15, 678 + 7, 784 = (10, 000 + 5, 000 + 600 + 70 + 8) + (7, 000 + 700 + 80 + 4)
= 10, 000 + (5, 000 + 7, 000) + (600 + 700) + (70 + 80) + (8 + 4)
= 10, 000 + 12, 000 + 1, 300 + 150 + 12
= 23, 462
1 5, 6 7 8
+ 7, 7 8 4
12
150
1, 3 0 0
1 2, 0 0 0
+ 1 0, 0 0 0
2 3, 4 6 2
4
1 1 1 1
1 5, 6 7 8
+ 7, 7 8 4
2 3, 4 6 2
115 + 500 = 500 + 115
(2 + 3) + 5 = 2 + (3 + 5)
28 + 0 = 28
3
(1 + 3) + 7 = (3 + 1) + 7
7
1+2
6+2
0+3=3
3+6
2+4
4+1
5+3
2+5
28 + 0
3+0=3
3+3
3+4=7
4+3=7
(2 + 3) + 5
115 + 500
1 + (3 + 7)
1, 259 + 742
12, 579 + 10, 351
(2 + 1) + 5 = 3 + 5 = 8
2 + (1 + 5) = 2 + 6 = 8
78, 987 + 8, 274
852, 976 + 148, 037
Adding Whole Numbers
Answers to Practice
1. Identify what property is being used.
(a) 115 + 500 = 500 + 115
commutative property of addition
(b) (2 + 3) + 5 = 2 + (3 + 5)
associative property of addition
(c) 28 + 0 = 28
additive identity property
(d) (1 + 3) + 7 = (3 + 1) + 7
commutative property of addition
(The grouping did not change, 1 + 3
changed to 3 + 1.)
2. Use the number line to find the sum.
(a) 1 + 2
1+ 2=3
(b) 2 + 4
2
0 1 2 3 4 5 6 7 8 9 10
+
4 = 6
0 1 2 3 4 5 6 7 8 9 10
(c) 5 + 3
5
+
3 = 8
0 1 2 3 4 5 6 7 8 9 10
3. Add.
(a) 28 + 0 = 28
(f) 12, 579 + 10, 351
1 1
(b) (2 + 3) + 5 = 5 + 5 = 10
1 2,5 7 9
+ 1 0,3 5 1
2 2,9 3
(c) 115 + 500
(g) 78, 987 + 8, 274
115
+5 0 0
615
1 1
7 8,9 8 7
+ 1 0,3 5 1
8 9,3 3 8
(d) 1 + (3 + 7) = 1 + 10 = 11
(h) 752, 976 + 148, 037
(e) 1, 259 + 742
1 1 1 1 1
1,2 5 9
+7 4 2
7 4 3,2 5 9
7 5 2,9 7 6
+ 1 4 8,0 3 7
9 0 1,0 1 3
1