Alright, let's solve the problem step-by-step.
### Step 1: Calculate Each Fraction
First, we need to multiply the fractions individually:
1. For the first expression:
[tex]\[
\frac{1}{10} \cdot \frac{3}{7} = \frac{1 \times 3}{10 \times 7} = \frac{3}{70}
\][/tex]
2. For the second expression:
[tex]\[
\frac{1}{4} \cdot \frac{5}{14} = \frac{1 \times 5}{4 \times 14} = \frac{5}{56}
\][/tex]
### Step 2: Convert Fractions to Decimal Form for Easier Comparison
Now, let's convert these fractions into decimal form to facilitate comparison:
1. For [tex]\(\frac{3}{70}\)[/tex]:
[tex]\[
\frac{3}{70} \approx 0.042857142857142864
\][/tex]
2. For [tex]\(\frac{5}{56}\)[/tex]:
[tex]\[
\frac{5}{56} \approx 0.08928571428571429
\][/tex]
### Step 3: Compare and Arrange the Decimals
Next, we will compare the decimal values and arrange them in decreasing order:
- [tex]\(\frac{5}{56} \approx 0.08928571428571429\)[/tex]
- [tex]\(\frac{3}{70} \approx 0.042857142857142864\)[/tex]
Clearly, [tex]\(0.08928571428571429\)[/tex] is greater than [tex]\(0.042857142857142864\)[/tex].
### Step 4: Write the Final Answer in Decreasing Order
Thus, the required arrangement of the fractions in decreasing order is:
[tex]\[
\frac{1}{4} \cdot \frac{5}{14}, \quad \frac{1}{10} \cdot \frac{3}{7}
\][/tex]
So, the fractions in decreasing order are:
[tex]\[
\frac{5}{56}, \quad \frac{3}{70}
\][/tex]
This is the correct arrangement of the given fractions in decreasing order.
