#### Answer

$A = \frac{7}{8}$ inches.

#### Work Step by Step

This question requires us to solve for length A. Because we know that the opposite length of this shape is 7 in., the lengths on the top side MUST add up to 7 in. as well. Therefore, we can solve for length A by adding up the known lengths on the top side, and subtracting this value from 7, to calculate length A.
1$\frac{7}{8}$ in + 1$\frac{1}{2}$ in + 1$\frac{1}{3}$ in + 1$\frac{5}{12}$ in
To add these values together, we must convert these fractions into values with the same denominator (bottom number).
Looking at the denominators, we have values 8, 2, 3, and 12. We need to find the lowest common denominator (LCD) between these 4 numbers. 8, 2, 3, and 12 are all factors of 24. So, we can use 24 as our LCD.
To give the fractions each a denominator of 24, multiply the numerator and denominator of each fraction by the value that will give a denominator of 24. So, we have:
1$\frac{21}{24}$ in + 1$\frac{12}{24}$ in + 1$\frac{8}{24}$ in + 1$\frac{10}{24}$ in
Now, we can add our fractions.
$\frac{21}{24}$ + $\frac{12}{24}$ + $\frac{8}{24}$ + $\frac{10}{24}$
21
12
8
+10
= 51
Adding our whole numbers gives: 1 + 1 + 1 + 1 = 4.
Therefore, we have 4 $\frac{51}{24}$ in.
We can reduce this fraction by dividing the numerator and denominator by 3:
$\frac{51}{24} \div \frac{3}{3} = \frac{17}{8}$.
Therefore, we have 4$\frac{17}{8}$ in. Converting this into a mixed number (keep the denominator, multiple the whole number by the denominator and add the numerator to get our converted numerator), we get $\frac{49}{8}$ as the length of our known values. We can now subtract this value from 7 inch, again, by using common denominators.
$\frac{7}{1} - \frac{49}{8}$
$ = \frac{56}{8} - \frac{49}{8}$
$ = \frac{7}{8}$
$\textbf{Therefore, we know that the value of length A is $ = \frac{7}{8}$ inch.}$