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Prove that commutative property if addition holds true for (7/8 + 2/5) + 8/3

User TomV
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Final answer:

The commutative property of addition is demonstrated by showing that the sum of (7/8 + 2/5) + 8/3 is equal to the sum when the order is reversed to 8/3 + (7/8 + 2/5), which, upon calculation, yields the same result of 3 113/120.

Step-by-step explanation:

To prove that the commutative property of addition holds for the expression (7/8 + 2/5) + 8/3, we must show that switching the order of addition does not change the result. By the commutative property, we know that A+B=B+A. For the given fractions, we apply this property. Let's start with the original order, which is (7/8 + 2/5) + 8/3: Find a common denominator for 7/8 and 2/5, which is 40. Convert the fractions accordingly: (35/40 + 16/40). Add the fractions with the common denominator: (35/40 + 16/40) = 51/40. Add the result to 8/3: (51/40) + (8/3). Find a common denominator for 51/40 and 8/3, which is 120. Convert the fractions accordingly: (153/120 + 320/120). Add these fractions: (153/120 + 320/120) = 473/120 or 3 113/120. Now, let's change the order of addition to 8/3 + (7/8 + 2/5): Add 8/3 to the fraction 7/8 first, after finding a common denominator, which is 24. Convert the fractions: (56/24 + 7/24). Add these fractions: (56/24 + 7/24) = 63/24 or 2 15/24, which simplifies to 2 5/8 or 21/8. Now add 2/5 to 21/8, after finding a common denominator, which is 40. Convert the fractions: (210/40 + 16/40). Add these fractions: (210/40 + 16/40) = 226/40 or 5 26/40, which simplifies to 5 13/20 or 113/20. After simplifying, we find that both (7/8 + 2/5) + 8/3 and 8/3 + (7/8 + 2/5) equal 3 113/120, thus proving the commutative property of addition holds for these numbers.

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