Whole Numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, ...

W = {0, 1, 2, 3, 4, ...}

Sum: The result of addition (e.g., 5 + 3 = 8, sum is 8)

Addend: Numbers being added (e.g., in 5 + 3, both 5 and 3 are addends)

Difference: The result of subtraction (e.g., 8 − 3 = 5, difference is 5)

Minuend: The number being subtracted from (e.g., in 8 − 3, 8 is the minuend)

Subtrahend: The number being subtracted (e.g., in 8 − 3, 3 is the subtrahend)

Step 1: Write numbers vertically, aligning place values (ones, tens, hundreds, etc.)

Step 2: Start adding from the rightmost column (ones place)

Step 3: If the sum in a column is 10 or more, carry the tens digit to the next column

Step 4: Continue adding each column from right to left

Step 5: Write the final sum

Problem: Add 456 + 287

Problem: Add 12,456 + 8,789

Problem: Add 256 + 322 + 418

Step 1: Write numbers vertically, aligning place values

Step 2: Write the larger number on top

Step 3: Start subtracting from the rightmost column (ones place)

Step 4: If needed, borrow (regroup) from the next column to the left

Step 5: Continue subtracting each column from right to left

Step 6: Write the final difference

Problem: Subtract 543 − 287

Problem: Subtract 5,000 − 2,347

Subtraction is the Opposite of Addition

If a − b = c, then a = b + c

Example: If 10 − 4 = 6, then 10 = 4 + 6

Addition: The sum of two whole numbers is always a whole number.

Example: 15 + 23 = 38 (whole number)

Subtraction: NOT closed (result may not be a whole number)

Example: 5 − 8 = −3 (NOT a whole number)

Addition: a + b = b + a

Example: 7 + 5 = 5 + 7 = 12

Subtraction: NOT commutative

Example: 7 − 5 ≠ 5 − 7

Addition: (a + b) + c = a + (b + c)

Example: (2 + 3) + 4 = 2 + (3 + 4) = 9

Subtraction: NOT associative

Example: (10 − 5) − 2 ≠ 10 − (5 − 2)

Additive Identity: Adding 0 to any number gives the same number

a + 0 = 0 + a = a

Example: 25 + 0 = 25

Step 1: Read the problem carefully

Step 2: Identify what you need to find

Step 3: Determine the operation (addition or subtraction)

Step 4: Set up the equation

Step 5: Solve and check your answer

Problem: A bookstore has 2,345 books in the fiction section and 1,876 books in the non-fiction section. How many books does the store have in total?

Problem: A school auditorium has 1,500 seats. If 876 seats are already taken, how many seats are still available?

Problem: Maria had 1,250 dollars. She earned 450 dollars more and then spent 675 dollars. How much money does she have now?

Problem: The population of City A is 45,678 and City B is 32,456. How many more people live in City A than City B?

✓ Always align place values vertically when adding or subtracting

✓ Start from the rightmost column (ones place)

✓ When adding, if sum ≥ 10, carry to the next column

✓ When subtracting, if top digit < bottom digit, borrow from the next column

✓ Addition is commutative: 5 + 3 = 3 + 5

✓ Subtraction is NOT commutative: 5 − 3 ≠ 3 − 5

✓ Check subtraction by adding: if 10 − 4 = 6, then 6 + 4 = 10

✓ In word problems, identify keywords to determine the operation

✓ Always check your answer by estimation or inverse operation

✓ Use commas to separate groups of three digits (e.g., 1,234,567)

Addition Trick:

"Start from the Right and Carry the Light!" (carry digits to the left)

Subtraction Trick:

"When you can't subtract, borrow from your neighbor!" (the column to the left)

Place Value:

"Ones, Tens, Hundreds, Thousands - Keep them straight and line them up!"

Word Problem Keywords:

"Total, Sum, All" = Addition

"Left, Difference, More" = Subtraction

Check Your Work:

"Addition checks subtraction, subtraction checks addition!"

If 12 + 5 = 17, then 17 − 5 = 12

Estimation:

Round numbers first to check if your answer makes sense!

Example: 498 + 523 ≈ 500 + 500 = 1,000