Lesson 1: Adding Whole Numbers and Money

Definition

To combine two or more numbers, we add. The numbers that are added together are called addends. The answer is called the sum.

Commutative Property of Addition: Changing the order of the addends does not change the sum. For example,

Identity Property of Addition: If one of two addends is zero, the sum of the addends is identical to the nonzero addend.

What’s next

Next, you'll see worked examples of adding whole numbers and money, and explore how addition relates to subtraction through fact families.

Property

Changing the order of the addends does not change the sum. For example, $3 + 6 = 6 + 3$.

Examples

• Simple but true: $7 + 9 = 16$ is the exact same as $9 + 7 = 16$.
• Even with three numbers, order doesn't matter: $10 + 20 + 5 = 35$ is the same as $20 + 5 + 10 = 35$.
• You can check that $456 + 89 = 545$ by flipping the order and adding $89 + 456 = 545$.

Explanation

Addition is super chill—it doesn't care which number goes first! Whether you add your allowance to your birthday money or the other way around, the total is the same. This cool property is also a sneaky way to double-check your addition answers to make sure they're right.

Property

When adding numbers, we add digits that have the same place value.

Examples

• To solve $456 + 89$, align the 6 over the 9 (ones) and the 5 over the 8 (tens). The sum is $545$.
• For $1234 + 567$, you must align the place values (ones, tens, hundreds) to get the correct sum of $1801$.
• Even with $9 + 23$, the 9 lines up under the 3, not the 2, for a final sum of $32$.

Explanation

Think of numbers having families: ones, tens, and hundreds. To add correctly, you must line them up so each family stays in its own column. It's like sorting LEGOs by color before you build—it prevents a big mess and helps you get the right answer every single time!

Property

If one of two addends is zero, the sum of the addends is identical to the nonzero addend.

Examples

1. You have 23 gummy bears and your friend gives you 0 more. You still have 23: $23 + 0 = 23$.
2. Your bank account has 500 dollars. You add 0 dollars. The balance remains 500 dollars: $500 + 0 = 500$.
3. This property works both ways, so $0 + 1999 = 1999$.

Explanation

Zero is the 'chillest' number in addition. Adding it is like giving another number a high-five—it's friendly, but it doesn't change anything. The number keeps its original 'identity' and value, which is why this property is so cool!