Tìm số thích hợp cho ?:
a) \(\dfrac{-2}{3}\cdot\dfrac{?}{4}=\dfrac{1}{2};\)
b) \(\dfrac{?}{3}\cdot\dfrac{5}{8}=\dfrac{-5}{12};\)
c) \(\dfrac{5}{6}\cdot\dfrac{3}{?}=\dfrac{1}{4}.\)
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HT
8 tháng 5 2017
\(A=\dfrac{\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}}{\left(\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}\right)-\dfrac{1}{2}.\dfrac{1}{3}.\dfrac{1}{4}}\)
\(\Rightarrow A=\dfrac{1}{1-\dfrac{1}{2}.\dfrac{1}{3}.\dfrac{1}{4}}\) ( Lượt \(\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}\) ở tử và mẫu )
\(\Rightarrow A=\dfrac{1}{1-\dfrac{1}{24}}\)
\(\Rightarrow A=\dfrac{1}{\dfrac{23}{24}}=\dfrac{24}{23}\)
Vậy \(A=\dfrac{24}{23}\)
H9
HT.Phong (9A5)
CTVHS
24 tháng 8 2023
a) \(\dfrac{2}{5}\times?=\dfrac{3}{10}\)
\(?=\dfrac{3}{10}:\dfrac{2}{5}=\dfrac{3}{4}\)
b) \(\dfrac{1}{8}:?=\dfrac{1}{5}\)
\(?=\dfrac{1}{8}:\dfrac{1}{5}=\dfrac{5}{8}\)
24 tháng 8 2023
a: Phân số cần tìm là: \(\dfrac{3}{10}:\dfrac{2}{5}=\dfrac{3}{10}\cdot\dfrac{5}{2}=\dfrac{15}{20}=\dfrac{3}{4}\)
b: Phân số cần tìm là \(\dfrac{1}{8}:\dfrac{1}{5}=\dfrac{5}{8}\)
ND
22 tháng 12 2017
a)Nhận xét
\(\dfrac{n^3+1}{n^3-1}=\dfrac{\left(n+1\right)\left(n^2-n+1\right)}{\left(n-1\right)\left(n^2+n+1\right)}=\dfrac{\left(n+1\right)\left[\left(n-0,5\right)^2+0;75\right]}{\left(n-1\right)\left[\left(n+0,5\right)^2+0,75\right]}\)
Áp dụng công thức trên:
\(A=\dfrac{2^3+1}{2^3-1}.\dfrac{3^3+1}{3^3-1}....\dfrac{9^3+1}{9^3-1}\)
\(=\dfrac{\left(2+1\right)\left[\left(2-0,5\right)^2+0,75\right]}{\left(2-1\right)\left[\left(2+0,5\right)^2+0,75\right]}.\dfrac{\left(3+1\right)\left[\left(3-0,5\right)^2+0,75\right]}{\left(3-1\right)\left[\left(3+0,5\right)^2+0,75\right]}...\dfrac{\left(9+1\right)\left[\left(9-0,5\right)^2+0,75\right]}{\left(9-1\right)\left[\left(9+0,5\right)^2+0,75\right]}\)
\(=\dfrac{3\left(1,5^2+0,75\right)}{\left(2,5^2+0,75\right)}.\dfrac{4\left(2,5^2+0,75\right)}{2\left(3,5^2+0,75\right)}...\dfrac{10\left(8,5^2+0,75\right)}{8\left(9,5^2+0,75\right)}\)
