Tìm phần nguyên của
\(A=\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+\frac{1}{11}+\frac{1}{13}\right).231\)
Tìm phần nguyên của
A= (\(\frac{1}{2}+\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+\frac{1}{11}+\frac{1}{13}\)nhân với 231
Để tìm phần nguyên của biểu thức \( A = \left( \frac{1}{2} + \frac{1}{3} + \frac{1}{5} + \frac{1}{7} + \frac{1}{11} + \frac{1}{13} \right) \times 231 \), chúng ta cần tính giá trị của \( A \) trước, sau đó lấy phần nguyên của kết quả.
Đầu tiên, tính tổng của các phân số:
\[ A = \left( \frac{1}{2} + \frac{1}{3} + \frac{1}{5} + \frac{1}{7} + \frac{1}{11} + \frac{1}{13} \right) \]
\[ = \frac{1}{2} + \frac{1}{3} + \frac{1}{5} + \frac{1}{7} + \frac{1}{11} + \frac{1}{13} \]
Bây giờ, hãy tính tổng này:
\[ A = \frac{1}{2} + \frac{1}{3} + \frac{1}{5} + \frac{1}{7} + \frac{1}{11} + \frac{1}{13} \]
\[ = \frac{4291}{4290} \]
Bây giờ, ta nhân \( A \) với 231:
\[ A \times 231 = \frac{4291}{4290} \times 231 \]
\[ = 231 + \frac{231}{2} + \frac{231}{3} + \frac{231}{5} + \frac{231}{7} + \frac{231}{11} + \frac{231}{13} \]
Sau đó, chúng ta sẽ lấy phần nguyên của tổng này. Tức là, phần nguyên của \( A \times 231 \) là 231 cộng với phần nguyên của các phân số dư:
\[ 231 + \left\lfloor \frac{231}{2} \right\rfloor + \left\lfloor \frac{231}{3} \right\rfloor + \left\lfloor \frac{231}{5} \right\rfloor + \left\lfloor \frac{231}{7} \right\rfloor + \left\lfloor \frac{231}{11} \right\rfloor + \left\lfloor \frac{231}{13} \right\rfloor \]
\[ = 231 + 115 + 77 + 46 + 33 + 21 + 17 \]
\[ = 231 + 309 \]
\[ = 540 \]
Vậy, phần nguyên của biểu thức \( A \times 231 \) là 540.
tìm phần nguyên
\(A=\left(\frac{-5}{11}\right).\frac{7}{15}+\frac{11}{-5}.\frac{30}{33}\)
\(B=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{x.\left(x+1\right)}\)(x∈Z)
\(C=\frac{1}{3}-\frac{3}{5}+\frac{5}{7}-\frac{7}{9}+\frac{9}{11}-\frac{11}{13}+\frac{11}{13}-\frac{9}{11}+\frac{7}{9}-\frac{5}{7}+\frac{3}{5}-\frac{1}{3}\)
\(D=\frac{1}{3}-\left[\left(-\frac{5}{4}\right)-\left(\frac{1}{4}+\frac{3}{8}\right)\right]\)
giúp mk nhé, mk tk, mk thanks nhiều
\(A=\left(-\frac{5}{11}\right).\frac{7}{15}+\frac{11}{-5}.\frac{30}{33}\)
\(A=-\frac{7}{33}+-2\)
\(A=-\frac{73}{33}\)
[ A] = -2
\(D=\frac{1}{3}-\left[\left(-\frac{5}{4}\right)-\left(\frac{1}{4}+\frac{3}{8}\right)\right]\)
\(D=\frac{1}{3}-\left[\left(-\frac{5}{4}\right)-\frac{5}{8}\right]\)
\(D=\frac{1}{3}-\left(-\frac{15}{8}\right)\)
\(D=\frac{53}{24}\)
\(\left[D\right]=2\)
Tính nhanh :
\(\frac{-3}{7}+\frac{15}{26}-\left(\frac{2}{13}-\frac{3}{7}\right)\)
\(2.\frac{3}{7}+\left(\frac{2}{9}-1\frac{3}{7}\right)-\frac{5}{3}:\frac{1}{9}\)
\(\frac{-11}{23}.\frac{6}{7}+\frac{8}{7}.\frac{-11}{23}-\frac{1}{23}\)
\(\left(\frac{377}{-231}-\frac{123}{89}+\frac{34}{791}\right).\left(\frac{1}{6}-\frac{1}{8}-\frac{1}{24}\right)\)
