Final answer:
The expression 3/4+(-3/8)+(-1/4) simplifies to 1/8 using the Associative Property of addition and properties of addition involving the additive inverse. The expression is regrouped and fractions are added by finding a common denominator.
Step-by-step explanation:
The student is asking to evaluate the expression 3/4+(-3/8)+(-1/4) and identify the properties used in each step. To solve this, we can use the Associative Property of addition, which allows us to regroup the numbers as -3/8+[3/4+(-1/4)]. This property states that the way in which numbers are grouped does not change their sum.
Continuing from where the student left off:
- -3/8 remains unchanged.
- For [3/4+(-1/4)], we are adding a number and its additive inverse, so this simplifies to 1/2.
- Therefore, the expression simplifies further to -3/8 + 1/2.
- To add these fractions, we need a common denominator, so we convert 1/2 to 4/8.
- Now we have -3/8 + 4/8, which simplifies to 1/8.
Thus, the final simplified form of the expression is 1/8, and we've used the associative property and properties of addition involving the additive inverse.