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.
