Hỗn số

`a, 11/3 + 1 1/2`

`= (22+9)/6`

`= 31/6`

`b, 31/2 xx 11/7`

`= 341/14`

`c, 32/5 - 11/10`

`= (64-11)/10 = 53/10`

`d, 41/6 : 21/3`

`= 41/6 xx 1/7`

`= 41/42`

\(a,1\dfrac{1}{3}+2\dfrac{1}{2}=\dfrac{4}{3}+\dfrac{5}{2}=\dfrac{23}{6}\)

\(b,3\dfrac{2}{5}-1\dfrac{1}{10}=\dfrac{17}{5}-\dfrac{11}{10}=\dfrac{23}{10}\)

\(c,3\dfrac{1}{2}\times1\dfrac{1}{7}=\dfrac{7}{2}\times\dfrac{8}{7}=4\)

\(d,4\dfrac{1}{6}:2\dfrac{1}{3}=\dfrac{25}{6}:\dfrac{7}{3}=\dfrac{25}{14}\)

\(3\dfrac{2}{5}=\dfrac{3\times5+2}{5}=\dfrac{17}{5}\)                                          \(2\dfrac{4}{9}=\dfrac{2\times9+4}{9}=\dfrac{22}{9}\)
 

\(7\dfrac{3}{8}=\dfrac{7\times8+3}{8}=\dfrac{59}{8}\)                                          \(15\dfrac{1}{10}=\dfrac{15\times10+1}{10}=\dfrac{151}{10}\)

Câu 2 :

\(3\dfrac{2}{5}=\dfrac{3\times5+2}{5}==\dfrac{17}{5}\)

\(2\dfrac{4}{9}=\dfrac{2\times9+4}{9}=\dfrac{22}{9}\)

\(7\dfrac{3}{8}=\dfrac{7\times8+3}{8}=\dfrac{59}{8}\)

\(15\dfrac{1}{10}=\dfrac{15\times10+1}{10}=\dfrac{151}{10}\)

\(3\dfrac{2}{5}=\dfrac{3\times5+2}{5}=\dfrac{17}{5}\)

\(2\dfrac{4}{9}=\dfrac{2\times9+4}{9}=\dfrac{22}{9}\)

\(7\dfrac{3}{8}=\dfrac{7\times8+3}{8}=\dfrac{59}{8}\)

\(15\dfrac{1}{10}=\dfrac{15\times10+1}{10}=\dfrac{151}{10}\)

a: \(=3+\dfrac{1}{2}+2+\dfrac{2}{5}=5+\dfrac{9}{10}=\dfrac{59}{10}\)

s: \(=\dfrac{2}{6}+\dfrac{63}{6}=\dfrac{65}{6}\)

b: \(\dfrac{53}{8}-\dfrac{12}{3}=\dfrac{53}{8}-4=\dfrac{21}{8}\)

`2 1/2`

\(\text{2}\dfrac{\text{1}}{2}\)

\(\dfrac{5}{6}\)

\(4\dfrac{1}{4}+3\dfrac{3}{8}-2\dfrac{1}{3}=\dfrac{17}{4}+\dfrac{28}{8}-\dfrac{7}{3}=\dfrac{102}{24}+\dfrac{84}{24}-\dfrac{56}{24}=\dfrac{130}{24}=\dfrac{65}{12}\)

`4 1/4 + 3 3/8 - 2 1/3`

`= [ (4 + 3 - 2) + ( 1/4 + 3/8 - 1/3)]`

`= 5 + ( 6/24 + 9/24 - 8/24)`

`= 5 + ( ( 6 + 9 -8)/24)`

`= 5 + 7/24`

`=120/24 + 7/24`

`=(120+7)/24`

`=127/24`

\(1\dfrac{1}{5}+1\dfrac{2}{4}=\dfrac{6}{5}+\dfrac{6}{4}=\dfrac{24}{20}+\dfrac{30}{20}=\dfrac{54}{40}\)

Cách chuyển hỗn số thành phân số :

\(1\dfrac{1}{5}=\dfrac{1x5+1}{5}=\dfrac{6}{5}\)

\(1\dfrac{2}{4}=\dfrac{1x4+2}{4}\dfrac{6}{4}\)

\(1\dfrac{1}{5}+1\dfrac{2}{4}=\dfrac{6}{5}+\dfrac{3}{2}=\dfrac{6\times2}{5\times2}+\dfrac{3\times5}{2\times5}=\dfrac{12}{10}+\dfrac{15}{10}=\dfrac{12+15}{10}=\dfrac{27}{10}.\)

\(\left(y+2\dfrac{1}{3}\right)+6\%=\left(2\dfrac{1}{3}+6\%\right)+2019\)

\(\left(y+\dfrac{7}{3}\right)+\dfrac{3}{50}=\left(\dfrac{7}{3}+\dfrac{3}{50}\right)+2019\)

\(\left(y+\dfrac{7}{3}\right)+\dfrac{3}{50}=\dfrac{359}{150}+2019\)

\(\left(y+\dfrac{7}{3}\right)+\dfrac{3}{50}=\dfrac{303209}{150}\)

\(y+\dfrac{7}{3}=\dfrac{303209}{150}-\dfrac{3}{50}\)

\(y+\dfrac{7}{3}=\dfrac{6064}{3}\)

\(y=\dfrac{6064}{3}-\dfrac{7}{3}\)

\(y=2019\)

\(\text{Cách 2}\) \(\left(y+2\dfrac{1}{3}\right)+6\%=\left(2\dfrac{1}{3}+6\%\right)+2019\)

             \(\left(y+\dfrac{7}{3}\right)+\dfrac{3}{50}=\left(\dfrac{7}{3}+\dfrac{3}{50}\right)+2019\)

              \(y+\left(\dfrac{7}{3}+\dfrac{3}{50}\right)=\left(\dfrac{7}{3}+\dfrac{3}{50}\right)+2019\)

              \(y-2019=\left(\dfrac{7}{3}+\dfrac{3}{50}\right)-\left(\dfrac{7}{3}+\dfrac{3}{50}\right)\)

              \(y-2019=0\)

              \(y=0+2019\)

              \(y=2019\)

5/6 - 1/4 = 20/24- 6/24= 14/24 = 7/12

\(\dfrac{5}{6}-\dfrac{1}{4}=\dfrac{20}{24}-\dfrac{6}{24}=\dfrac{14}{24}=\dfrac{7}{12}\)

2/3

\(\dfrac{3}{4}+1\dfrac{5}{6}=\dfrac{3}{4}+\dfrac{11}{6}=\dfrac{9}{12}+\dfrac{22}{12}=\dfrac{31}{12}\)

=3/4+11/6=31/12

3/4 + 11/6= 31/12

\(x-3\dfrac{2}{5}=1\dfrac{1}{5}\)

\(\Leftrightarrow x-\dfrac{17}{5}=\dfrac{6}{5}\)

\(\Leftrightarrow x=\dfrac{6}{5}+\dfrac{17}{5}\)

\(\Leftrightarrow x=\dfrac{23}{5}\)