Cho \(A=\frac{5}{17}+\frac{-4}{9}-\frac{20}{31}+\frac{12}{17}-\frac{11}{31}\)
\(B=\frac{-3}{7}+\frac{7}{15}+\frac{-4}{7}+\frac{8}{15}-\frac{-2}{3}\)
Tính số nguyên x sao cho \(A< \frac{x}{9}\le B\)
Tìm số nguyên x
a) \(\frac{1}{3}+\frac{-2}{5}+\frac{1}{6}+\frac{-1}{5}\le x< \frac{-3}{4}+\frac{2}{7}+\frac{-1}{4}+\frac{3}{5}+\frac{5}{7}\)
b)\(\frac{5}{17}+\frac{-9}{4}+\frac{-26}{31}+\frac{12}{17}+\frac{-11}{31}< \frac{x}{9}\le\frac{-3}{7}+\frac{7}{15}+\frac{4}{-7}+\frac{8}{15}\)
\(a)\frac{1}{3}+\frac{-2}{5}+\frac{1}{6}+\frac{-1}{5}\le x< \frac{-3}{4}+\frac{2}{7}+\frac{-1}{4}+\frac{3}{5}+\frac{5}{7}\)
\(\Rightarrow\frac{1}{3}+\frac{1}{6}+\frac{-2}{5}+\frac{-1}{5}\le x< \frac{-3}{4}+\frac{-1}{4}+\frac{2}{7}+\frac{5}{7}+\frac{3}{5}\)
\(\Rightarrow\frac{2}{6}+\frac{1}{6}+\frac{-3}{5}\le x< -1+1+\frac{3}{5}\)
\(\Rightarrow\frac{1}{2}+\frac{-3}{5}\le x< \frac{3}{5}\)
\(\Rightarrow\frac{-1}{10}\le x< \frac{6}{10}\)
\(\Rightarrow-1\le x< 6\)
\(\Rightarrow x\in\left\{-1;0;1;2;3;4;5\right\}\)
Bài b tương tự
bạn ơi bạn giải câu b được ko. mk ko biết làm câu b
Cho \(A=\frac{5}{17}+\frac{-4}{9}-\frac{20}{31}+\frac{12}{17}-\frac{11}{31}\)
\(B=\frac{-3}{7}+\frac{7}{15}+\frac{-4}{7}+\frac{8}{15}+\frac{-2}{3}\)
\(A=\left(\frac{5}{17}+\frac{12}{17}\right)+\left(-\frac{20}{31}-\frac{11}{31}\right)+-\frac{4}{9}\)
\(A=1+\left(-1\right)+\frac{-4}{9}\)
\(A=0+\frac{-4}{9}=\frac{-4}{9}\)
\(B=\left(\frac{-3}{7}+\frac{-4}{7}\right)+\left(\frac{7}{15}+\frac{8}{15}\right)+\frac{-2}{3}\)
\(B=-1+1+\frac{-2}{3}\)
\(B=\frac{-2}{3}\)
\(A=\frac{5}{17}+-\frac{4}{9}-\frac{20}{31}+\frac{12}{17}-\frac{11}{31}\)
\(=\left(\frac{5}{17}+\frac{12}{17}\right)+\frac{-4}{9}-\left(\frac{20}{31}+\frac{11}{31}\right)\)
\(=\frac{17}{17}+\frac{-4}{9}-\frac{31}{31}\)
\(=1+\frac{-4}{9}-1=-\frac{4}{9}\)
Ps : Câu tiếp bạn lm giống vậy. Thấy cùng mẫu thì cko nó vào riêng dấu ngoặc nhé!
