To solve the problem of arranging the given expression in ascending order, we should first simplify the expression step-by-step to find the final product of the given fractions.
Let's consider the fractions we need to multiply:
[tex]\[
\frac{2}{3}, \, \frac{1}{4}, \, \frac{5}{6}, \, \frac{3}{8}
\][/tex]
1. Step 1: Multiply all the numerators together to get the numerator of the resulting fraction.
[tex]\[
2 \times 1 \times 5 \times 3 = 30
\][/tex]
2. Step 2: Multiply all the denominators together to get the denominator of the resulting fraction.
[tex]\[
3 \times 4 \times 6 \times 8 = 576
\][/tex]
3. Step 3: Write down the product of the fractions obtained:
[tex]\[
\frac{30}{576}
\][/tex]
4. Step 4: Simplify the fraction [tex]\(\frac{30}{576}\)[/tex].
To simplify, we need to find the greatest common divisor (GCD) of the numerator and the denominator and divide both by the GCD:
The GCD of 30 and 576 is 6.
[tex]\[
\frac{30 \div 6}{576 \div 6} = \frac{5}{96}
\][/tex]
Therefore, the product of the given fractions is:
[tex]\[
\frac{5}{96}
\][/tex]
5. Step 5: Convert the simplified fraction into decimal form to clearly compare it.
[tex]\[
\frac{5}{96} \approx 0.052083333333333336
\][/tex]
6. Step 6: Arrange the result (since it's alone) in ascending order.
When arranged, the result is:
[tex]\[
[0.052083333333333336]
\][/tex]
