a) \(-\dfrac{47}{53}=\dfrac{-47\cdot101}{53\cdot101}=\dfrac{-4747}{5353}\)

b)\(\dfrac{-19}{21}< 0\)

\(\dfrac{1}{50}>0\)

\(\Rightarrow-\dfrac{19}{21}< \dfrac{1}{50}\)

c)\(\dfrac{-31\cdot\left(-212\right)}{128\cdot\left(-212\right)}=\dfrac{-6572}{212\cdot128}\)

\(\dfrac{55\cdot128}{128\cdot\left(-212\right)}=\dfrac{-7040}{128\cdot212}\)

\(\Rightarrow\dfrac{-31}{128}>\dfrac{55}{-212}\)

d)

\(\dfrac{23456}{-23457}>-1\)

\(\dfrac{-4321}{4320}< -1\)

\(\Rightarrow\dfrac{23456}{-23457}>\dfrac{-4321}{4320}\)

e)

Học năm lớp 6 , giờ quên rồi :)))

e ) \(A=\dfrac{19^{16}+1}{19^{17}+1};B=\dfrac{19^{15}+1}{19^{16}+1}\)

\(\Rightarrow19A=\dfrac{19^{17}+19}{19^{17}+1}=1+\dfrac{18}{19^{17}+1}\)

\(19B=\dfrac{19^{16}+19}{19^{16}+1}=1+\dfrac{18}{19^{16}+1}\)

Do \(\dfrac{18}{19^{16}+1}>\dfrac{18}{19^{17}+1}\)

\(\Rightarrow1+\dfrac{18}{19^{16}+1}>1+\dfrac{18}{19^{17}+1}\)

\(\Rightarrow19B>19A\)

\(\Rightarrow B>A\)

(x+2)(16-x)=15

=>(x+2;16-x)∈{(1;15);(15;1);(-1;-15);(-15;-1);(3;5);(5;3);(-5;-3);(-3;-5)}

Theo Bảng, ta có: không có giá trị nguyên nào của x thỏa mãn yêu cầu bài toán, hay bài toán chỉ có giá trị thực

(x+2)(16-x)=15

=>\(16x-x^2+_{}32-2x=15\)

=>\(-x^2+14x+17=0\)

=>\(x^2-14x-17=0\)

=>\(x^2-14x+49-66=0\)

=>\(\left(x-7\right)^2=66\)

=>\(\left[\begin{array}{l}x-7=\sqrt{66}\\ x-7=-\sqrt{66}\end{array}\right.\Rightarrow\left[\begin{array}{l}x=\sqrt{66}+7\\ x=-\sqrt{66}+7\end{array}\right.\)

3/ Chu vi hình chữ nhật:

\(\left(\dfrac{1}{4}+\dfrac{3}{10}\right)\cdot2=\dfrac{11}{10}\) (chưa biết đơn vị)

Diện tích hình chữ nhật:

\(\dfrac{1}{4}\cdot\dfrac{3}{10}=\dfrac{11}{20}\) (chưa biết đơn vị)

Đơn vị trong ngoặc ghi là đơn vị diện tích nhá!

Bài 4:

a; \(\dfrac{1}{4}\) - \(\dfrac{1}{5}\) = \(\dfrac{5}{20}\) - \(\dfrac{4}{20}\) = \(\dfrac{1}{20}\)

b; \(\dfrac{3}{5}\) - \(\dfrac{-1}{2}\) = \(\dfrac{6}{10}\) + \(\dfrac{5}{10}\) = \(\dfrac{11}{10}\)

c; \(\dfrac{3}{5}\) - \(\dfrac{-1}{3}\) = \(\dfrac{9}{15}\) + \(\dfrac{5}{15}\) = \(\dfrac{14}{15}\)

d; \(\dfrac{-5}{7}\) - \(\dfrac{1}{3}\)= \(\dfrac{-15}{21}\) - \(\dfrac{7}{21}\)= \(\dfrac{-22}{21}\)

Bài 5

a; 1 + \(\dfrac{3}{4}\) = \(\dfrac{4}{4}\) + \(\dfrac{3}{4}\) = \(\dfrac{7}{4}\)       b; 1 - \(\dfrac{1}{2}\) = \(\dfrac{2}{2}\) - \(\dfrac{1}{2}\) = \(\dfrac{1}{2}\)

c; \(\dfrac{1}{5}\) - 2 = \(\dfrac{1}{5}\) - \(\dfrac{10}{5}\) = \(\dfrac{-9}{5}\)     d; -5 - \(\dfrac{1}{6}\) = \(\dfrac{-30}{6}\) - \(\dfrac{1}{6}\) = \(\dfrac{-31}{6}\)

e; - 3 - \(\dfrac{2}{7}\)= \(\dfrac{-21}{7}\) - \(\dfrac{2}{7}\)= \(\dfrac{-23}{7}\)     f; - 3 + \(\dfrac{2}{5}\) = \(\dfrac{-15}{5}\) + \(\dfrac{2}{5}\)= - \(\dfrac{13}{5}\)

g; - 3 - \(\dfrac{2}{3}\) = \(\dfrac{-9}{3}\) - \(\dfrac{2}{3}\) = \(\dfrac{-11}{3}\)     h; - 4 - \(\dfrac{-5}{7}\) = \(\dfrac{-28}{7}\)+ \(\dfrac{5}{7}\) = - \(\dfrac{23}{7}\)

a)

\(175\cdot19+38\cdot175+43\cdot175\\ =175\cdot19+175\cdot38+175\cdot43\\ =175\cdot\left(19+38+43\right)\\ =175\cdot100\\ =17500\)

b)

\(125\cdot75+125\cdot13-80\cdot125\\ =125\cdot75+125\cdot13-125\cdot80\\ =125\cdot\left(75+13-80\right)\\ =125\cdot10\\ =125\cdot8\\ =1000\)

a, 175. 19 + 38. 175 + 43. 175

= 175. 19 + 175. 38 + 175. 43

= 175.(19 + 38 + 43)

= 175. 100

= 17500