Answer:
To solve the given addition problems involving fractions and mixed numbers, let's calculate each one step by step:
1. ½ + 2/3 + 3/4:
To add fractions, we need to find a common denominator. In this case, the least common denominator (LCD) is 12.
Converting each fraction to have a denominator of 12:
½ = 6/12
2/3 = 8/12
3/4 = 9/12
Now, we can add the fractions:
6/12 + 8/12 + 9/12 = 23/12
The sum is 23/12.
2. 5/8 + 7/12:
Again, we need to find a common denominator. The LCD here is 24.
Converting each fraction to have a denominator of 24:
5/8 = 15/24
7/12 = 14/24
Adding the fractions:
15/24 + 14/24 = 29/24
The sum is 29/24.
3. 42/5 + 3 1/5:
To add a whole number and a fraction, we need to convert the whole number to a fraction with the same denominator as the fraction part.
The fraction part is already in fifths, so we convert 3 to fifths:
3 = 15/5
Now, we can add the fractions:
42/5 + 15/5 = 57/5
The sum is 57/5.
4. 6¼ + 3 3/8:
First, we need to convert the mixed numbers to improper fractions.
6¼ = 25/4
3 3/8 = 27/8
Adding the fractions:
25/4 + 27/8 = 50/8 + 27/8 = 77/8
The sum is 77/8.
Therefore, the solutions to the given addition problems are:
1. ½ + 2/3 + 3/4 = 23/12
2. 5/8 + 7/12 = 29/24
3. 42/5 + 3 1/5 = 57/5
4. 6¼ + 3 3/8 = 77/8