Subtracting Decimals for 5th Grade: Regrouping and Practice

Subtracting decimals is essential for finding differences in money, measurements, and quantities. In Grade 5, students subtract decimals to hundredths or thousandths by aligning decimal points and subtracting place by place, with regrouping (borrowing) when needed. The key is to align decimal points so that tenths are subtracted from tenths, hundredths from hundredths, and so on. This skill helps students find change, compare lengths, compute differences in weights or times, and solve real-world problems.

When we subtract decimals, we use the same place-value logic as whole numbers: we subtract ones from ones, tenths from tenths, and hundredths from hundredths. The decimal point in the difference goes directly below the decimal points in the minuend and subtrahend. If the numbers have different numbers of decimal places, append zeros to the right of the shorter decimal so that we can subtract place by place. Regroup (borrow) when a digit in the minuend is smaller than the corresponding digit in the subtrahend.

DETAILED EXPLANATION

Steps to subtract decimals:

1. Write the numbers vertically with the larger number on top and decimal points aligned. Use additional zeros on the right if needed so both numbers have the same number of decimal places.

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2. Subtract from right to left, place by place. Regroup (borrow) when the digit on top is smaller than the digit below.

3. Place the decimal point in the difference directly below the decimal points in the original numbers.

4. Check by adding the difference and the subtrahend; the result should equal the minuend.

Example: 5.75 − 2.38. Align: 5.75 − 2.38. Subtract: 5−8 requires regrouping: 15−8=7; 6−3=3; 5−2=3. Difference: 3.37.

WORKED EXAMPLES WITH STEP BY STEP SOLUTIONS

Example 1

Maya had $5.75. She spent $2.38. How much does she have left?

Solutions:

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Step 1: We need to subtract 2.38 from 5.75. Write vertically with decimal points aligned:

5.75

– 2.38

Step 2: Subtract from right to left. Hundredths: 5 − 8. We need to regroup. Borrow 1 from the tenths (7 becomes 6). 15 − 8 = 7. Write 7.

Step 3: Tenths: 6 − 3 = 3. Write 3.

Step 4: Ones: 5 − 2 = 3. Write 3.

Step 5: Place the decimal point in the difference directly below the others. Difference: 3.37.

Step 6: Maya has $3.37 left.

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Answer: $3.37

Example 2

Subtract 12.5 − 3.67

Solutions:

Step 1: Write 12.5 as 12.50 so both numbers have two decimal places. Align:

12.50

– 3.67

Step 2: Hundredths: 0 − 7. Regroup. Borrow from tenths (5→4). 10 − 7 = 3. Write 3.

Step 3: Tenths: 4 − 6. Regroup. Borrow from ones (2→1). 14 − 6 = 8. Write 8.

Step 4: Ones: 1 − 3. Regroup. Borrow from tens (1→0). 11 − 3 = 8. Write 8.

Step 5: Tens: 0 − 0 = 0 (we don’t write leading zeros). Place decimal point. Difference: 8.83.

Answer: 8.83

Example 3

A rope is 10.0 meters. 3.456 meters is cut off. How much remains?

Solutions:

Step 1: Subtract 3.456 from 10.0. Write 10.0 as 10.000 so both have three decimal places. Align:

10.000

– 3.456

Step 2: Thousandths: 0 − 6. Regroup. Borrow from hundredths. 10 − 6 = 4. Write 4.

Step 3: Hundredths: 9 − 5 = 4 (after borrowing). Tenths: 9 − 4 = 5. Ones: 9 − 3 = 6. Tens: 0 − 0 = 0.

Step 4: Difference: 6.544 meters.

Answer: 6.544 meters

Example 4

Subtract 5.2 − 2.87

Solutions:

Step 1: Write 5.2 as 5.20. Align:

5.20

– 2.87

Step 2: Hundredths: 0 − 7. Regroup. 10 − 7 = 3. Tenths: 1 − 8. Regroup. 11 − 8 = 3. Ones: 4 − 2 = 2.

Step 3: Difference: 2.33.

Answer: 2.33