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\(\frac{8}{19}< \frac{16}{?}< \frac{8}{18}\)
\(\Leftrightarrow\frac{16}{38}< \frac{16}{?}< \frac{16}{36}\)
Từ đây dễ thấy ? = 37
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1+2-3-4+5+6-7-8+9+10-11-12+13+14....................+301+302
=1+(2-3-4+5)+(6-7-8+9)+(10-11-12+13)+...................+(298-299-300+301)+302
=1+302
=303
1 + 2 - 3 - 4 + 5 + 6 - 7 - 8 + 9 + 10 - 11 - 12 + 13 + 14 + ... + 301 + 302
= (1 + 2 - 3 - 4) + (5 + 6 - 7 - 8) + (9 + 10 - 11 - 12) + ... + (297 + 298 - 299 - 300) + 301 + 302
= -4 - 4 - 4 - ... - 4 + 301 + 302
= -(4 + 4 + ... + 4) + 603
= -300 + 603 = 303
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\(\frac{4}{3}:\frac{5}{4}:\frac{6}{5}:\frac{7}{6}:\frac{8}{7}:\frac{9}{8}\)
=\(\frac{4}{3}\times\frac{4}{5}\times\frac{5}{6}\times\frac{6}{7}\times\frac{7}{8}\times\frac{8}{9}\)
=\(\frac{16}{27}\)
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\(\frac{6\cdot35\cdot24}{7\cdot18\cdot96}=\frac{6\cdot7\cdot5\cdot24}{7\cdot6\cdot3\cdot24\cdot4}=\frac{5}{12}\)
Chọn a
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1. a
\(\dfrac{8}{5}-\dfrac{5}{6}\cdot\dfrac{3}{4}\)
\(=\dfrac{8}{5}-\dfrac{5\cdot3}{3\cdot2\cdot4}\)
\(=\dfrac{8}{5}-\dfrac{5}{8}=\dfrac{39}{40}\)
1.b
\(=\dfrac{7}{8}+\dfrac{5}{6}\cdot\dfrac{3}{2}\)
\(=\dfrac{7}{8}+\dfrac{5\cdot3}{3\cdot2\cdot2}\)
\(=\dfrac{7}{8}+\dfrac{5}{4}=\dfrac{17}{8}\)
2.a
\(\dfrac{4}{5}+x=\dfrac{11}{10}\)
\(x=\dfrac{11}{10}-\dfrac{4}{5}=\dfrac{3}{10}\)
2.b
\(x-\dfrac{3}{4}=\dfrac{5}{7}\)
\(x=\dfrac{5}{7}+\dfrac{3}{4}=\dfrac{41}{28}\)
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Câu 1 bạn làm vậy đúng rồi
Câu 2
ab x 8 +ab = 2ab
abx8 = 2ab-ab
abx8 =200
ab = 200 : 8
ab = 25
câu 2 này:
ab x 8 + ab =2ab
ab x 8 =2ab-ab
ab x 8 =200
ab =200:8
ab = 25
Vậy ab bằng 25 thử lại 25 x 8 +25=225 (đúng)
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\(\frac{5}{6}+\frac{7}{9}:\frac{5}{6}-\frac{1}{6}\)
\(=\left(\frac{5}{6}-\frac{1}{6}\right)+\frac{7}{9}.\frac{6}{5}\)
\(=\frac{2}{3}+\frac{14}{15}\)
\(=\frac{10}{15}+\frac{14}{15}=\frac{24}{15}\)
\(\frac{8}{11}.\frac{7}{8}+\frac{8}{11}:\frac{4}{5}\)
\(=\frac{7}{11}+\frac{8}{11}.\frac{5}{4}\)
\(=\frac{7}{11}+\frac{10}{11}\)
\(=\frac{17}{11}\)
\(\frac{5}{6}+\frac{7}{9}:\frac{5}{6}-\frac{1}{6}\) \(\frac{8}{11}x\frac{7}{8}+\frac{8}{11}:\frac{4}{5}\)
\(=\frac{5}{6}+\frac{14}{15}-\frac{1}{6}\) \(=\frac{8}{11}x\frac{7}{8}+\frac{8}{11}x\frac{5}{4}\)
\(=\left(\frac{5}{6}-\frac{1}{6}\right)+\frac{14}{15}\) \(=\frac{8}{11}x\left(\frac{7}{8}+\frac{5}{4}\right)\)
