Question

[Nguyễn Đức Trường]

Bài 1 : Thực hiện phép tính :

a, \(\frac{4}{5}+1\frac{1}{6}\cdot\frac{3}{4}\)

b, \(\frac{2}{3}:(\frac{3}{4}\cdot\frac{4}{3})+\text{2}\)

c, \(\frac{1}{2}\cdot\left(\frac{2}{3}+\frac{3}{5}\cdot\frac{3}{7}\right)+1\frac{1}{3}\)

Bài 2 : Tìm \(x\inℤ\), biết :

a, \(\frac{2}{3}< \frac{x}{6}\le\frac{10}{3}\)

b, \(\frac{1}{3}+x=1\frac{1}{\text{2}}\)

c, \(\frac{1}{7}+x=\frac{25}{14}+\frac{5}{14}\)

Answer 1

[Hn . never die !]

Bài 1 : Thực hiện phép tính :

a, \(\frac{4}{5}+1\frac{1}{6}\cdot\frac{3}{4}\)

= \(\frac{4}{5}+\frac{7}{6}\cdot\frac{3}{4}\)

= \(\frac{4}{5}+\frac{7}{8}\)

= \(\frac{32+35}{40}=\frac{67}{40}\)

b, \(\frac{2}{3}:\left(\frac{3}{4}\cdot\frac{4}{3}\right)+2\)

\(=\frac{2}{3}:1+2\)

\(=\frac{2}{3}+2=\frac{2+6}{3}=\frac{8}{3}\)

c, \(\frac{1}{2}\times\left(\frac{2}{3}+\frac{3}{5}\cdot\frac{5}{7}\right)+1\frac{1}{3}\)

\(=\frac{1}{2}\cdot\left(\frac{2}{3}+\frac{9}{35}\right)+\frac{4}{3}\)

\(=\frac{1}{2}\cdot\frac{97}{105}+\frac{4}{3}\)

\(=\frac{97}{210}+\frac{4}{3}=\frac{377}{210}\)

Bài 2 : Tìm \(x\inℤ\), biết :

a, \(\frac{2}{3}< \frac{x}{6}\le\frac{10}{3}\)

\(\Leftrightarrow\frac{4}{6}< \frac{x}{6}\le\frac{20}{6}\)

mà \(x\inℤ\Rightarrow\text{x}\in\) {\(5;6;7;8;9;10;11;12;13;14;15;16;17;18;19;20\)}

b, \(\frac{1}{3}+x=1\frac{1}{2}\)

\(\frac{1}{3}+x=\frac{3}{2}\)

\(x=\frac{3}{2}+\frac{\left(-1\right)}{3}\)

\(x=\frac{7}{6}\) (loại vì \(x\notinℤ\))

\(\Rightarrow x\in\varnothing\)

c, \(\frac{1}{7}+x=\frac{25}{14}+\frac{5}{14}\)

\(\frac{1}{7}+x=\frac{15}{7}\)

\(x=\frac{15}{7}+\frac{(-1)}{7}\)

\(x=\frac{14}{7}=2\).