Sure, let's solve the given problem step-by-step:
Given Expression:
[tex]\[
\left(3 \frac{3}{10} + 5 \frac{19}{20}\right) \cdot \left(\frac{3}{4} + \frac{7}{20}\right)
\][/tex]
First, we need to convert the mixed fractions to improper fractions and then to decimals for simplicity.
1. Convert mixed fractions to improper fractions:
[tex]\[
3 \frac{3}{10} = 3 + \frac{3}{10} = 3.3
\][/tex]
[tex]\[
5 \frac{19}{20} = 5 + \frac{19}{20} = 5.95
\][/tex]
2. Convert the fractions to decimals:
[tex]\[
\frac{3}{4} = 0.75
\][/tex]
[tex]\[
\frac{7}{20} = 0.35
\][/tex]
3. Add the individual fractions:
Add the converted mixed fractions:
[tex]\[
3.3 + 5.95 = 9.25
\][/tex]
Add the simple fractions:
[tex]\[
0.75 + 0.35 = 1.1
\][/tex]
4. Multiply the sums of the fractions:
[tex]\[
9.25 \times 1.1
\][/tex]
5. Multiply the results:
[tex]\[
9.25 \times 1.1 = 10.175
\][/tex]
Therefore, the result of the given expression [tex]\(\left(3 \frac{3}{10} + 5 \frac{19}{20}\right) \cdot\left(\frac{3}{4}+\frac{7}{20}\right)\)[/tex] is:
[tex]\[
10.175
\][/tex]
