Sure, let's work through the problem step by step:
We need to determine how many [tex]\(\frac{1}{8}\)[/tex] yard pieces can be cut from a pipe that is [tex]\(\frac{3}{4}\)[/tex] yard long.
1. Understand the problem:
- We have a pipe that is [tex]\(\frac{3}{4}\)[/tex] yard long.
- We want to cut this pipe into smaller pieces where each piece is [tex]\(\frac{1}{8}\)[/tex] yard long.
2. Set up the calculation:
- To determine how many [tex]\(\frac{1}{8}\)[/tex] yard pieces fit into [tex]\(\frac{3}{4}\)[/tex] yard, we need to divide the total length of the pipe by the length of each smaller piece.
- This means we need to calculate [tex]\(\frac{3}{4} \div \frac{1}{8}\)[/tex].
3. Performing the division of fractions:
- When we divide by a fraction, we multiply by its reciprocal. The reciprocal of [tex]\(\frac{1}{8}\)[/tex] is [tex]\(8\)[/tex].
- Therefore, we calculate [tex]\(\frac{3}{4} \times 8\)[/tex].
4. Multiplication step:
- To multiply these fractions, we multiply the numerators and the denominators:
[tex]\[\frac{3}{4} \times 8 = \frac{3 \times 8}{4}\][/tex]
5. Simplifying the expression:
- Now, perform the multiplication in the numerator and then divide by the denominator:
[tex]\[\frac{3 \times 8}{4} = \frac{24}{4} = 6\][/tex]
So, the number of [tex]\(\frac{1}{8}\)[/tex] yard pieces that can be cut from a [tex]\(\frac{3}{4}\)[/tex] yard long pipe is [tex]\(6\)[/tex]. Therefore, the correct answer is:
[tex]\[ \boxed{6} \][/tex]
