Question

Prove that extend is associative. in in other words, if you have three rational numbers, then verify the associative property of addition.. a=2/3, b=-5/6, c=3/4​.

Verify:
(i) a + (b + c) = (a + b) + C (Associative property of addition)

Answer 1

After computing a + (b + c) and (a + b) + c using the given rational numbers a = 2/3, b = -5/6, and c = 3/4, it is verified that both expressions result in 7/12, confirming that addition is associative for rational numbers.

Step-by-step explanation:

Proving that addition is associative means showing that, for any three rational numbers, the groupings of the numbers does not affect the sum. Let's take the given rational numbers a = 2/3, b = -5/6, and c = 3/4 to verify the associative property of addition.

First, let's calculate a + (b + c):

• b + c = -5/6 + 3/4 = (-5 × 4 + 3 × 6) / (6 × 4) = (-20 + 18) / 24 = -2/24 = -1/12
• a + (b + c) = 2/3 + (-1/12) = (2 × 12 - 1 × 3) / (3 × 12) = (24 - 3) / 36 = 21/36 = 7/12

Now, let's calculate (a + b) + c:

• a + b = 2/3 - 5/6 = (2 × 6 - 5 × 3) / (3 × 6) = (12 - 15) / 18 = -3/18 = -1/6
• (a + b) + c = -1/6 + 3/4 = (-1 × 4 + 3 × 6) / (6 × 4) = (-4 + 18) / 24 = 14/24 = 7/12

We see that a + (b + c) and (a + b) + c both equal 7/12, confirming that addition of rational numbers is associative.