To convert 880 miles to yards, we need to use the correct conversion ratio that relates miles to yards. Given that there are 1,760 yards in one mile, we need a ratio that allows us to multiply by the number of miles (880) and get the number of yards.
To do this, we should use the ratio that has "yards" in the numerator and "miles" in the denominator. This way, when we multiply by 880 miles, the units of miles will cancel out, and we will be left with yards.
Let's examine the options given:
A. [tex]\(\frac{1 \text { yard }}{1,760 \text { miles }}\)[/tex]
- This ratio is incorrect because it would convert from miles to a very small fraction of a yard, not directly provide the number of yards in 880 miles.
B. [tex]\(\frac{1 \text { mile }}{1,760 \text { yards }}\)[/tex]
- This ratio is incorrect because it is the inverse of what we need; it tells us how many miles are in 1,760 yards, not how many yards are in one mile.
C. [tex]\(\frac{1,760 \text { yards }}{1 \text { mile }}\)[/tex]
- This ratio is correct because it directly tells us how many yards are in one mile, which is what we need to convert 880 miles to yards.
D. [tex]\(\frac{860 \text { yards }}{1 \text { mile }}\)[/tex]
- This ratio is incorrect because 860 yards do not equate to one mile.
Therefore, the correct ratio to use is provided in choice C:
[tex]\[
\frac{1,760 \text { yards }}{1 \text { mile }}
\][/tex]
Now, by using this ratio, we can convert 880 miles to yards as follows:
[tex]\[
880 \text { miles} \times \frac{1,760 \text { yards}}{1 \text { mile}} = 880 \times 1,760 \text { yards}
\][/tex]
Thus, to convert 880 miles to yards, we should use the ratio [tex]\(\frac{1,760 \text { yards }}{1 \text { mile }}\)[/tex], which means the correct choice is C.
