Answer:

1. 199/10

2. The value of N is 351/15.

3. The sum of 10 3/4, 8 1/3, 15 5/6, and 11 7/8 is 1123/24.

Step-by-step explanation:

1. To find the sum of 12 4/5 and 7 1/10, we need to convert both mixed numbers to improper fractions.12 4/5 can be written as (12 * 5 + 4)/5 = 64/5.7 1/10 can be written as (7 * 10 + 1)/10 = 71/10.Now, we can add the two fractions together:64/5 + 71/10To add these fractions, we need to find a common denominator. The least common multiple of 5 and 10 is 10.So, we can rewrite the fractions with a common denominator of 10:(64/5) * (2/2) = 128/1071/10Now, we can add the fractions:128/10 + 71/10 = (128 + 71)/10 = 199/10Therefore, the sum of 12 4/5 and 7 1/10 is 199/10.

2. To find the value of N, we need to add the given numbers together.First, let's convert the mixed numbers to improper fractions:5 2/3 = (5 * 3 + 2)/3 = 17/3 16 4/5 = (16 * 5 + 4)/5 = 84/5Now, we can add the fractions:17/3 + 14/15 + 84/5To add these fractions, we need to find a common denominator. The least common multiple of 3, 15, and 5 is 15.Converting the fractions to have a denominator of 15:(17/3) * (5/5) = 85/15 (14/15) (84/5) * (3/3) = 252/15Now, we can add the fractions:85/15 + 14/15 + 252/15 = (85 + 14 + 252)/15 = 351/15Therefore, the value of N is 351/15.

3.To find the sum of these mixed numbers, we need to convert them to improper fractions first.10 3/4 = (10 * 4 + 3)/4 = 43/4 8 1/3 = (8 * 3 + 1)/3 = 25/3 15 5/6 = (15 * 6 + 5)/6 = 95/6 11 7/8 = (11 * 8 + 7)/8 = 95/8Now, we can add these fractions together:43/4 + 25/3 + 95/6 + 95/8To add these fractions, we need to find a common denominator. The least common multiple of 4, 3, 6, and 8 is 24.Multiplying the numerator and denominator of each fraction by the appropriate factor to get a denominator of 24:(43/4) * (6/6) = 258/24 (25/3) * (8/8) = 200/24 (95/6) * (4/4) = 380/24 (95/8) * (3/3) = 285/24Now, we can add the fractions:258/24 + 200/24 + 380/24 + 285/24 = (258 + 200 + 380 + 285)/24 = 1123/24So, the sum of 10 3/4, 8 1/3, 15 5/6, and 11 7/8 is 1123/24.