How to Subtract with Decimals: Solved Exercises for Grade 4

Master subtracting decimals: aligning decimal points, borrowing across zeros, and word problems through these 3 detailed exercises.

Solution: Exercises 1 to 3
1 Basic decimal subtraction
Exercise 1
Subtract:
\(8.75 - 3.23\)
Definition:

Decimal subtraction: Align decimal points and subtract each place value column

Subtraction method:
  1. Line up the decimal points
  2. Add zeros if needed to make columns match
  3. Subtract each column starting from the right
  4. Place the decimal point in the answer
Setup
\(8.75\)
\(−3.23\)
Subtraction
\(5.52\)
Step 1: Align decimal points

\(8.75\)
\(−3.23\)
\(\overline{~~~~~~}\)

Step 2: Subtract hundredths column

\(5 - 3 = 2\)

Step 3: Subtract tenths column

\(7 - 2 = 5\)

Step 4: Subtract ones column

\(8 - 3 = 5\)

\(8.75 - 3.23 = 5.52\)
Final answer:

\(8.75 - 3.23 = 5.52\)

Applied rules:

• Alignment: Always line up decimal points before subtracting

• Place value: Subtract digits in the same place value columns

• Decimal point: Place decimal point in the answer directly below others

2 Borrowing across zeros
Exercise 2
Subtract:
\(5.00 - 2.47\)
Definition:

Borrowing across zeros: When subtracting and the top digit is smaller, borrow from the next column

Setup
\(5.00\)
\(−2.47\)
Borrowing
\(4.99 + 0.01\)
Result
\(2.53\)
Step 1: Align decimal points

\(5.00\)
\(−2.47\)
\(\overline{~~~~~~}\)

Step 2: Need to borrow in hundredths

We can't subtract \(7\) from \(0\), so we borrow from tenths

Step 3: Borrow from tenths

Tenths has \(0\), so we borrow from ones: \(5.00 = 4.99 + 0.01\)

Step 4: Complete subtraction

Hundredths: \(10 - 7 = 3\)
Tenths: \(9 - 4 = 5\)
Ones: \(4 - 2 = 2\)

\(5.00 - 2.47 = 2.53\)
Final answer:

\(5.00 - 2.47 = 2.53\)

Applied rules:

• Borrowing rule: When top digit is smaller, borrow from next higher place value

• Zero borrowing: If a zero needs to borrow, it becomes \(9\) and borrows from the next column

• Decimal point: Keep aligned in final answer

3 Word problem
Exercise 3
Sarah had $12.50. She bought a book for $7.85. How much money does she have left?
Definition:

Word problem: Identify key information and convert to mathematical expression

Initial amount
\$12.50
Amount spent
\$7.85
Money left
\$4.65
Step 1: Identify the operation

Money left = Initial money − Money spent

\$12.50 − \$7.85

Step 2: Set up subtraction

\(12.50\)
\(−7.85\)
\(\overline{~~~~~~}\)

Step 3: Subtract hundredths

We can't subtract \(5\) from \(0\), so we borrow: \(12.50 = 12.49 + 0.01\)

\(10 - 5 = 5\)

Step 4: Continue subtraction

Tenths: \(4 - 8\) (borrow from ones): \(14 - 8 = 6\)
Ones: \(11 - 7 = 4\)
Tens: \(1 - 0 = 1\)

Sarah has \$4.65 left
Final answer:

Sarah has \$4.65 left

Applied rules:

• Problem solving: Identify operation from context ("left" indicates subtraction)

• Decimal alignment: Align decimal points when subtracting money

• Borrowing: Use when top digit is smaller than bottom digit

Decimal Subtraction Rules and Methods
\(8.75 - 3.23 = 5.52\)
Basic Decimal Subtraction
Rule 1
Align Decimal Points
Always line up decimal points before subtracting
Rule 2
Borrow When Needed
If top digit is smaller, borrow from next column
Rule 3
Same Place Values
Subtract digits in the same place value columns
Key definitions:

Decimal: A number that has a decimal point separating whole numbers from fractional parts

Decimal point: The dot that separates the whole number part from the fractional part

Place value: The value of a digit based on its position (ones, tenths, hundredths, etc.)

