Gọi nhà đầu tiên được đánh số nhỏ nhất là \(x\), nhà tiếp theo là \(x+2\), nhà cuối cùng là \(x+38\)

Theo đề bài ra, có:

\(x+x+2+x+4+...+x+38=900\)

\(\Rightarrow20x+2+4+...+38=900\)

\(\Rightarrow20x+\left(2+38\right).19:2=900\)

\(\Rightarrow20x+380=900\)

\(\Rightarrow20x=520\)

\(\Rightarrow x=26\)

Vậy nhà đầu tiên trong dãy phố được đánh là số 26.

Ta có :

 \(\dfrac{1}{2}>\dfrac{1}{5}\)

\(\dfrac{1}{3}>\dfrac{1}{5}\)

\(\dfrac{1}{4}>\dfrac{1}{5}\)

\(\Rightarrow\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}>\dfrac{1}{5}+\dfrac{1}{5}+\dfrac{1}{5}+\dfrac{1}{5}\)

\(\Rightarrow\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}>\dfrac{4}{5}\)

\(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}\)

\(=\dfrac{7}{6}+\dfrac{1}{4}+\dfrac{1}{5}\)

\(=\dfrac{17}{12}+\dfrac{1}{5}\)

\(=\dfrac{97}{60}\)

\(\dfrac{4}{5}=\dfrac{4.12}{5.12}=\dfrac{48}{60}\)

Mà \(\dfrac{97}{60}>\dfrac{48}{60}\)

\(\Rightarrow\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}>\dfrac{4}{5}\left(đpcm\right)\).

a) \(\dfrac{17}{8}:\left(\dfrac{27}{8}+\dfrac{-11}{2}\right)\)

\(=\dfrac{17}{8}.\dfrac{-8}{17}\)

\(=-1\)

b) \(7,63.21,15+7,63.\left(-121,15\right)\)

\(=7,63.\left(21,15-121,15\right)\)

\(=7,63.\left(-100\right)\)

\(=-763\)

c) \(\left(-\dfrac{5}{24}-0,75\right):\left(-2\dfrac{7}{8}\right)\)

\(=\left(-\dfrac{5}{24}-\dfrac{3}{4}\right):\left(-\dfrac{7}{4}\right)\)

\(=\dfrac{-23}{24}.\dfrac{-4}{7}\)

\(=\dfrac{23}{42}\).

\(a.\dfrac{17}{8}:\left(\dfrac{27}{8}+\dfrac{-11}{2}\right)\text{=}\dfrac{17}{8}:\dfrac{-17}{8}\text{=}-1\)

\(b.7,63.21,15+7,63.-121,15\text{=}7,63.\left(21,15-121,15\right)\text{=}7,63.-100\text{=}-763\)

\(c.\left(\dfrac{-5}{24}-0,75\right):\dfrac{-23}{8}\text{=}\dfrac{-23}{24}.\dfrac{-8}{23}\text{=}\dfrac{1}{3}\)

\(1-\dfrac{13}{9}:\dfrac{8}{19}+-\dfrac{11}{9}:\dfrac{8}{9}\)
\(=1-\dfrac{13}{9}.\dfrac{19}{8}-\dfrac{11}{9}.\dfrac{9}{8}\)
\(=1-\dfrac{247}{72}-\dfrac{11}{8}\)
\(=\dfrac{72}{72}-\dfrac{247}{72}-\dfrac{99}{72}\)
\(-\dfrac{137}{36}\)

( 3/8 - x ) + 2\(\dfrac{1}{3}\) : 4/3 = 75%

( 3/8 - x) + 7/3 x 3/4 = 75/100

( 3/8 - x) + 7/4 = 3/4

3/8 -  x = 3/4 - 7/4

3/8 - x = -1

         x = 3/8 + 1

         x = 11/8 

-15 

\(A=\dfrac{1}{101}+\dfrac{2}{101}+\dfrac{3}{101}+...+\dfrac{99}{101}+\dfrac{100}{101}\)
\(=\dfrac{1+2+3+...+99+100}{101}\)
Đặt \(B=1+2+3+...+99+100\)
Số số hạng của B là:
\(\left(100-1\right):1+1=100\left(số\right)\)
Tổng của B:
\(\dfrac{\left(1+100\right)\times100}{2}=5050\)
\(\Rightarrow A=\dfrac{1+2+3+...+99+100}{101}\)
\(=\dfrac{B}{101}\)
\(=\dfrac{5050}{101}=50\)
Vậy \(A=50\)

50

a) c1 := -2/-5+-5/-6+4/5

=2/5+5/6+4/5

=12/30+25/30+24/30

=61/30

c2:=(2/5+4/5)+4/5

=(2/5+4/5)+5/6

=6/5+5/6

=36/30+25/30

=61/30

b)c1:=-3/-4+11/-15+-1/2

=3/4+-11/15+-1/2

=45/60+-44/30+-30/60

-29/30

c2:=3/4+(-11/15+-1/2)

=(3/4+-1/2)+-11/15

=(3/4+-2/4)+-11/5

=1/4+-11/15

=15/60+-44/60

=-29/60