Answer :

Sure, let's go through this step-by-step.

The initial equation is:

[tex]\[ 6 \frac{4}{5} \div y = 8 \frac{1}{2} \][/tex]

First, let's convert the mixed numbers into improper fractions:

[tex]\[ 6 \frac{4}{5} = 6 + \frac{4}{5} = \frac{30}{5} + \frac{4}{5} = \frac{34}{5} \][/tex]

[tex]\[ 8 \frac{1}{2} = 8 + \frac{1}{2} = \frac{16}{2} + \frac{1}{2} = \frac{17}{2} \][/tex]

So the equation now looks like this:

[tex]\[ \frac{34}{5} \div y = \frac{17}{2} \][/tex]

When we divide fractions, we multiply by the reciprocal. Therefore:

[tex]\[ \frac{34}{5} \times \frac{1}{y} = \frac{17}{2} \][/tex]

Let's solve for [tex]\( y \)[/tex]:

[tex]\[ \frac{34}{5} \times \frac{1}{y} = \frac{17}{2} \][/tex]

We rearrange to isolate [tex]\( y \)[/tex]:

[tex]\[ \frac{34}{5} = \frac{17}{2} \times y \][/tex]

Multiply both sides by [tex]\( \frac{2}{17} \)[/tex]:

[tex]\[ y = \frac{34}{5} \times \frac{2}{17} \][/tex]

Let's simplify this:

[tex]\[ y = \frac{34 \times 2}{5 \times 17} = \frac{68}{85} \][/tex]

Simplify the fraction [tex]\( \frac{68}{85} \)[/tex]:

If you divide both the numerator and the denominator by their greatest common divisor, which is 17:

[tex]\[ \frac{68 \div 17}{85 \div 17} = \frac{4}{5} \approx 0.8 \][/tex]

Thus, the value of [tex]\( y \)[/tex] is approximately 0.8.