Certainly! Let’s tackle the given problem step-by-step.
We need to evaluate the expression:
[tex]\[ \frac{7}{5} \times \frac{33}{10} + \frac{1}{5} \times \frac{3}{10} \][/tex]
### Step 1: Multiply the Fractions
First, we multiply the fractions [tex]\(\frac{7}{5}\)[/tex] and [tex]\(\frac{33}{10}\)[/tex].
[tex]\[
\frac{7}{5} \times \frac{33}{10} = \frac{7 \times 33}{5 \times 10} = \frac{231}{50}
\][/tex]
Now, let’s convert [tex]\(\frac{231}{50}\)[/tex] to a decimal:
[tex]\[
\frac{231}{50} = 4.62
\][/tex]
Hence, the first term evaluates to approximately:
[tex]\[
\frac{7}{5} \times \frac{33}{10} = 4.62
\][/tex]
### Step 2: Multiply the Second Pair of Fractions
Next, we multiply [tex]\(\frac{1}{5}\)[/tex] and [tex]\(\frac{3}{10}\)[/tex].
[tex]\[
\frac{1}{5} \times \frac{3}{10} = \frac{1 \times 3}{5 \times 10} = \frac{3}{50}
\][/tex]
Convert [tex]\(\frac{3}{50}\)[/tex] to a decimal:
[tex]\[
\frac{3}{50} = 0.06
\][/tex]
Therefore, the second term evaluates to:
[tex]\[
\frac{1}{5} \times \frac{3}{10} = 0.06
\][/tex]
### Step 3: Add the Results
Finally, we add the two results from Step 1 and Step 2:
[tex]\[
4.62 + 0.06 = 4.68
\][/tex]
So, the expression evaluates to:
[tex]\[ \frac{7}{5} \times \frac{33}{10} + \frac{1}{5} \times \frac{3}{10} = 4.68 \][/tex]
Hence, the detailed solution to the given problem is:
[tex]\[ \boxed{4.68} \][/tex]
