Consider the steps to simplify the expression. What property of operation is used in Step 2?
Expression: -437 + 7 - 347
Step 1: = -4 3/7 + 7 + (-3 4/7)
Step 2: = -4 3/7 + (-3 4/7) + 7
Step 3: = -4 + (-37) + (-3) + (-47) + 7
Step 4: = -4 + (-37) + (-47) + (-3) + 7
Step 5: = -4 + (-1) + (-3) + 7
Step 6: = -8 + 7
Step 7: = -1
Responses
A Apply the associate property of addition.Apply the associate property of addition.
B Apply the commutative property of addition.Apply the commutative property of addition.
C The opposite of a sum is the sum of it's opposites.The opposite of a sum is the sum of it's opposites.
D Subtracting a number is the same as adding the inverse.
C The opposite of a sum is the sum of its opposites.
Simplify this expression.
4/21 − (−3/7) − 5/9
Responses
A −13/21
B −19/36
C 11/12
D 4/63
To simplify the expression 4/21 - (-3/7) - 5/9, we can first simplify the expression inside the parenthesis:
4/21 + 3/7 - 5/9
To add fractions, we need to find a common denominator. In this case, the least common denominator (LCD) is 63:
(4/21)(3/3) + (3/7)(9/9) - (5/9)(7/7)
= 12/63 + 27/63 - 35/63
Now we can combine the fractions:
12/63 + 27/63 - 35/63 = (12 + 27 - 35)/63
= 4/63
So the simplified expression is 4/63.
Therefore, the correct response is D. 4/63.
The property of operation used in Step 2 is the commutative property of addition. This property allows us to change the order of the terms being added without changing the value of the expression.
The correct answer is D - Subtracting a number is the same as adding the inverse.
In Step 2, the property of operation used is the commutative property of addition. This property states that you can change the order of the terms without changing the result. In this case, the expression is rearranged so that the negative number (-3 4/7) is added first before the positive number (7).
However, it's worth noting that the question asks for the property used in Step 2, not the correct answer choice. The property used in Step 2 is the commutative property of addition, but the correct answer choice is D - Subtracting a number is the same as adding the inverse, which is used in Step 4 to rewrite subtraction as addition.