Final answer:
The commutative property of addition is proven for the fractions 7/8 and 4/6 by finding a common denominator, which shows that the sum is the same regardless of the order of the addends, thereby confirming the property holds true for these fractions.
Step-by-step explanation:
The student is asking to prove the commutative property of addition using the fractions 7/8 and 4/6. The commutative property states that changing the order of addends does not change the sum, which can be written as A+B=B+A. To prove this with fractions, we must first express both fractions with a common denominator, then add them to see if this property holds true.
To find a common denominator for 7/8 and 4/6, we can multiply the denominators of each fraction: 8 * 6 = 48. Now we adjust the numerators accordingly to keep the value of the fractions the same:
- 7/8 = (7*6)/(8*6) = 42/48
- 4/6 = (4*8)/(6*8) = 32/48
Now we can add the fractions:
- 42/48 + 32/48 = (42 + 32)/48 = 74/48
And if we reverse the order of the addends:
- 32/48 + 42/48 = (32 + 42)/48 = 74/48
Since both ways give us the same result, 74/48, we can conclude that the commutative property of addition holds true for the fractions 7/8 and 4/6.