Lesson 16: Expanded Form, More on Missing Numbers in Subtraction

New Concept

The number 365 means "3 hundreds and 6 tens and 5 ones." We can write this as $300 + 60 + 5$. This is the expanded form of 365.

What’s next

Next, you’ll practice writing numbers in expanded form and use place value logic to find missing numbers in subtraction problems.

Property

Expanded form shows a number as the sum of its place values. For example, the number 365, meaning "3 hundreds, 6 tens, and 5 ones," is written as $300 + 60 + 5$.

Examples

• The expanded form of 482 is $400 + 80 + 2$.
• For a number with a zero like 603, we write $600 + 3$.
• A two-digit number like 94 becomes $90 + 4$.

Explanation

Think of this as deconstructing a number into its LEGO building blocks—hundreds, tens, and ones—to see its true value. It’s like number anatomy, showing what it's made of!

Property

Find a missing number in subtraction by "subtracting down" from the top number or "adding up" from the bottom, working one column at a time.

Examples

• Subtract Down: In $78 - w = 35$, we see $w=43$ because $8-3=5$ and $7-4=3$.
• Add Up: In $n - 25 = 51$, we see $n=76$ because $1+5=6$ and $5+2=7$.

Explanation

Think like a detective! Use the given numbers as clues to find the missing digit in each column. Solve the puzzle one piece at a time, from right to left.

Property

Addition and subtraction are inverse operations—they undo each other. This means the subtraction fact $a - b = c$ is the same as the addition fact $c + b = a$.

Examples

• To solve $n - 30 = 50$, just use addition: $50 + 30 = 80$. So, $n=80$.
• After solving $64 - 33 = 31$, you can check your work: $31 + 33 = 64$.

Explanation

Think of it as a round trip! Subtracting a number is one direction; adding it is the return trip. This powerful link lets you use addition to solve subtraction puzzles.