a+1 7/8=5 1/2

To solve the equation \( a + 1\frac{7}{8} = 5\frac{1}{2} \), we first need to convert the mixed numbers into improper fractions.

1. Convert \( 1\frac{7}{8} \) into an improper fraction: \[ 1\frac{7}{8} = 1 \times 8 + 7 = 8 + 7 = 15/8 \]

2. Convert \( 5\frac{1}{2} \) into an improper fraction: \[ 5\frac{1}{2} = 5 \times 2 + 1 = 10 + 1 = 11/2 \]

So, the equation becomes: \[ a + \frac{15}{8} = \frac{11}{2} \]

3. Now, let's subtract \( \frac{15}{8} \) from both sides: \[ a = \frac{11}{2} - \frac{15}{8} \]

To perform this subtraction, we need a common denominator. The least common multiple of 2 and 8 is 8.

4. Convert \( \frac{11}{2} \) to have a denominator of 8: \[ \frac{11}{2} = \frac{11 \times 4}{2 \times 4} = \frac{44}{8} \]

Now, we can subtract: \[ a = \frac{44}{8} - \frac{15}{8} = \frac{44 - 15}{8} = \frac{29}{8} \]

Thus, the solution is: \[ a = \frac{29}{8} \]

If you need it in mixed number form: \[ a = 3\frac{5}{8} \]

So, \( a = \frac{29}{8} \) or \( 3\frac{5}{8} \).