The simplified solutions are:
1. 5/6 + 1/3 = 3/2
2. 7/4 - 2/5 = 19/20
3. 3/8 + 2/3 - 5/24 = 3/1
Let's evaluate the expressions one by one:
1. 5/6 + 1/3
Adding the fractions with the least common denominator of 6, we get:
(5 * 1) / (6 * 1) + (2 * 2) / (6 * 2) = 5/6 + 4/6 = 9/6
Simplifying the fraction, we get:
9/6 = 3/2
2. 7/4 - 2/5
Finding a common denominator for 4 and 5, we get 20:
(7 * 5) / (4 * 5) - (4 * 4) / (5 * 4) = 35/20 - 16/20 = 19/20
3. 3/8 + 2/3 - 5/24
First, let's find a common denominator for 8, 3, and 24:
(3 * 3) / (8 * 3) + (8 * 8) / (3 * 8) - (1 * 1) / (24 * 1) = 9/24 + 64/24 - 1/24 = 72/24
Simplifying the fraction, we get:
72/24 = 3/1
Question:
Compute the following operations with rational numbers:
1. 5/6 + 1/3
2. 7/4 - 2/5
3. 3/8 + 2/3 - 5/24
Perform addition and subtraction for each pair of rational numbers, simplifying the results where possible.