Sure, let's go through the process of multiplying these rational numbers step by step.
### a) [tex]\(\frac{4}{7} \times 5\)[/tex]
To multiply a fraction by a whole number, multiply the numerator of the fraction by the whole number and keep the denominator unchanged:
[tex]\[
\frac{4 \times 5}{7} = \frac{20}{7}
\][/tex]
Now, convert this fraction to a decimal:
[tex]\[
\frac{20}{7} \approx 2.857
\][/tex]
### b) [tex]\(\frac{-7}{8} \times \frac{5}{8}\)[/tex]
Multiply the numerators together and the denominators together:
[tex]\[
\frac{-7 \times 5}{8 \times 8} = \frac{-35}{64}
\][/tex]
Now, convert this fraction to a decimal:
[tex]\[
\frac{-35}{64} \approx -0.547
\][/tex]
### c) [tex]\(\frac{9}{2} \times \frac{-7}{4}\)[/tex]
Again, multiply the numerators together and the denominators together:
[tex]\[
\frac{9 \times -7}{2 \times 4} = \frac{-63}{8}
\][/tex]
Now, convert this fraction to a decimal:
[tex]\[
\frac{-63}{8} \approx -7.875
\][/tex]
### d) [tex]\(\frac{2}{3} \times \frac{-5}{9}\)[/tex]
Multiply the numerators together and the denominators together:
[tex]\[
\frac{2 \times -5}{3 \times 9} = \frac{-10}{27}
\][/tex]
Now, convert this fraction to a decimal:
[tex]\[
\frac{-10}{27} \approx -0.370
\][/tex]
### e) [tex]\(\frac{-7}{5} \times (-2)\)[/tex]
To multiply a fraction by a whole number, multiply the numerator of the fraction by the whole number and keep the denominator unchanged. Also, note that multiplying two negative numbers results in a positive number:
[tex]\[
\frac{-7 \times -2}{5} = \frac{14}{5}
\][/tex]
Now, convert this fraction to a decimal:
[tex]\[
\frac{14}{5} \approx 2.8
\][/tex]
So, the detailed step-by-step results are:
a) [tex]\(\frac{4}{7} \times 5 = 2.857\)[/tex]
b) [tex]\(\frac{-7}{8} \times \frac{5}{8} = -0.547\)[/tex]
c) [tex]\(\frac{9}{2} \times \frac{-7}{4} = -7.875\)[/tex]
d) [tex]\(\frac{2}{3} \times \frac{-5}{9} = -0.370\)[/tex]
e) [tex]\(\frac{-7}{5} \times (-2) = 2.8\)[/tex]
