To solve the multiplication of the mixed fractions [tex]\(1 \frac{5}{7} \times 2 \frac{2}{4}\)[/tex], follow these steps:
1. Convert each mixed fraction to an improper fraction:
- For [tex]\(1 \frac{5}{7}\)[/tex]:
[tex]\[
1 \frac{5}{7} = 1 + \frac{5}{7} = \frac{7}{7} + \frac{5}{7} = \frac{12}{7}
\][/tex]
- For [tex]\(2 \frac{2}{4}\)[/tex]:
[tex]\[
2 \frac{2}{4} = 2 + \frac{2}{4} = \frac{8}{4} + \frac{2}{4} = \frac{10}{4}
\][/tex]
2. Multiply the improper fractions:
- Multiply the numerators together:
[tex]\[
12 \times 10 = 120
\][/tex]
- Multiply the denominators together:
[tex]\[
7 \times 4 = 28
\][/tex]
- The result of the multiplication is:
[tex]\[
\frac{120}{28}
\][/tex]
3. Simplify the fraction (if needed):
- In this case, we don't need to simplify further to get the final numerical result.
4. Convert the improper fraction to a decimal:
- Divide the numerator by the denominator to get the decimal form:
[tex]\[
\frac{120}{28} \approx 4.285714285714286
\][/tex]
Therefore, the solution is:
- The numerator and the denominator are [tex]\(120\)[/tex] and [tex]\(28\)[/tex], respectively.
- The result in decimal form is approximately [tex]\(4.285714285714286\)[/tex].
