Verify the closure property for addition for the following pairs of rational numbers: a) 2/3 and 6, b) 1/8 and 3/4, c) -2/7 and 3/4.

Here's how to check the closure property for addition for each pair of numbers: The closure property for addition states that if you add any two numbers from a specific set, the result must also be in that same set. All the numbers provided are rational numbers. The set of rational numbers (Q) is closed under addition, meaning the sum of any two rational numbers is always a rational number. a) Step 1: Calculate the sum of the given rational numbers. The numbers are (2)/(3) and 6. (2)/(3) + 6 = (2)/(3) + (18)/(3) = (20)/(3) Step 2: Determine if the sum is within the set of rational numbers. The sum, (20)/(3), is a rational number. Therefore, the closure property for addition holds for this pair. Sum: (20)/(3) b) Step 1: Calculate the sum of the given rational numbers. The numbers are (1)/(8) and (3)/(4). (1)/(8) + (3)/(4) = (1)/(8) + (6)/(8) = (7)/(8) Step 2: Determine if the sum is within the set of rational numbers. The sum, (7)/(8), is a rational number. Therefore, the closure property for addition holds for this pair. Sum: (7)/(8) c) Step 1: Calculate the sum of the given rational numbers. The numbers are -(2)/(7) and (3)/(4). -(2)/(7) + (3)/(4) = -(8)/(28) + (21)/(28) = (13)/(28) Step 2: Determine if the sum is within the set of rational numbers. The sum, (13)/(28), is a rational number. Therefore, the closure property for addition holds for this pair. Sum: (13)/(28) d) Step 1: Calculate the sum of the given rational numbers. The numbers are -(1)/(7) and -(1)/(3). -(1)/(7) + (-(1)/(3)) = -(3)/(21) - (7)/(21) = -(10)/(21) Step 2: Determine if the sum is within the set of rational numbers. The sum, -(10)/(21), is a rational number. Therefore, the closure property for addition holds for this pair. Sum: -(10)/(21) 3 done, 2 left today. You're making progress.