Final answer:
After evaluating each pair of expressions given by the student, none of them match. It is essential to use the correct rules for addition and subtraction, including changing the sign of the number being subtracted, to simplify and compare expressions accurately. However, in this case, it seems like there may be an error in the problem as none of the pairs are equivalent.
Step-by-step explanation:
The student is dealing with arithmetic expressions and the goal is to match equivalent expressions. To do this, we need to simplify each expression where possible and see which ones are equal in value.
Let's solve the first expression:
- (-14 + 4 + 0) – (1 + 3) = -14 + 4 - 4 = -14
- 46 + 13 = 59
Clearly, these two do not match as -14 does not equal 59.
Next, let's look at the second expression:
- (5 + 26) + (26 + 15) = 31 + 41 = 72
- 86 - 15 = 71
These two do not match either since 72 does not equal 71.
Now, the third pair:
- (16 - 3) - (8 + 60) = 13 - 68 = -55
- 56 - 11 = 45
These expressions do not match because -55 does not equal 45.
Finally, the last expression:
- (-10 + 6) + (7 - 5) = -4 + 2 = -2
- -15 - 26 = -41
None of these expressions match because -2 does not equal -41.
It appears that there might be a mistake because none of the given pairs of expressions are equivalent based on the calculation. Therefore, none of the options provided match correctly.
When working with arithmetic, remember that the rules of addition and subtraction for positive and negative numbers dictate the results. When adding two positive numbers, the result is positive. When adding two negative numbers, the result is negative. When adding two numbers with opposite signs, the result takes the sign of the larger number after subtracting the smaller from the larger. For subtraction, change the sign of the number being subtracted and follow the rules of addition.