Chapter 2: Add and Subtract Whole Numbers
Addition Properties
Commutative Property – this is when the number move around or
change their order. It is also known as the order property. It does
not matter which order you put them in, they will always add up to the
same sum. You learned this in first grade when you were taught your
family facts.
35 + 25 = 60
25 + 35 = 60
Associative – This is also known as the grouping property. It says that
it does not matter how you group the addends, the sum is still the
same.
(2 + 3) + 4 = 2 + (3 + 4)
Identity Property - is also known as the zero property. This property
tells us that we can add 0 to any number and the number and the sum is
that number.
8+0=8
Estimate Sums & Differences
To Estimate means to find an answer close to an exact answer.
One way to estimate is to use Rounding. Rounding means to replace a
number with another number that tells about how many or how much.
Example:
1) Estimate 34, 221 + 38,899
Round each number to the nearest thousand.
34,221
34,000
+38,899
+39,000
73,000
2) Estimate 5,372 +1,497
Round each number to the nearest ten thousand.
86,017
90,000
-35,572
- 40,000
50,000
Try it:
1)
279
2) 7,939
3) 65,461
+ 645
- 4,209
+ 23,780
Answers:
1.
900
2.
4,000
3.
90,000
Another way to estimate is to use Front-End Estimation. This means
to add or subtract the value of the first number, or the “front”
number.
Example:
1)
Estimate 34,221 + 38,899
Add the value of the front digits.
34, 221 + 38,899
Add the value of the first number, or the “front” number.
34,221
30,000
+ 38,899
+30,000
60,000
2)
Estimate 45,017 - 21,700
Subtract the value of the front digits.
45,017 – 21,700.
Subtract the value of the first number, or the “front” number.
45,017
40,000
- 21,700
20,000
20,000
Try It:
1)
257
-123
Answers:
2) 1,936
3)$13,024
+ 7,483
+ $58,417
1) 100
2) 8,000
3) $60,000
Using either of these two strategies, you can estimate answers to
addition and subtraction problems! 
Add & Subtract to 4-Digit Numbers

When adding and subtracting numbers, line up your numbers and start with
the ones column, working your way to the left.

In addition: Numbers that are 10 and over must be regrouped, by carrying
the ten to the next column.

In subtraction: Numbers that are 10 and over must be regrouped by
borrowing from the next column.

You can estimate to help check your answer.
Example:
1) Find the sum. 9,910 + 7,340
Estimate:10,000 + 7,000 = 17,000
Add the ones
9,910
+7,340
0
Add the tens.
9,910
+7,340
50
Add the hundreds. Regroup the “twelve” hundreds.
1
9,910
+7,340
250
Add the thousands.
1
9,910
+7,340
17,250
2) Find the difference. 9,910-7,340
Estimate:10,000 - 7,000 = 3,000
Subtract the ones
9,910
+7,340
0
Regroup the hundreds. Subtract the tens.
8 11
9, 9 1 0
-7, 3 4 0
70
Subtract the hundreds.
8 11
9, 9 1 0
-7, 3 4 0
570
Subtract the thousands.
8 11
9, 9 1 0
-7, 3 4 0
2,5 7 0
Try It:
1)
899
+267
2)
674
-406
3)
8,902
-5,730
4)
9,201
+1,321
Answers:
1) 1,166
2) 268
3) 3,172
4) 10,522
Subtract Across Zeroes

Line up your numbers and start with the ones column, working your way to
the left.

In subtraction: Numbers that are 10 and over must be regrouped by
borrowing from the next column.

You can estimate to help check your answer.
Example:
1) Find the difference. 7,100 – 1,315
Estimate:7,000 – 1,000= 6,000
Subtract the ones. Regroup 1 hundred as 9 tens and 10 ones.
9
0 10 10
7, 1 0 0
-1 , 3 1 5
5
Subtract the tens.
9
0 10 10
7, 1 0 0
-1 , 3 1 5
85
Subtract the hundreds. Regroup 7 thousands as 6 thousands and 10 hundreds.
10 9
10 9
6 0 10 10
7, 1 0 0
-1 , 3 1 5
7 8 5
Subtract the thousands.
10 9
6 0 10 10
7, 1 0 0
-1 , 3 1 5
5,7 8 5
Try It:
5)
400
-287
6)
3,700
- 1,692
7)
$300
- $163
8)
2,100
- 594
Answers:
5) 113
6) 2,008
7) $137
8) 1,506