a) \(\frac{-3}{7}+\frac{15}{26}-\left(\frac{2}{13}-\frac{3}{7}\right)=\frac{-3}{7}+\frac{15}{26}-\frac{2}{13}+\frac{3}{7}=\left(\frac{-3}{7}+\frac{3}{7}\right)+\left(\frac{15}{26}-\frac{2}{13}\right)\)
\(=\frac{15-4}{26}=\frac{11}{26}\)
c) \(\frac{-11}{23}.\frac{6}{7}+\frac{8}{7}.\frac{-11}{23}-\frac{1}{23}=\frac{-11}{23}.\left(\frac{6}{7}+\frac{8}{7}\right)-\frac{1}{23}\)
\(=\frac{-11}{23}.2-\frac{1}{23}=\frac{-22-1}{23}=\frac{-23}{23}=-1\)
d) Đặt \(\frac{377}{-231}-\frac{123}{89}+\frac{34}{791}=A\)
Ta có: \(A.\left(\frac{1}{6}-\frac{1}{8}-\frac{1}{24}\right)=A.\left(\frac{4-3-1}{24}\right)=A.0=0\)
tính nhanh :
a) \(\frac{-3}{7}+\frac{15}{26}-\left(\frac{2}{13}-\frac{3}{7}\right)\)
b) \(2.\frac{3}{7}+\left(\frac{2}{9}-1\frac{3}{7}\right)-\frac{5}{3}:\frac{1}{9}\)
c) \(\frac{-11}{23}.\frac{6}{7}+\frac{8}{7}.\frac{-11}{23}-\frac{1}{23}\)
d) \(\left(\frac{377}{-231}-\frac{123}{89}+\frac{34}{791}\right).\left(\frac{1}{6}-\frac{1}{8}-\frac{1}{24}\right)\)
a. \(\frac{-3}{7}+\frac{15}{26}-\left(\frac{2}{13}-\frac{3}{7}\right)=\frac{-3}{7}+\frac{15}{26}-\frac{2}{13}+\frac{3}{7}=\frac{15}{13.2}-\frac{2}{13}=\frac{15}{13.2}-\frac{2.2}{13.2}=\frac{15-4}{26}=\frac{11}{26}\)
C. \(\frac{-11}{23}.\frac{6}{7}+\frac{8}{7}.\frac{-11}{23}-\frac{1}{23}=\frac{1}{23}.\left(-11.\frac{6}{7}-11.\frac{8}{7}-1\right)=\frac{1}{23}.\left(-22-1\right)=\frac{1}{23}.\left(-23\right)=-1\)
a.
\(-\frac{3}{7}+\frac{15}{26}-\left(\frac{2}{13}-\frac{3}{7}\right)\)
\(=-\frac{3}{7}+\frac{15}{26}-\frac{2}{13}+\frac{3}{7}\)
\(=\left(\frac{3}{7}-\frac{3}{7}\right)+\left(\frac{15}{26}-\frac{2}{13}\right)\)
\(=0+\left(\frac{15-4}{26}\right)\)
\(=\frac{11}{26}\)
c.
\(-\frac{11}{23}\times\frac{6}{7}+\frac{8}{7}\times\frac{-11}{23}-\frac{1}{23}\)
\(=-\frac{11}{23}\times\left(\frac{6}{7}+\frac{8}{7}\right)-\frac{1}{23}\)
\(=-\frac{11}{23}\times\frac{14}{7}\)
\(=-\frac{11}{23}\times2-\frac{1}{23}\)
\(=-\frac{22}{23}-\frac{1}{23}\)
\(=-\frac{23}{23}\)
\(=-1\)
d.
\(\left(\frac{377}{-231}-\frac{123}{89}+\frac{34}{791}\right)\times\left(\frac{1}{6}-\frac{1}{8}-\frac{1}{24}\right)\)
\(=\left(\frac{377}{-231}-\frac{123}{89}+\frac{34}{791}\right)\times\left(\frac{4-3-1}{24}\right)\)
\(=\left(\frac{377}{-231}-\frac{123}{89}+\frac{34}{791}\right)\times\frac{0}{24}\)
\(=0\)
Chúc bạn học tốt
Tính nhanh ( nếu có thể):
\(a,-3^2+\left\{-52:[\left(-3\right)^2\right\}\) \(d,(\frac{377}{-231}-\frac{123}{89}+\frac{34}{791}):(\frac{1}{6}-\frac{1}{8}-\frac{1}{24})\)
\(b,2\frac{3}{7}+(\frac{2}{9}-1\frac{3}{7})-\frac{5}{3}:\frac{1}{9}\) \(e,\frac{-5}{13}:\frac{3}{7}-\frac{2}{7}.\frac{8}{13}+\frac{5}{13}.\frac{1}{7}\)
\(c,\frac{-11}{23}.\frac{6}{7}+\frac{8}{7}.\frac{-11}{23}-\frac{1}{23}\)
a: \(=-9+\left\{-52:9\right\}=-9+\dfrac{-52}{9}=-\dfrac{133}{9}\)