Tìm x thoả mãn
a) \(-\frac{8}{3}+\frac{7}{5}+\frac{-71}{15}\)< x < \(-\frac{13}{7}+\frac{19}{14}+\frac{-7}{2}\)
b) \(\frac{5}{17}+\frac{-4}{9}+\frac{-20}{31}+\frac{12}{17}+\frac{-11}{31}\) < \(\frac{x}{9}\) < \(\frac{-3}{7}+\frac{7}{15}+\frac{4}{-7}+\frac{8}{15}+\frac{2}{3}\)
a) \(\frac{-8}{3}+\frac{7}{5}+\frac{-71}{15}\)< \(x\) < \(\frac{-13}{7}+\frac{19}{14}+\frac{-7}{2}\)
Ta có: \(\frac{-8}{3}+\frac{7}{5}+\frac{-71}{15}\)
=\(\frac{-40}{15}+\frac{21}{15}+\frac{-71}{15}\)
=\(\frac{-90}{15}\)
=\(-6\)
Ta có: \(\frac{-13}{7}+\frac{19}{14}+\frac{-7}{2}\)
=\(\frac{-26}{14}+\frac{19}{14}+\frac{-49}{14}\)
=\(\frac{-56}{14}\)
=\(-4\)
=> \(-6\)< \(x\)<\(-4\)
=> \(x=-5\)
b)\(\frac{5}{17}+\frac{-4}{9}+\frac{-20}{31}+\frac{12}{17}+\frac{-11}{31}\)< \(\frac{x}{9}\)<\(\frac{-3}{7}+\frac{7}{15}+\frac{4}{-7}+\frac{8}{15}+\frac{2}{3}\)
Ta có: \(\frac{5}{17}+\frac{-4}{9}+\frac{-20}{31}+\frac{12}{17}+\frac{-11}{31}\)
=\(\left(\frac{5}{17}+\frac{12}{17}\right)+\left(\frac{-20}{31}+\frac{-11}{31}\right)+\frac{-4}{9}\)
=\(1+\left(-1\right)+\frac{-4}{9}\)
=\(0+\frac{-4}{9}\)
=\(\frac{-4}{9}\)
Ta có: \(\frac{-3}{7}+\frac{7}{15}+\frac{4}{-7}+\frac{8}{15}+\frac{2}{3}\)
=\(\frac{-3}{7}+\frac{7}{15}+\frac{-4}{7}+\frac{8}{15}+\frac{2}{3}\)
=\(\left(\frac{-3}{7}+\frac{-4}{7}\right)+\left(\frac{7}{15}+\frac{8}{15}\right)+\frac{2}{3}\)
=\(\left(-1\right)+1+\frac{2}{3}\)
=\(0+\frac{2}{3}\)
=\(\frac{2}{3}\)
=> \(\frac{-4}{9}\)< \(\frac{x}{9}\)<\(\frac{2}{3}\)
=
=> \(\frac{-4}{9}\)<\(\frac{x}{9}\)<\(\frac{6}{9}\)
=> \(-4\)< \(x\)<\(6\)
=>\(x\in\left\{-3;-2;-1;0;1;2;3;4;5\right\}\)
BT1: Tìm số nguyên x, biết:
\(\frac{5}{17}\)+ \(\frac{-4}{9}\) + \(\frac{-20}{31}\) + \(\frac{12}{17}\) + \(\frac{-11}{31}\) \(\le\) \(\frac{x}{9}\) \(\le\) \(\frac{-3}{7}\) + \(\frac{7}{15}\) + \(\frac{4}{-7}\) + \(\frac{8}{15}\) + \(\frac{2}{3}\)
=>(5/17+12/17)+(-20/31-11/31)-4/9<=x/9<=(-3/7-4/7)+(7/15+8/15)+2/3
=>-4/9<=x/9<=6/9
=>-4<=x<=6
hay \(x\in\left\{-4;-3;-2;-1;0;...;6\right\}\)
1) Tính nhanh
a) A=\(\frac{3}{11\text{x}13}+\frac{3}{13\text{x}15}+\frac{3}{15\text{x}17}+...+\frac{3}{97\text{x}99}\)
b) B=\(\frac{4}{7\text{x}31}+\frac{6}{7\text{x}11}+\frac{9}{10\text{x}41}+\frac{7}{10\text{x}57}\)
3) Chứng tỏ phân số \(\frac{8n+5}{6n+4}\)tối giản với mọi số nguyên khác 0
\(A=\frac{3}{2}\times\left(\frac{1}{13\times11}+\frac{1}{13\times15}+\frac{1}{15\times17}+.....+\frac{1}{97\times99}\right)\)
\(A=\frac{3}{2}\times\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+......+\frac{1}{97}-\frac{1}{99}\right)\)
\(A=\frac{3}{2}\times\left(\frac{1}{11}-\frac{1}{99}\right)\)
\(A=\frac{3}{2}\times\frac{8}{99}\)
\(A=\frac{4}{33}\)
b] \(\frac{A}{5}=\frac{4}{31.35}+\frac{6}{35.41}+\frac{9}{41.50}+\frac{7}{50.57}\)
\(\frac{A}{5}=\frac{1}{31}-\frac{1}{35}+\frac{1}{35}-\frac{1}{41}+\frac{1}{41}-\frac{1}{50}+\frac{1}{50}-\frac{1}{57}\)
\(\frac{A}{5}=\frac{1}{31}-\frac{1}{57}\)
\(\Rightarrow A=5\left(\frac{1}{31}-\frac{1}{57}\right)=\frac{130}{1767}\)
c] Ta đặt \(\left(8n+5,6n+4\right)=d\)
\(\Rightarrow\frac{8n+5\div d}{6n+4\div d}\Rightarrow4\times\left(6n+4\right)-3\times\left(8n+5\right)=\left(24n+16\right)-\left(24n+15\right):d\)\(\Rightarrow d=1\)