\(=\frac{2}{3}+\frac{14}{15}\) \(=\frac{8}{11}x\frac{17}{8}\)
\(=\frac{8}{5}\) \(=\frac{17}{11}\)
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1.3.77−1+3.7.99−3+7.9.1313−7+9.13.1515−9+\frac{19-13}{13.15.19}+13.15.1919−13
=\frac{1}{1.3}-\frac{1}{3.7}+\frac{1}{3.7}-\frac{1}{7.9}+\frac{1}{7.9}-\frac{1}{9.13}+\frac{1}{9.13}-\frac{1}{13.15}+\frac{1}{13.15}-\frac{1}{15.19}=1.31−3.71+3.71−7.91+7.91−9.131+9.131−13.151+13.151−15.191
=\frac{1}{1.3}-\frac{1}{15.19}=\frac{95}{285}-\frac{1}{285}=\frac{94}{285}=1.31−15.191=28595−2851=28594
b,=\frac{1}{6}.\left(\frac{6}{1.3.7}+\frac{6}{3.7.9}+\frac{6}{7.9.13}+\frac{6}{9.13.15}+\frac{6}{13.15.19}\right)b,=61.(1.3.76+3.7.96+7.9.136+9.13.156+13.15.196)
làm giống như trên
c,=\frac{1}{8}.\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{48.49.50}\right)c,=81.(1.2.31+2.3.41+3.4.51+...+48.49.501)
=\frac{1}{16}.\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{48.49.50}\right)=161.(1.2.32+2.3.42+3.4.52+...+48.49.502)
=\frac{1}{16}.\left(\frac{3-1}{1.2.3}+\frac{4-2}{2.3.4}+\frac{5-3}{3.4.5}+...+\frac{50-48}{48.49.50}\right)=161.(1.2.33−1+2.3.44−2+3.4.55−3+...+48.49.5050−48)
=\frac{1}{16}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{48.49}-\frac{1}{49.50}\right)=161.(1.21−2.31+2.31−3.41+3.41−4.51+...+48.491−49.501)
=\frac{1}{16}.\left(\frac{1}{2}-\frac{1}{2450}\right)=\frac{1}{16}.\left(\frac{1225}{2450}-\frac{1}{2450}\right)=\frac{153}{4900}=161.(21−24501)=161.(24501225−24501)=4900153
d,=\frac{5}{7}.\left(\frac{7}{1.5.8}+\frac{7}{5.8.12}+\frac{7}{8.12.15}+...+\frac{7}{33.36.40}\right)d,=75.(1.5.87+5.8.127+8.12.157+...+33.36.407)
=\frac{5}{7}.\left(\frac{8-1}{1.5.8}+\frac{12-5}{5.8.12}+\frac{15-8}{8.12.15}+...+\frac{40-33}{33.36.40}\right)=75.(1.5.88−1+5.8.1212−5+8.12.1515−8+...+33.36.4040−33)
=\frac{5}{7}.\left(\frac{1}{1.5}-\frac{1}{5.8}+\frac{1}{5.8}-\frac{1}{8.12}+\frac{1}{8.12}-\frac{1}{12.15}+...+\frac{1}{33.36}-\frac{1}{36.40}\right)=75.(1.51−5.81+5.81−8.121+8.121−12.151+...+33.361−36.401)
=\frac{5}{7}.\left(\frac{1}{5}-\frac{1}{1440}\right)=\frac{5}{7}.\left(\frac{288}{1440}-\frac{1}{1440}\right)=\frac{41}{288}=75.(51−14401)=75.(1440288−14401)=28841
P/S: . là nhân nha
Gọi số ở chỗ trống đó là x
\(\dfrac{6}{8}< \dfrac{x}{18}< \dfrac{7}{8}\)
\(\dfrac{6\times9}{8\times9}< \dfrac{4\times x}{18\times4}< \dfrac{7\times9}{8\times9}\)
\(\dfrac{54}{72}< \dfrac{4\times x}{72}< \dfrac{63}{72}\)
\(54< 4\times x< 63\)
\(52< 4\times x< 60\)
\(\dfrac{52}{4}< x< \dfrac{60}{4}\)
\(13< x< 15\)
\(x=14\)
Vậy số cần điền vào ... là 14
đáp án là khoảng từ 13.5 đến 15.75