Answer:
Exact Form = 25/12
Decimal Form = 2.083
Mixed Number Form = 2 1/12
The solution of ( 9 + 1/6 ) ÷ ( 1.8 + 2 3/5 ) is [tex]\frac{25}{12}[/tex]
Solution:
Given expression is [tex]\left(9+\frac{1}{6}\right) \div\left(1.8+2 \frac{3}{5}\right)[/tex]
We have to simplify it.
Now take the expression,
[tex]\Rightarrow \left(9+\frac{1}{6}\right) \div\left(1.8+2 \frac{3}{5}\right)[/tex]
Converting the mixed fraction [tex]2\frac{3}{5}[/tex] we get,
[tex]\begin{array}{ll}{\rightarrow} & {\left(9+\frac{1}{6}\right) /\left(1.8+\frac{2 \times 5+3}{5}\right)} \\\\ {\rightarrow} & {\left(9+\frac{1}{6}\right) /\left(1.8+\frac{10+3}{5}\right)}\end{array}[/tex]
[tex]\begin{array}{ll}{\rightarrow} & {\left(2+\frac{1}{6}\right) /\left(1.8+\frac{13}{5}\right)} \\\\ {\rightarrow} & {\left(\frac{9 \times 6+1}{6}\right) /\left(\frac{1.8 \times 5+13}{5}\right)}\end{array}[/tex]
[tex]\begin{array}{c}{\rightarrow \quad\left(\frac{54+1}{6}\right) /\left(\frac{9+13}{5}\right)} \\\\ {\rightarrow \frac{55}{6} / \frac{22}{5}}\end{array}[/tex]
[tex]\begin{array}{c}{\Rightarrow \quad \frac{55}{6} \times \frac{5}{22}}\\\\ {\Rightarrow \quad \frac{5}{6} \times \frac{5}{2}}\\\\ {\Rightarrow \quad \frac{25}{12}}\end{array}[/tex]
Hence, the value of the given expression is [tex]\frac{25}{12}[/tex]
