Page 10 - ArithBook5thEd ~ BCC
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1.0.1 Exercises
1. 35 stands for
2. 209 stands for
3. 9532 stands for
4. 21045 stands for
1.1 Adding Whole Numbers
When we add two or more integers, the result is called the sum.We assume you know the sums of
single-digit numbers. For practice, do the following example.
Example 2. Fill in the missing squares in the digit-addition table below. For example, the number in
the row labelled 3 and the column labelled 4 is the sum 3 + 4 = 7.
+ 0 1 2 3 4 5 6 7 8 9
0 0 1 2 3 4 5 6 7 8 9
1
2
3 7
4
5
6
7 12
8
9
Table 1.1: The digit addition table
1. Do you notice any patterns or regularities in the digit-addition table? Can you explain them?
2. Why is the second line from the top identical to the top line?
3. What can you say about the left-most column and the second-from-left column?
1.1.1 Commutativity, Associativity, Identity
The first question above leads us to an important property of addition, namely, that for any two numbers
x and y,
x + y = y + x.
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