Let's break down and solve the given problem step by step.
### Addition of Fractions
First, we have the task of adding [tex]\(\frac{3}{5}\)[/tex] and [tex]\(\frac{4}{5}\)[/tex].
1. Identify the Fractions:
- First term: [tex]\(\frac{3}{5}\)[/tex]
- Second term: [tex]\(\frac{4}{5}\)[/tex]
2. Check the Denominator:
Since both fractions have the same denominator, we can add the numerators directly.
3. Add the Numerators:
[tex]\[
3 + 4 = 7
\][/tex]
4. Keep the Same Denominator:
[tex]\[
\frac{3}{5} + \frac{4}{5} = \frac{7}{5}
\][/tex]
5. Convert the Fraction to a Decimal:
[tex]\[
\frac{7}{5} = 1.4
\][/tex]
So, the result of the addition is [tex]\(\frac{7}{5}\)[/tex] or [tex]\(1.4\)[/tex].
### Multiplication of Fractions
Next, we need to multiply [tex]\(\frac{3}{5}\)[/tex] by [tex]\(\frac{7}{3}\)[/tex].
1. Identify the Fractions:
- First fraction: [tex]\(\frac{3}{5}\)[/tex]
- Second fraction: [tex]\(\frac{7}{3}\)[/tex]
2. Multiply the Numerators:
[tex]\[
3 \times 7 = 21
\][/tex]
3. Multiply the Denominators:
[tex]\[
5 \times 3 = 15
\][/tex]
4. Form the Product Fraction:
[tex]\[
\frac{3}{5} \times \frac{7}{3} = \frac{21}{15}
\][/tex]
5. Simplify the Fraction:
To simplify [tex]\(\frac{21}{15}\)[/tex], we can divide both the numerator and the denominator by their greatest common divisor. However, [tex]\(\frac{21}{15}\)[/tex] already simplified to its simplest form, but for easier understanding:
[tex]\[
21 \div 3 = 7, \quad 15 \div 3 = 5
\][/tex]
Thus, [tex]\(\frac{21}{15} = \frac{7}{5}\)[/tex]
6. Convert the Fraction to a Decimal:
[tex]\[
\frac{21}{15} = 1.4
\][/tex]
So, the result of the multiplication is [tex]\(\frac{21}{15}\)[/tex] or [tex]\(1.4\)[/tex].
### Summary of Results
- The result of the addition is: [tex]\(\frac{7}{5}\)[/tex] or [tex]\(1.4\)[/tex].
- The result of the multiplication is: [tex]\(\frac{21}{15}\)[/tex] or [tex]\(1.4\)[/tex].
To summarize:
- The addition result is [tex]\(1.4\)[/tex].
- The multiplication result is [tex]\(1.4\)[/tex].
- The numerators and denominators of the intermediate results are:
- Addition: Numerator = 7, Denominator = 5
- Multiplication: Numerator = 21, Denominator = 15