\(=\dfrac{3.4....10}{1.2.....8}.\dfrac{1,5^2+0,75}{9,5^2+0,75}\)
\(=\dfrac{9.10}{2}.\dfrac{3}{91}\)
\(=\dfrac{3}{2}.\dfrac{90}{91}< \dfrac{3}{2}\)
\(\Rightarrowđpcm\)
b) Làm tương tự
KV
30 tháng 10 2023
a) 11/24 - 5/41 + 13/24 + 0,5 - 36/41
= (11/24 + 13/24) - (5/41 + 36/41) + 0,5
= 1 - 1 + 0,5
= 0,5
b) 1/2 . 3/4 + 1/2 . 1/4 + 1/2
= 1/2 . (3/4 + 1/4) + 1/2
= 1/2 . 1 + 1/2
= 1/2 + 1/2
= 1
c) (-3/4)² : (-1/4)² + 9 . (-1/9) + (-3/2)
= 9/16 : 1/16 - 1 - 3/2
= 9 - 1 - 3/2
= 8 - 3/2
= 13/2
d) √0,25 . (-3)³ - √(1/81) : (-1/3)³
= 1/2 . (-27) - 1/9 : (-1/27)
= -27/2 + 3
= -21/2
QH
27 tháng 11 2017
1. \(A=\dfrac{2\left(\dfrac{1}{5}+\dfrac{1}{7}-\dfrac{1}{9}-\dfrac{1}{11}\right)}{4\left(\dfrac{1}{5}+\dfrac{1}{7}-\dfrac{1}{9}-\dfrac{1}{11}\right)}=\dfrac{2}{4}=\dfrac{1}{2}\)
2. \(B=\dfrac{1^2.2^2.3^2.4^2}{1.2^2.3^2.4^2.5}=\dfrac{1}{5}\)
3.\(C=\dfrac{2^2.3^2.\text{4^2.5^2}.5^2}{1.2^2.3^2.4^2.5.6^2}=\dfrac{125}{36}\)
4.D=\(D=\left(\dfrac{4}{5}-\dfrac{1}{6}\right).\dfrac{4}{9}.\dfrac{1}{16}=\dfrac{19}{30}.\dfrac{1}{36}=\dfrac{19}{1080}\)
\(a.\)
\(-\dfrac{2}{3}\cdot\dfrac{?}{4}=\dfrac{1}{2}\)
\(\Leftrightarrow\dfrac{?}{4}=\dfrac{1}{2}:-\dfrac{2}{3}=\dfrac{1}{2}\cdot-\dfrac{3}{2}=-\dfrac{3}{4}\)
\(\Leftrightarrow?=-3\)
\(b.\)
\(\dfrac{?}{3}\cdot\dfrac{5}{8}=-\dfrac{5}{12}\)
\(\Leftrightarrow\dfrac{?}{3}=\dfrac{-5}{12}:\dfrac{5}{8}=\dfrac{-5}{12}\cdot\dfrac{8}{5}=-\dfrac{2}{3}\)
\(\Leftrightarrow?=-2\)
\(c.\)
\(\dfrac{5}{6}\cdot\dfrac{3}{?}=\dfrac{1}{4}\)
\(\Leftrightarrow\dfrac{3}{?}=\dfrac{1}{4}:\dfrac{5}{6}=\dfrac{1}{4}\cdot\dfrac{6}{5}=\dfrac{3}{10}\)
\(\Leftrightarrow?=10\)
Mk gọi ? = x nha
a) \(\dfrac{-2}{3}.\dfrac{x}{4}=\dfrac{1}{2}\)
\(\dfrac{x}{4}=\dfrac{1}{2}:\dfrac{-2}{3}\)
\(\dfrac{x}{4}=\dfrac{-3}{4}\)
⇒x=-3
b)\(\dfrac{x}{3}.\dfrac{5}{8}=\dfrac{-5}{12}\)
\(\dfrac{x}{3}=\dfrac{-5}{12}:\dfrac{5}{8}\)
\(\dfrac{x}{3}=\dfrac{-2}{3}\)
⇒x=-2
c)\(\dfrac{5}{6}.\dfrac{3}{x}=\dfrac{1}{4}\)
\(\dfrac{3}{x}=\dfrac{1}{4}:\dfrac{5}{6}\)
\(\dfrac{3}{x}=\dfrac{3}{10}\)
⇒x=10