To solve these problems, we need to identify and apply the properties of addition: the Identity Property, the Associative Property, and the Commutative Property.
(a) The Identity Property of Addition states that adding zero to any number does not change the number. Therefore, the missing number is 8.
(b) The Associative Property of Addition states that the way in which numbers are grouped does not change their sum. Therefore, the missing number is 9.
(c) The Commutative Property of Addition states that the order of numbers does not affect their sum. Therefore, the missing number is 9.
Using the Identity Property of Addition, we know that adding zero to any number does not change the number. Therefore, we can express this as:
\[
0 + x = 8
\]
Thus, the missing number \( x \) is:
\[
x = 8
\]
Applying the Associative Property of Addition, which states that the grouping of numbers does not affect their sum, we have:
\[
(9 + 6) + 3 = x + (6 + 3)
\]
To find \( x \), we can simplify the left side:
\[
15 + 3 = x + 9
\]
This gives us:
\[
18 = x + 9
\]
Solving for \( x \):
\[
x = 18 - 9 = 9
\]
Using the Commutative Property of Addition, which states that the order of numbers does not affect their sum, we can express this as:
\[
9 + 8 = 8 + x
\]
To find \( x \), we can simplify the left side:
\[
17 = 8 + x
\]
Solving for \( x \):
\[
x = 17 - 8 = 9
\]
The missing numbers are:
- For \( a \): \( \boxed{8} \)
- For \( b \): \( \boxed{9} \)
- For \( c \): \( \boxed{9} \)
Answered
