Question

A new account is started with a
$
0
balance. The next three transactions are shown.



A deposit of
$
81.75
An online purchase with a debit card for
$
47.19
A parking fee paid with a debit card for
$
19.75
The new balance is found by
81.75
−
47.19
−
19.75
.



Which TWO strategies and reasons show how to determine the new balance on the account?



A.
81.75
+
(
−
19.75
)
+
(
−
47.19
)
; subtracting rational numbers is the same as adding the opposite rational number

B.
81.75
−
(
−
19.75
)
−
(
−
47.19
)
; subtracting rational numbers is the same as subtracting the opposite rational number

C.
(
81
+
(
−
47
)
+
(
−
19
)
)
+
(
0.75
+
(
−
0.19
)
+
(
−
0.75
)
)
; subtracting rational numbers is the same as adding the opposite rational number and that the Commutative Property of Addition is applied correctly

D.
(
81
−
(
−
47
)
−
(
−
19
)
)
−
(
0.75
−
(
−
0.19
)
−
(
−
0.75
)
)
; subtracting rational numbers is the same as subtracting the opposite rational number and that the Commutative Property of Addition is applied correctly

E.
(
81
+
(
−
47
)
+
(
−
19
)
)
+
(
0.75
+
(
−
0.19
)
+
(
−
0.75
)
)
; subtracting rational numbers is the same as adding the opposite rational number and that integers and decimal numbers can be added together

Answer 1

A and C.

- A rewrites each subtraction as adding the opposite: 81.75 + (−47.19) + (−19.75), which is equivalent and valid.
- C decomposes the decimals into integer and fractional parts and groups like terms: (81 + (−47) + (−19)) + (0.75 + (−0.19) + (−0.75)), using adding opposites and the commutative property to combine correctly.