Sure, let's analyze both sides of the given expression to determine if they are equal and understand which property of rational numbers this demonstrates.
### Left Side: [tex]\(\left(\frac{1}{4} \div \frac{1}{7}\right) \div \frac{1}{8}\)[/tex]
1. Simplifying [tex]\(\frac{1}{4} \div \frac{1}{7}\)[/tex]:
[tex]\[
\frac{1}{4} \div \frac{1}{7} = \frac{1}{4} \times \frac{7}{1} = \frac{7}{4}
\][/tex]
2. Now, simplifying [tex]\(\frac{7}{4} \div \frac{1}{8}\)[/tex]:
[tex]\[
\frac{7}{4} \div \frac{1}{8} = \frac{7}{4} \times \frac{8}{1} = \frac{7 \times 8}{4 \times 1} = \frac{56}{4} = 14
\][/tex]
So, the left side simplifies to [tex]\(14\)[/tex].
### Right Side: [tex]\(\frac{1}{4} \div \left(\frac{1}{7} \div \frac{1}{8}\right)\)[/tex]
1. Simplifying [tex]\(\frac{1}{7} \div \frac{1}{8}\)[/tex]:
[tex]\[
\frac{1}{7} \div \frac{1}{8} = \frac{1}{7} \times \frac{8}{1} = \frac{8}{7}
\][/tex]
2. Now, simplifying [tex]\(\frac{1}{4} \div \frac{8}{7}\)[/tex]:
[tex]\[
\frac{1}{4} \div \frac{8}{7} = \frac{1}{4} \times \frac{7}{8} = \frac{1 \times 7}{4 \times 8} = \frac{7}{32}
\][/tex]
So, the right side simplifies to [tex]\(\frac{7}{32}\)[/tex], which is approximately [tex]\(0.21875\)[/tex].
Comparing the results from both sides:
- Left side: [tex]\(14\)[/tex]
- Right side: [tex]\(\frac{7}{32}\)[/tex] or approximately [tex]\(0.21875\)[/tex]
### Conclusion:
The two sides yield different results. The left side simplifies to [tex]\(14\)[/tex], whereas the right side simplifies to approximately [tex]\(0.21875\)[/tex].
This demonstrates that division of rational numbers is not associative. Hence, the property being illustrated here is the Non-Associative property of division in rational numbers.
