a: \(\dfrac{16}{5}\cdot\dfrac{5}{6}-\left(\dfrac{3}{5}+\dfrac{1}{3}\right):2\)

\(=\dfrac{16}{6}-\dfrac{9+5}{15}:2\)

\(=\dfrac{8}{3}-\dfrac{14}{30}=\dfrac{8}{3}-\dfrac{7}{15}\)\(=\dfrac{40}{15}-\dfrac{7}{15}=\dfrac{33}{15}=\dfrac{11}{5}\)

b: \(\dfrac{7}{19}\cdot\dfrac{8}{11}+\dfrac{7}{19}:\dfrac{11}{3}+\dfrac{12}{19}\)

\(=\dfrac{7}{19}\cdot\dfrac{8}{11}+\dfrac{7}{19}\cdot\dfrac{3}{11}+\dfrac{12}{19}\)

\(=\dfrac{7}{19}\left(\dfrac{8}{11}+\dfrac{3}{11}\right)+\dfrac{12}{19}=\dfrac{7}{19}+\dfrac{12}{19}=\dfrac{19}{19}=1\)

c: \(\left(-\dfrac{2}{5}\right)^2+\dfrac{1}{2}\left(4,5-2\right)-25\%\)

\(=\dfrac{4}{25}+\dfrac{1}{2}\cdot2,5-0,25\)

\(=\dfrac{4}{25}+1,25-0,25=\dfrac{4}{25}+1=\dfrac{29}{25}\)

d: \(\left(2,07+3,005\right)-\left(12,005-4,23\right)\)

\(=2,07+3,005-12,005+4,23\)

=6,3-9

=-2,7

-14/13 nhé bạn

4/-13 hay -4/13 nhe

bài 1:

1: \(A=-5^{22}-\left\{-222-\left[-122-\left(100-5^{22}\right)+2022\right]\right\}\)

\(=-5^{22}+222+\left[-122-100+5^{22}+2022\right]\)

\(=-5^{22}+222-122-100+5^{22}+2022=2022\)

2: Đặt \(N=4^{2022}+4^{2021}+...+4+1\)

=>\(4N=4^{2023}+4^{2022}+...+4^2+4\)

=>\(4N-N=4^{2023}+4^{2022}+...+4^2+4-4^{2022}-4^{2021}-...-4^2-4-1\)

=>\(3N=4^{2023}-1\)

\(M=75\left(4^{2022}+4^{2021}+...+4^2+4+1\right)+25\)

\(=25\cdot3N+25=25\left(3N+1\right)=25\cdot4^{2023}\)

\(=100\cdot4^{2021}⋮100\)

2: 

TH1: p=5

p+6=11; p+18=23; p+12=17; p+24=29

=>Nhận

TH2: p=5k+1

p+24=5k+1+24=5(k+5) chia hết cho 5

=>Loại

TH3: p=5k+2

p+18=5k+2+18=5k+20=5(k+4) chia hết cho 5

=>Loại

TH4: p=5k+3

p+12=5k+3+12=5k+15=5(k+3) chia hết cho 5

=>Loại

TH5: p=5k+4

p+6=5k+4+6=5k+10=5(k+2) chia hết cho 5

=>Loại

Bà Lan lãi số tiền là :

400 000 000 :100x5=20 000 000 (đồng)

Sau 1 năm , bà nhận được là :

400 000 000 +20 000 000 = 420 000 000 đồng

                     Giải:

Số tiền bà nhận được cả gốc lẫn lãi sau một năm chiếm số phần trăm là: 

          100% + 5% = 105% 

Sau một năm cả gốc lẫn lãi bà nhận được số tiền cả gốc lẫn lãi là:

        400 000 000  x 105 : 100 =  420 000 000 (đồng)

Đáp số:.. 

\(-0,48=\dfrac{-48}{100}=\dfrac{-12}{25}\)

`-0,48 = -48/100 = -12/25.`

Lời giải:

$-S=\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}$

$-S=\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}$

$-S=\frac{5-4}{4.5}+\frac{6-5}{5.6}+\frac{7-6}{6.7}+\frac{8-7}{7.8}+\frac{9-8}{8.9}+\frac{10-9}{9.10}$

$-S=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}$

$-S=\frac{1}{4}-\frac{1}{10}=\frac{3}{20}$

$S=\frac{-3}{20}$

\(S=\dfrac{-1}{20}+\dfrac{-1}{30}+\dfrac{-1}{40}+\dfrac{-1}{50}+\dfrac{-1}{60}+\dfrac{-1}{70}+\dfrac{-1}{80}+\dfrac{-1}{90}\)

\(S=\dfrac{-1}{90}+\left(\dfrac{-1}{20}+\dfrac{-1}{30}+\dfrac{-1}{40}+\dfrac{-1}{50}+\dfrac{-1}{60}+\dfrac{-1}{70}+\dfrac{-1}{80}\right)\)

\(S=\dfrac{-1}{90}+\left(\dfrac{-1}{2.10}+\dfrac{-1}{3.10}+\dfrac{-1}{4.10}+\dfrac{-1}{5.10}+\dfrac{-1}{6.10}+\dfrac{-1}{7.10}+\dfrac{-1}{8.10}\right)\)

\(S=\dfrac{-1}{90}+\left(\dfrac{-1}{2}-\dfrac{-1}{10}+\dfrac{-1}{3}-\dfrac{-1}{10}+\dfrac{-1}{4}+\dfrac{-1}{5}-\dfrac{-1}{10}+\dfrac{-1}{6}-\dfrac{-1}{10}+\dfrac{-1}{7}-\dfrac{-1}{10}+\dfrac{-1}{8}-\dfrac{-1}{10}\right)\)\(S=\dfrac{-1}{90}+\left(\dfrac{-1}{2}+\dfrac{-1}{3}+\dfrac{-1}{4}+\dfrac{-1}{5}+\dfrac{-1}{6}+\dfrac{-1}{7}+\dfrac{-1}{8}\right)\)

\(B=\dfrac{1}{2^2}-\dfrac{1}{3^2}+\dfrac{1}{3^2}-\dfrac{1}{4^2}+...+\dfrac{1}{9^2}-\dfrac{1}{10^2}\)
\(B=\dfrac{1}{4}-\dfrac{1}{100}=\dfrac{6}{25}\)

\(A=-\dfrac{1}{1.2}-\dfrac{1}{2.3}-...-\dfrac{1}{49.50}\)
\(=-\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{49.50}\right)\)
\(=-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{49}-\dfrac{1}{50}\right)\)
\(=-\left(1-\dfrac{1}{50}\right)\)
\(=-\dfrac{49}{50}\)

nhanh thế