Certainly! Let's work through each operation step-by-step to arrive at the final results.
1. First Operation:
[tex]\(\frac{6}{2} : \frac{4}{5}\)[/tex]
This translates to:
[tex]\[
\frac{\frac{6}{2}}{\frac{4}{5}} = \frac{6}{2} \times \frac{5}{4}
\][/tex]
Simplifying [tex]\(\frac{6}{2}\)[/tex] gives [tex]\(3\)[/tex]:
[tex]\[
\frac{6}{2} = 3
\][/tex]
Now, multiply:
[tex]\[
3 \times \frac{5}{4} = \frac{3 \times 5}{4} = \frac{15}{4} = 3.75
\][/tex]
2. Second Operation:
[tex]\(\frac{3}{4} : \frac{3}{5}\)[/tex]
This translates to:
[tex]\[
\frac{\frac{3}{4}}{\frac{3}{5}} = \frac{3}{4} \times \frac{5}{3}
\][/tex]
Simplify [tex]\(\frac{3}{3}\)[/tex]:
[tex]\[
\frac{3 \times 5}{4 \times 3} = \frac{15}{12} = \frac{5}{4} = 1.25
\][/tex]
3. Third Operation:
[tex]\(\frac{6}{2} \times \frac{3}{6}\)[/tex]
Simplifying each fraction:
[tex]\[
\frac{6}{2} = 3 \quad \text{and} \quad \frac{3}{6} = \frac{1}{2}
\][/tex]
Now, multiply:
[tex]\[
3 \times \frac{1}{2} = \frac{3 \times 1}{1 \times 2} = \frac{3}{2} = 1.5
\][/tex]
4. Fourth Operation:
[tex]\(\frac{5}{6} : \frac{5}{2}\)[/tex]
This translates to:
[tex]\[
\frac{\frac{5}{6}}{\frac{5}{2}} = \frac{5}{6} \times \frac{2}{5}
\][/tex]
Simplify [tex]\(\frac{5}{5}\)[/tex]:
[tex]\[
\frac{5 \times 2}{6 \times 5} = \frac{10}{30} = \frac{1}{3} = 0.3333333333333333\overline{3}
\][/tex]
So, the results of the operations are:
1. [tex]\(\frac{6}{2} : \frac{4}{5} = 3.75\)[/tex]
2. [tex]\(\frac{3}{4} : \frac{3}{5} = 1.25\)[/tex]
3. [tex]\(\frac{6}{2} \times \frac{3}{6} = 1.5\)[/tex]
4. [tex]\(\frac{5}{6} : \frac{5}{2} = 0.33333333333333337\)[/tex]
These are the final answers.
