13/15<.../22<14/15
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\(\dfrac{12}{17}.\dfrac{9}{13}-\dfrac{7}{15}.\dfrac{6}{13}+\dfrac{5}{17}.\dfrac{9}{13}-\dfrac{8}{15}.\dfrac{6}{13}\)
\(=\dfrac{9}{13}.\left(\dfrac{12}{17}+\dfrac{5}{17}\right)-\dfrac{6}{13}.\left(\dfrac{7}{15}+\dfrac{8}{15}\right)\)
\(=\dfrac{9}{13}.\dfrac{17}{17}-\dfrac{6}{13}.\dfrac{15}{15}\)
\(=\dfrac{9}{13}.1-\dfrac{6}{13}.1\)
\(=\dfrac{9}{13}-\dfrac{6}{13}\)
\(=\dfrac{9-6}{13}\)
\(=\dfrac{3}{13}\)
\(\dfrac{11}{15}+\dfrac{7}{13}-\left(\dfrac{13}{15}+\dfrac{7}{13}\right)\)
\(=\dfrac{11}{15}+\dfrac{7}{13}-\dfrac{13}{15}-\dfrac{7}{13}\)
\(=\left(\dfrac{11}{15}-\dfrac{13}{15}\right)+\left(\dfrac{7}{13}-\dfrac{7}{13}\right)\)
\(=\dfrac{-2}{15}+0\)
\(=\dfrac{-2}{15}\)
#DatNe
= 11/15+7/13-13/15+7/13
= (11/15-13/15) + 7/13
= (-2/15)+7/15
= 5/15
= 1/3
\(\dfrac{7}{15};\dfrac{11}{15};\dfrac{13}{15};\dfrac{19}{13};\dfrac{42}{21};\dfrac{30}{13};\dfrac{14}{5};\dfrac{16}{5};5\)
\(\dfrac{5}{13}.\dfrac{8}{15}+\dfrac{5}{13}.\dfrac{26}{15}-\dfrac{5}{13}.\dfrac{8}{15}.\\ =\dfrac{5}{13}.\left(\dfrac{8}{15}+\dfrac{26}{15}-\dfrac{8}{15}\right).\\ =\dfrac{5}{13}.\dfrac{26}{15}=\dfrac{2}{3}.\)
\(\frac{15}{17}x\frac{45}{13}-\frac{15}{17}x\frac{10}{13}-\frac{9}{13}x\frac{15}{17}-\frac{15}{17}\)
\(=\frac{15}{17}x\left(\frac{45}{13}-\frac{10}{13}-\frac{9}{13}-1\right)\\ =\frac{15}{17}x1=\frac{15}{17}\)
\(\frac{15}{17}\times\frac{45}{13}-\frac{15}{17}\times\frac{10}{13}-\frac{9}{13}\times\frac{15}{17}-\frac{15}{17}\)
\(=\frac{15}{17}\times\left(\frac{45}{13}-\frac{10}{13}-\frac{9}{13}-1\right)\)
\(=\frac{15}{17}\times1\)
\(=\frac{15}{17}\)
...=-15-9=-24
...=4+7=11
...=-12-13=-25
...=13+10=23
...=-4-7=-11
...=-9+13=4
...=12+0=12
...=0-7=-7
...=0+3=3
...=15-17=-2
...=-6
...=-23
...=15-15=0
a/\(\dfrac{26}{15}+-\dfrac{7}{13}+-\dfrac{6}{13}-\dfrac{11}{15}\)
\(=\left(\dfrac{26}{15}-\dfrac{11}{15}\right)-\left(\dfrac{7}{13}+\dfrac{6}{13}\right)\)
\(=1-1\)
\(=0\)
b/Sửa đề:
\(-\dfrac{3}{4}\cdot\dfrac{4}{13}+-\dfrac{3}{4}\cdot\dfrac{9}{13}+\dfrac{3}{4}\)
\(=-\dfrac{3}{4}\cdot\left(\dfrac{4}{13}+\dfrac{9}{13}\right)+\dfrac{3}{4}\)
\(=-\dfrac{3}{4}\cdot1+\dfrac{3}{4}\)
\(=-\dfrac{3}{4}+\dfrac{3}{4}\)
\(=0\)
\(\dfrac{13}{15}< \dfrac{x}{22}< \dfrac{14}{15}\\ \dfrac{13\times22}{15\times22}< \dfrac{x\times15}{15\times22}< \dfrac{14\times22}{15\times22}\\ 286< 15\times x< 308\)
Mà x là số tự nhiên
Suy ra : x = 20 ( Vì : 286<300<308 )
Vậy ... cần điền là : 20
Gọi x là số cần tìm
13/15 = 286/330
14/15 = 308/330
286 < x < 308
⇒ x ∈ {287; 288; 289; ...; 306; 307}