Decimal Subtraction
Problem String
Getting to Friendly Numbers
📋 Standards & Objectives
- Use the "get to a friendly number" strategy to subtract decimals
- Connect decimal subtraction to money (dollars and cents)
- Model subtraction strategies on a number line
💰 The Money Connection
Decimals are everywhere—especially in your wallet!
When we work with decimals, think about money!
3.7 = $3.70 = 3 dollars and 70 cents
0.46 = $0.46 = 46 cents
7.46 = $7.46 = 7 dollars and 46 cents
If you have $3.70 and spend 70 cents, what's an easy way to figure out what's left?
🧠 Key Strategy
Getting to a "Friendly Number"
A "friendly number" is a number that's easy to work with—like a whole number!
- 1 Find the nearest "friendly number" (usually a whole number)
- 2 Subtract to get there first
- 3 Then subtract whatever is left
Example: Instead of subtracting 0.9 all at once, first subtract 0.7 to get to a whole number, then subtract the remaining 0.2!
👨🏫 Problem 1
Watch how I solve this!
3.7 is the same as $3.70 (3 dollars and 70 cents)
If I take away 70 cents, I'm left with just the dollars!
This is a "one jump" problem—we land right on a friendly number!
Number Line Model
👥 Problem 2
Let's solve this together!
Use what you learned from Problem 1 to help!
- 1 First, subtract 0.7 to get to 3.0 (the friendly number!)
- 2 We still need to subtract 0.2 more (because 0.7 + 0.2 = 0.9)
- 3 3.0 − 0.2 = 2.8
Number Line Model
💬 Turn & Talk
How did solving 3.7 − 0.7 first help us solve 3.7 − 0.9?
Think about:
- What did the first problem help us find?
- Why is 3.0 called a "friendly number"?
- How is this like making change with money?
👥 Problem 3
Another helper problem!
Just like the first problem! Taking away 20 cents from $4.20 leaves us with exactly $4.00—a friendly whole number!
Number Line Model
👥 Problem 4
Use Problem 3 to help!
- 1 First, subtract 0.2 to get to 4.0 (the friendly number!)
- 2 We still need to subtract 0.1 more (because 0.2 + 0.1 = 0.3)
- 3 4.0 − 0.1 = 3.9
In money terms: We're taking away 2 dimes, then 1 more dime!
Number Line Model
💵 Hundredths: Pennies!
Now we're working with dollars AND cents
When decimals have two places, think of the second place as pennies!
7.46
7 dollars, 4 dimes, 6 pennies
= $7.46
0.52
0 dollars, 5 dimes, 2 pennies
= 52 cents
The friendly number is still the nearest whole dollar!
👥 Problem 5
Dollars and cents!
Think about it: If you have $7.46 and spend exactly 46 cents, you're left with exactly $7.00!
The 46 cents is all the "extra" beyond the whole dollar.
Number Line Model
👥 Problem 6
Use Problem 5 to help!
- 1 First, subtract 0.46 to get to 7.00 (the friendly number!)
- 2 We still need to subtract 0.06 more (because 0.46 + 0.06 = 0.52)
- 3 7.00 − 0.06 = 6.94
Think of it as: Take away 46 pennies to get to $7, then take away 6 more pennies!
Number Line Model
💬 Turn & Talk
Why does thinking about money help us subtract decimals?
Consider:
- What does the number before the decimal represent?
- What do the numbers after the decimal represent?
- Why is it easier to think "46 cents" instead of "0.46"?
🚀 Challenge Time!
No helper problems—YOU find the friendly number!
For the next problems, there's no helper problem.
You need to figure out the friendly number on your own!
- 1 Look at the starting number
- 2 Find the nearest whole number (friendly number)
- 3 Figure out how to break up your subtraction to get there first
✏️ Problem 7
Try this one on your own!
Hint: What's the friendly number near 1.82?
The friendly number near 1.82 is 1.00!
- 1 First, subtract 0.82 to get to 1.00
- 2 We still need to subtract 0.01 more (because 0.82 + 0.01 = 0.83)
- 3 1.00 − 0.01 = 0.99
In money: Remove 82 cents to get to $1, then remove 1 more penny!
Number Line Model
✏️ Problem 8
Final challenge!
Hint: You might need more than two jumps!
The friendly number near 28.32 is 28.00!
- 1 First, subtract 0.32 to get to 28.00
- 2 We still need to subtract 0.16 more (because 0.32 + 0.16 = 0.48)
- 3 Break it up: subtract 0.10 to get 27.90
- 4 Then subtract 0.06 to get 27.84
Number Line Model
📝 Key Takeaways
Today we learned the "Get to a Friendly Number" strategy!
- 1 Identify the friendly number — the nearest whole number
- 2 Jump to the friendly number first — subtract to get there
- 3 Then subtract what's left — finish the subtraction
💡 Pro Tip
Thinking about decimals as money makes it easier to visualize what you're taking away!
🎫 Exit Ticket
Show what you learned!
5.6 − 0.8
Use the friendly number strategy. Show your jumps!
6.35 − 0.47
Think about money! What's the friendly number?
Why is it helpful to "get to a friendly number" when subtracting decimals?