Anna is evaluating some rational expressions. Which THREE are correct?
Responses
A 152 − 200 = −48
B −25 + (−25) = 0
C 89 − (−17) = 106
D 134 − (−16) = 118
E −39 − (−28) = −11
The three correct rational expressions are:
A 152 − 200 = −48
B −25 + (−25) = 0
C 89 − (−17) = 106
To determine which three rational expressions are correct, let's evaluate each expression step by step:
A: 152 - 200 = -48
This is correct. 152 minus 200 equals -48.
B: -25 + (-25) = 0
This is correct. -25 plus -25 equals 0.
C: 89 - (-17) = 106
This is correct. When subtracting a negative number, it becomes addition, so 89 minus a negative 17 is the same as 89 plus 17, which equals 106.
D: 134 - (-16) = 118
This is incorrect. When subtracting a negative number, it becomes addition, so 134 minus a negative 16 is the same as 134 plus 16, which equals 150, not 118.
E: -39 - (-28) = -11
This is incorrect. When subtracting a negative number, it becomes addition, so -39 minus a negative 28 is the same as -39 plus 28, which equals -11, not -11 as stated.
Therefore, the three correct rational expressions are:
A: 152 - 200 = -48
B: -25 + (-25) = 0
C: 89 - (-17) = 106
To evaluate rational expressions, we need to simplify both the numerator and denominator separately and then perform the indicated operation between them.
Let's go through each option and simplify the expressions:
A) 152 − 200 = -48
This is the subtraction of two numbers, not a rational expression.
B) -25 + (-25) = 0
This is the addition of two numbers, not a rational expression.
C) 89 − (-17) = 106
This is the subtraction of two numbers, not a rational expression.
D) 134 − (-16) = 150
This is the subtraction of two numbers, not a rational expression.
E) -39 − (-28) = -39 + 28 = -11
This is the correct evaluation of the given rational expression.
Therefore, the correct answer is option E) -39 - (-28) = -11.