Lesson 2: Add Whole Numbers

New Concept

Master adding whole numbers by learning the notation, visualizing with models, and practicing the standard method. You'll translate word problems into addition expressions and apply your skills to real-world scenarios, like calculating totals and perimeters.

What’s next

This card is your starting point. Next, you'll work through interactive examples and practice cards to build your skills step-by-step.

Property

The operation of addition combines numbers to get a sum. The numbers being added are called the addends. A math statement that includes numbers and operations is called an expression.

Examples

• The expression $8 + 5$ is read as 'eight plus five' and represents 'the sum of 8 and 5'.
• In the equation $12 + 9 = 21$, the numbers $12$ and $9$ are the addends, and $21$ is the sum.
• Modeling the addition $4 + 5$ means combining a group of 4 items with a group of 5 items to get a total of 9 items.

Explanation

Addition is simply combining quantities to find a total. We use the '+' sign to show we're adding. The numbers we add are 'addends,' and the final answer is the 'sum.' It's like putting two piles of cookies together.

Property

The sum of any number $a$ and 0 is the number. Zero is called the additive identity.

Examples

• For the number 25, adding zero gives the same number back: $25 + 0 = 25$.
• If you start with zero and add a number, the result is that number: $0 + 150 = 150$.
• Maria has 8 books and receives 0 new books for her birthday. She still has a total of 8 books, demonstrating that $8 + 0 = 8$.

Explanation

Think of zero as the 'do nothing' number in addition. Adding zero to any number doesn't change it at all—the number keeps its original identity. It's like getting zero extra toys; you still have the same number of toys.

Property

Changing the order of the addends $a$ and $b$ does not change their sum.

Examples

• The sum of $9 + 7$ is $16$, which is the same as the sum of $7 + 9$, also $16$.
• A recipe calls for 2 cups of flour and 1 cup of sugar. The total volume is $2+1=3$ cups, which is the same as adding the sugar first: $1+2=3$ cups.
• Calculating $50 + 112$ gives $162$, and reversing the order to $112 + 50$ also gives $162$.

Explanation

This property means you can swap the numbers in an addition problem, and the answer will be the same. It's like putting on your shoes; whether you put on the left or right one first, you end up with both on.

Property

To add whole numbers:
Step 1. Write the numbers so each place value lines up vertically.
Step 2. Add the digits in each place value. Work from right to left starting with the ones place. If a sum in a place value is more than 9, carry to the next place value.
Step 3. Continue adding each place value from right to left, adding each place value and carrying if needed.

Examples

• To add $57 + 26$, align them vertically. Add the ones: $7 + 6 = 13$. Write down 3, carry 1 to the tens place. Add the tens: $1 + 5 + 2 = 8$. The sum is $83$.
• For $481 + 352$, add the ones: $1+2=3$. Add the tens: $8+5=13$. Write 3, carry 1. Add the hundreds: $1+4+3=8$. The sum is $833$.
• To add $5,280 + 945$, align the numbers carefully. The sum is $6,225$. Adding $0+5=5$, $8+4=12$ (carry 1), $1+2+9=12$ (carry 1), and $1+5=6$.

Explanation

To add big numbers, stack them up so the ones, tens, and hundreds places align. Add each column from right to left. If a column's sum is 10 or more, write down the last digit and 'carry' the other digit to the next column.

Property

Word phrases can be translated into math notation. Key phrases for addition include:

Examples

• The phrase 'the sum of 25 and 10' translates to the expression $25 + 10$, which equals $35$.
• '42 increased by 15' means you start with 42 and add 15, so the expression is $42 + 15$, and the result is $57$.
• 'The total of 150, 25, and 10' translates to adding all three numbers: $150 + 25 + 10 = 185$.

Explanation

Word problems use 'code words' for addition. Phrases like 'total of', 'increased by', or 'more than' are clues that you need to add numbers together to find the answer. Translating words to symbols is the first step in solving.