Vậy \(\frac{8n+5}{6n+4}\)là phân số tối giản
B1: Thực hiện phép tính :
a, \(11\frac{3}{4}-(6\frac{5}{6}-4\frac{1}{2})+1\frac{2}{3}\)
b, \(2\frac{17}{20}-1\frac{11}{5}+6\frac{9}{20}:3\)
c, \(4\frac{3}{7}:\left(\frac{7}{5}.4\frac{3}{7}\right)\)
d, \(\left(3\frac{2}{9}.\frac{15}{23}.1\frac{7}{29}\right):\frac{5}{23}\)
B2: Thực hiện phép tính:
\(a,11\frac{3}{4}-(6\frac{5}{6}4\frac{1}{2}+1\frac{2}{3})\\ b,\left(5\frac{7}{8}-2\frac{1}{4}-0,5\right):\frac{23}{26}\)
\(c,\left(17\frac{13}{15}-3\frac{3}{7}\right)-\left(2\frac{12}{15}-4\right)\\ d,2\frac{2}{3}.\frac{-4}{5}.0,375-\left(-10\right).\frac{-15}{24}\)
Bài 1 :Thực hiện phép tính :
a) M =(\(\frac{-6}{13}+\frac{15}{26}-\frac{47}{39}-\frac{1}{78}\)) : (\(99\frac{17}{65}-100\frac{5}{52}+\frac{1}{130}\))
b) N = \(\frac{(\frac{3}{5}-0,435+\frac{1}{200}):\left(-0,04\right)}{30,75+\frac{1}{12}+3\frac{1}{6}}\)
c) P = (\(\frac{-5}{6}:\frac{-10}{11}\))+\(\frac{\frac{1}{4}+\frac{5}{8}-\frac{7}{13}}{\frac{-2}{12}-\frac{10}{24}+\frac{14}{39}}\)
Bài 2 : Thực hiện phép tính :V
a) P =\(\frac{\frac{1}{5}-\frac{1}{9}+\frac{1}{13}}{\frac{9}{5}-1+\frac{9}{13}}+\frac{\frac{10}{7}-\frac{10}{11}-\frac{10}{17}}{\frac{12}{7}-\frac{12}{11}-\frac{12}{17}}\)
b) Q = \(\frac{\frac{1}{14}-\frac{1}{30}-\frac{1}{46}}{\frac{2}{35}-\frac{2}{75}-\frac{2}{115}}:\frac{\frac{3}{8}-\frac{15}{17}+\frac{30}{31}}{\frac{1}{6}-\frac{20}{51}+\frac{40}{93}}\)
có rất nhiều câu dễ ở trong đề sao bạn Ko thử làm đi rồi câu nào khó lại hỏi
BÀI ÔN SỐ HỌC
1. Thực hiện mỗi phép tính sau bằng 2 cách:
a)\(3\frac{4}{9}+5\frac{1}{6}\)
Ví dụ :
Cách 1: \(3\frac{4}{9}+5\frac{1}{6}=\frac{31}{9}+\frac{31}{6}=\frac{62}{18}+\frac{93}{18}=\frac{155}{18}=8\frac{11}{18}\)
Cách 2:\(3\frac{4}{9}+5\frac{1}{6}=3\frac{8}{18}+5\frac{3}{18}=8\frac{11}{18}\)
b)\(8\frac{1}{14}-6\frac{3}{7}\)
c)\(7-3\frac{6}{7}\)
2. Áp dụng tính chất phép tính & qui tắc dấu ngoặc để tính giá trị các biểu thức sau:
a)A =\(11\frac{3}{13}-\left(3\frac{4}{7}+6\frac{3}{13}\right)\)
b)B =\(\left(7\frac{4}{9}+3\frac{8}{13}\right)-5\frac{4}{3}\)
c)C =\(\frac{-2}{7}.\frac{5}{11}+\frac{-2}{7}.\frac{6}{11}+5\frac{4}{7}\)
d)D =\(0,7.1\frac{3}{5}.30.0,375.\frac{4}{7}\)
3.Tìm các số nghịch đảo của các số sau : \(\frac{4}{7};6\frac{3}{8};\frac{-3}{17};0.37\)
4.Tìm x, biết :
0,5-\(\frac{2}{3}x=\frac{5}{12}\)
Tính
a/ \(A=17\frac{2}{31}-\left(\frac{15}{17}+6\frac{2}{31}\right)\)
b/ \(B=\left(31\frac{6}{13}+5\frac{9}{41}\right)-36\frac{6}{13}\)
c/ \(C=27\frac{51}{59}-\left(7\frac{51}{59}-\frac{1}{3}\right)\)
d/ \(D=\left(13\frac{29}{31}-3\frac{7}{8}\right)-\left(2\frac{28}{31}-4\right)\)
\(A=17\frac{2}{31}-\left(\frac{15}{17}+6\frac{2}{31}\right)=\left(17\frac{2}{31}-6\frac{2}{31}\right)-\frac{15}{17}=11-\frac{15}{17}=10+\left(1-\frac{15}{17}\right)=10\frac{2}{17}\)
\(B=\left(31\frac{6}{13}-36\frac{6}{13}\right)+5\frac{9}{41}=-5+5\frac{9}{41}=\frac{9}{41}\)
C=\(\left(27\frac{51}{59}-7\frac{51}{59}\right)+\frac{1}{3}=20+\frac{1}{3}=20\frac{1}{3}\)
\(D=\left(13\frac{29}{31}-2\frac{28}{31}\right)+\left(4-3\frac{7}{8}\right)=11\frac{1}{31}+\frac{1}{8}=11\frac{8+31}{31.8}=11\frac{39}{248}\)