➕➖ Add and Subtract Decimals - Grade 5
Complete notes & formulae for Grade 5 Math
Core Concepts
- Adding decimals means combining (finding the sum of) two or more decimal numbers.
- Subtracting decimals means finding the difference between two decimal numbers.
- Always line up decimal points before adding or subtracting.
1️⃣ Addition of Decimals
Steps for Addition
- 1 Write numbers in a column lining up the decimal points.
- 2 Add zeros as placeholders if the numbers don’t have the same number of decimal places.
- 3 Add digit by digit starting from the right (smallest place value).
- 4 Place the decimal point directly below the others in your answer.
Example: \( 5.34 + 2.7 \)
- Line up the decimals:
\(5.34\)
+\(2.70\) - Add: \(4 + 0 = 4\), \(3 + 7 = 10\) (write 0, carry 1), \(5 + 2 + 1 = 8\).
- Write the decimal point in the answer: \(5.34 + 2.7 = 8.04\)
Addition Formula
\( a.bcd + x.yz = \) (Line up decimals and add digit by digit)
2️⃣ Subtraction of Decimals
Steps for Subtraction
- 1 Write the numbers lining up the decimal points.
- 2 Add zeros as placeholders if needed.
- 3 Subtract digit by digit starting from the right.
- 4 Put the decimal point directly under the others in your answer.
Example: \( 16.28 - 4.3 \)
- Pad to equal decimal places:
\(16.28\)
−\(4.30\) - Subtract: \(8 - 0 = 8\), \(2 - 3 =\) can't do, borrow: \(12 - 3 = 9\), \(15 - 4 = 11\) (if needed for bigger numbers).
- Answer: \(16.28 - 4.3 = 11.98\)
Subtraction Formula
\( x.yz - a.bc = \) (Line up decimals and subtract digit by digit)
3️⃣ Visual: Using Base 10 Blocks
- Simplest way to see decimal operations is with base 10 blocks.
- One block = 1 unit, rod = 0.1 (1/10), small cube = 0.01 (1/100)
- Add or take away blocks to visualize decimal addition/subtraction.
(Try using an online base 10 blocks tool or printables.)
4️⃣ Properties of Decimal Addition
- Commutative property: \(a + b = b + a\)
- Associative property: \((a + b) + c = a + (b + c)\)
- Identity property: \(a + 0 = a\)
Example (Using properties):
\(0.4 + 0.2 + 0.6 = (0.4 + 0.6) + 0.2 = 1.0 + 0.2 = 1.2\)
\(0.4 + 0.2 + 0.6 = (0.4 + 0.6) + 0.2 = 1.0 + 0.2 = 1.2\)
5️⃣ Compensation Strategy
Compensation means rearranging for easier mental math:
- For \(2.9 + 0.7\), think: \(2.9 + 1 = 3.9\), but subtract 0.3 (since you added 0.3 too much): \(3.9 - 0.3 = 3.6\).
- For \(5.2 - 1.8\), think: \(5.2 - 2 = 3.2\), then add back 0.2: \(3.2 + 0.2 = 3.4\).
6️⃣ Estimating Sums and Differences
Rounding:
- Round decimals to the nearest whole, tenth, or hundredth for quick estimates.
- Rules for rounding decimals:
- If the digit to the right is 5 or more, round up.
- If it is 4 or less, round down.
- Benchmarks: Use familiar numbers like 0, 0.25, 0.5, 0.75, 1 as quick estimates.
Estimate: \( 6.78 + 2.14 \approx 7 + 2 = 9 \)
Estimate: \( 5.43 - 1.97 \approx 5 - 2 = 3 \)
Overestimates & Underestimates:
Overestimate: Your estimate is larger than the actual answer.
Underestimate: Your estimate is smaller than the actual answer.
Use rounding or benchmarks as appropriate.
Overestimate: Your estimate is larger than the actual answer.
Underestimate: Your estimate is smaller than the actual answer.
Use rounding or benchmarks as appropriate.
7️⃣ Word Problems & Comparing Sums or Differences
Example 1: Pari walks \(2.15\) km in morning, \(1.35\) km in evening. How far in total?
Solution: \(2.15 + 1.35 = 3.50\) km.
Example 2: A bottle had \(5.60\) L of water. \(2.05\) L was used. How much is left?
Solution: \(5.60 - 2.05 = 3.55\) L.
Solution: \(2.15 + 1.35 = 3.50\) km.
Example 2: A bottle had \(5.60\) L of water. \(2.05\) L was used. How much is left?
Solution: \(5.60 - 2.05 = 3.55\) L.
Comparing sums:
Which is greater: \(4.29 + 3.8\) or \(8.01 – 0.1\)?
\(4.29 + 3.8 = 8.09\); \(8.01 – 0.1 = 7.91\); so, \(4.29 + 3.8\) is greater.
Which is greater: \(4.29 + 3.8\) or \(8.01 – 0.1\)?
\(4.29 + 3.8 = 8.09\); \(8.01 – 0.1 = 7.91\); so, \(4.29 + 3.8\) is greater.
8️⃣ Sequence & Completing Equations
Find missing numbers:
- \(x + 1.42 = 3.71 \implies x = 3.71 - 1.42 = 2.29\)
- \(5.5 - x = 2.3 \implies x = 5.5 - 2.3 = 3.2\)
9️⃣ Quick Reference Table
| Core Operation | Key Step |
|---|---|
| Add decimals | Line up decimal points, add digits, carry over |
| Subtract decimals | Line up decimal points, subtract digits, borrow if needed |
| Estimate sum/difference | Round or use benchmarks before adding/subtracting |
| Properties | Commutative, Associative, Identity (for addition) |
Practice Problems!
- \(3.25 + 7.1 =\) _____
- \(4.05 - 0.29 =\) _____
- \(6.39 + 0.6 + 2 =\) _____
- Estimate: \(4.96 + 2.05 \approx\) _____
- Solve for \(x\): \(x + 0.75 = 1.2\)
Answers: 1) 10.35 2) 3.76 3) 8.99 4) 5 + 2 = 7 5) \(x = 0.45\)