Complete methodology:
  1. Read the problem: Understand what is being asked
  2. Identify numbers: Find the decimal numbers to subtract
  3. Align decimals: Line up decimal points vertically
  4. Fill in zeros: Add zeros to make columns match if needed
  5. Subtract column by column: Start from the rightmost column
  6. Place decimal point: Put it directly below the others
Tip 1: Always align decimal points first - this is the most important step!
Tip 2: Add zeros at the end of shorter decimals to make subtraction easier.
Tip 3: Check your answer by adding the result to the number you subtracted.
Tip 4: When borrowing across zeros, turn zeros into nines and borrow from the next non-zero digit.
Common errors: Misaligning decimal points, forgetting to borrow, subtracting bottom from top regardless of size.
Practice tips: Start with simple decimals, practice borrowing across zeros, use money examples for real-world context.
Decimal Subtraction: Key Concepts and Practice
\(5.00 - 2.47 = 2.53\)
Borrowing Across Zeros
Place Values
Ones.Tenths.Hundredths
Position determines value of each digit
Borrowing Rule
Borrow 1 from Left
When top digit is smaller than bottom digit
Checking Answer
Add Result Back
Verify by adding difference to subtracted amount
More definitions:

Minuend: The number being subtracted from (top number)

Subtrahend: The number being subtracted (bottom number)

Difference: The result of the subtraction

Steps for borrowing across zeros:
  1. Look at the column where you need to borrow
  2. If the digit is zero, move to the next non-zero digit to the left
  3. Decrease that digit by 1
  4. Turn all zeros in between into nines
  5. Now you can borrow from the rightmost zero
Memory aid: "If you see a zero, go to the hero!" - borrow from the first non-zero digit to the left.
Real world: Think of decimal subtraction as taking away money, weight, or distance.
Important facts to remember:

• Always align decimal points before subtracting

• Add zeros to make decimal places equal if needed

• When borrowing, decrease the left digit by 1

• The decimal point in the answer lines up with the others

• Check your answer by adding the difference to the subtrahend

Questions & Answers

Question: Why is it important to line up the decimal points when subtracting decimals? Can't I just subtract them like regular numbers?

Answer: Great question! Lining up decimal points is crucial because it ensures you're subtracting digits with the same place value. Look at this example:

Without lining up:
8.75
-3.2
----
5.72 ← This is wrong!

With decimal points lined up:
8.75
-3.20 ← Added zero to make columns match
----
5.55 ← This is correct!

When you don't align decimal points, you might subtract tenths from ones or hundredths from tenths, which gives incorrect results. The decimal point acts as a reference point that keeps place values organized.

Question: My child gets confused when subtracting decimals like 5.00 - 2.47. How can I help them understand borrowing across zeros?

Answer: Borrowing across zeros can be tricky! Here's a helpful approach:

Visual method: Think of 5.00 as 500 hundredths. Then subtract 247 hundredths from 500 hundredths, which equals 253 hundredths or 2.53.

Step-by-step:

  • Start at the rightmost column (hundredths): Can't subtract 7 from 0
  • Move to tenths: Can't subtract 4 from 0
  • Go to ones: Borrow 1 from 5, making it 4
  • This turns the 0 in tenths into 10, then borrow 1 from that, making it 9
  • The 0 in hundredths becomes 10, now you can subtract: 10-7=3

A fun memory trick: "If you see a zero, go to the hero!" - borrow from the first non-zero digit to the left.

Question: How can I check if my decimal subtraction is correct? I want to make sure I got the right answer.

Answer: There's a great way to check your decimal subtraction answers! It's called the "addition check" method:

Example: If you calculated 8.75 - 3.23 = 5.52

Check: Add your answer (5.52) to the number you subtracted (3.23)
5.52 + 3.23 = 8.75 ✓

If your addition gives you back the original number (8.75), then your subtraction was correct!

Another quick check: Estimate the answer first. For 8.75 - 3.23, think "about 9 - 3 = 6", so your answer should be close to 6. Since 5.52 is close to 6, that's another sign your answer is reasonable.