b: \(=\dfrac{17}{7}+\left(\dfrac{-76}{63}\right):15\)
\(=\dfrac{17}{7}-\dfrac{76}{63}\cdot\dfrac{1}{15}=\dfrac{317}{135}\)
e: \(=\dfrac{-5}{13}\cdot\dfrac{7}{3}-\dfrac{2}{7}\cdot\dfrac{8}{13}+\dfrac{5}{13}\cdot\dfrac{1}{7}\)
\(=\dfrac{5}{13}\left(-\dfrac{7}{3}+\dfrac{1}{7}\right)-\dfrac{2}{7}\cdot\dfrac{8}{13}\)
\(=\dfrac{5}{13}\cdot\dfrac{-46}{21}-\dfrac{16}{91}=\dfrac{-278}{273}\)
Tính nhanh:
a) \(2.\frac{3}{7}+\left(\frac{2}{9}-1\frac{3}{7}\right)-\frac{5}{3}:\frac{1}{9}\)
b) \(\frac{-11}{23}.\frac{6}{7}+\frac{8}{7}.\frac{-11}{23}-\frac{1}{23}\)
c )\(\left(\frac{377}{-231}-\frac{123}{89}+\frac{34}{791}\right).\left(\frac{1}{6}-\frac{1}{8}-\frac{1}{24}\right)\)
d) \(19\frac{5}{8}:\frac{7}{12}-15\frac{1}{4}:\frac{7}{12}\)
e) \(\frac{2}{5}.\frac{1}{3}-\frac{2}{15}:\frac{1}{5}+\frac{3}{5}.\frac{1}{3}\)
a: \(=\dfrac{17}{7}+\dfrac{2}{9}-\dfrac{10}{7}-\dfrac{5}{3}\cdot9=1+\dfrac{2}{9}-15=-14+\dfrac{2}{9}=-\dfrac{126}{9}+\dfrac{2}{9}=-\dfrac{124}{9}\)
b: \(=\dfrac{-11}{23}\left(\dfrac{6}{7}+\dfrac{8}{7}\right)-\dfrac{1}{23}=\dfrac{-22}{23}-\dfrac{1}{23}=-1\)
c: \(=\left(\dfrac{377}{-231}-\dfrac{123}{89}+\dfrac{34}{791}\right)\cdot\dfrac{4-3-1}{24}=0\)
d: \(=\dfrac{12}{7}\left(19+\dfrac{5}{8}-15-\dfrac{1}{4}\right)=\dfrac{12}{7}\cdot\dfrac{35}{8}=\dfrac{15}{2}\)
Tìm số nguyên âm a biết:
\(a^2-\left(\frac{3}{5}\right)^2=\frac{1}{1\cdot2}+\frac{1}{2\cdot7}+\frac{1}{7\cdot5}+\frac{1}{5\cdot13}+\frac{1}{13\cdot8}+\frac{1}{8\cdot19}+\frac{1}{19\cdot11}+\frac{1}{11\cdot25}\)
bÀI LÀM
a) x4+x3+2x2+x+1=(x4+x3+x2)+(x2+x+1)=x2(x2+x+1)+(x2+x+1)=(x2+x+1)(x2+1)
b)a3+b3+c3-3abc=a3+3ab(a+b)+b3+c3 -(3ab(a+b)+3abc)=(a+b)3+c3-3ab(a+b+c)
=(a+b+c)((a+b)2-(a+b)c+c2)-3ab(a+b+c)=(a+b+c)(a2+2ab+b2-ac-ab+c2-3ab)=(a+b+c)(a2+b2+c2-ab-ac-bc)
c)Đặt x-y=a;y-z=b;z-x=c
a+b+c=x-y-z+z-x=o
đưa về như bài b
d)nhóm 2 hạng tử đầu lại và 2hangj tử sau lại để 2 hạng tử sau ở trong ngoặc sau đó áp dụng hằng đẳng thức dề tính sau đó dặt nhân tử chung
e)x2(y-z)+y2(z-x)+z2(x-y)=x2(y-z)-y2((y-z)+(x-y))+z2(x-y)
=x2(y-z)-y2(y-z)-y2(x-y)+z2(x-y)=(y-z)(x2-y2)-(x-y)(y2-z2)=(y-z)(x2-2y2+xy+xz+yz)
12)\(0,2.\frac{15}{36}-\left(\frac{2}{5}+\frac{2}{3}\right):1\frac{1}{5}\)
13)\(1\frac{13}{15}.0,75-\left(\frac{8}{15}+0,25\right).\frac{24}{27}\)
16)\(\frac{1}{2}+\frac{3}{4}-\left(\frac{3}{4}-\frac{4}{5}\right).\left(-2,75\right)\)
18)\(\left(\frac{7}{8}-\frac{3}{4}\right).1\frac{1}{3}-\frac{2}{7}.\left(3.5\right)^2\)
22)\(1\frac{13}{15}.0,75-\left(\frac{11}{20}+25\%\right):\frac{7}{3}\)
23)\(\frac{\left(\frac{2}{3}-0,75\right).\left(0,2-\frac{2}{5}\right)}{\frac{5}{9}-1\frac{1}{12}}\)
33)\(\left(25\%+\frac{1}{3}+0,75\right):\left(4\frac{3}{4}-3\frac{1}{2}\right)\)
35)\(\left(\frac{377}{-231}-\frac{123}{89}+\frac{34}{791}\right).\left(\frac{1}{6}-\frac{1}{8}-\frac{1}{24}\right)\)