{8}\) là những phân số rút gọn bằng \(\dfrac{5}{8}\).
Vd:\(\dfrac{10}{16}=\dfrac{5}{8}\).
phân số thứ 1 :10 / 16 ; phân số thứ 2 : 15 / 24 ;phân số thứ 3 :
20 / 32
\(A=\dfrac{1}{1.2}+\dfrac{1}{3.4}+\dfrac{1}{5.6}+\dfrac{1}{7.8}+...+\dfrac{1}{59.60}\)
\(A=1-\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{7}-\dfrac{1}{8}+...+\dfrac{1}{59}-\dfrac{1}{60}\)
\(A=\left(1+\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{60}\right)-2\left(\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{6}+\dfrac{1}{8}+...+\dfrac{1}{60}\right)\)
\(A=\left(1+\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{60}\right)-\left(1+\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{30}\right)\)
\(A=\dfrac{1}{31}+\dfrac{1}{32}+\dfrac{1}{33}+...+\dfrac{1}{60}\)
Ta tách A thành 3 nhóm\(A=\left(\dfrac{1}{31}+\dfrac{1}{32}+...+\dfrac{1}{40}\right)+\left(\dfrac{1}{41}+\dfrac{1}{42}+...+\dfrac{1}{50}\right)+\left(\dfrac{1}{51}+\dfrac{1}{52}+...+\dfrac{1}{60}\right)\)\(A>\dfrac{1}{40}.10+\dfrac{1}{50}.10+\dfrac{1}{60}.10\)
\(A>\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{1}{6}\)
\(A>\dfrac{37}{60}>\dfrac{7}{12}\)
\(\Rightarrow A>\dfrac{7}{12}\)
a) \(\dfrac{2}{7}-\dfrac{2}{7}\times\dfrac{7}{12}\)
= \(\dfrac{2}{7}-\dfrac{1}{6}\)
= \(\dfrac{5}{42}\)
b) \(\dfrac{-11}{12}\times\dfrac{18}{25}+\dfrac{-11}{12}\times\dfrac{7}{25}+\dfrac{5}{12}\)
= \(\dfrac{-11}{12}\times\left(\dfrac{18}{25}+\dfrac{7}{25}\right)+\dfrac{5}{12}\)
= \(\dfrac{-11}{12}\times1+\dfrac{5}{12}\)
= \(\dfrac{-11}{12}+\dfrac{5}{12}\)
= \(\dfrac{-1}{2}\)
c) \(\left(x-\dfrac{1}{3}\right)\div\dfrac{1}{2}+\dfrac{3}{7}=5\dfrac{3}{7}\)
\(\left(x-\dfrac{1}{3}\right)\times2+\dfrac{3}{7}=5\dfrac{3}{7}\)
\(\left(x-\dfrac{1}{3}\right)\times2=5\dfrac{3}{7}-\dfrac{3}{7}\)
= \(\left(x-\dfrac{1}{3}\right)\times2=5\)
\(x-\dfrac{1}{3}=5\div2\)
\(x-\dfrac{1}{3}=\dfrac{5}{2}\)
\(x=\dfrac{5}{2}+\dfrac{1}{3}\)
\(x=\dfrac{17}{6}\)
Vậy \(x=\dfrac{17}{6}\)
e) \(\dfrac{-2}{3}x+\dfrac{1}{5}x=\dfrac{-14}{15}\)
\(x\left(\dfrac{-2}{3}+\dfrac{1}{5}\right)=\dfrac{-14}{15}\)
\(x\times\dfrac{-7}{15}=\dfrac{-14}{15}\)
\(x=\dfrac{-14}{15}:\dfrac{-7}{15}\)
\(x=2\)
Vậy \(x=2\)