Grade 5 Mathematics Numbers – Subtraction Notes
Mathematics — Numbers
Subtopic: Subtraction (for age 10 / Kenyan context)
Subtraction means taking away or finding the difference between two numbers. We write it like this:
Minuend − Subtrahend = Difference
Example: 8 − 3 = 5 (we take away 3 from 8, leaving 5)
- Minuend: the number you start with (e.g., 8 in 8 − 3)
- Subtrahend: the number you take away (e.g., 3)
- Difference: the answer (e.g., 5)
- Take away, less than, subtract
- Take away objects (concrete): Remove items and count what remains.
- Use a number line: Count backwards from the minuend by the subtrahend.
- Use the vertical method (column subtraction) for larger numbers.
🍎 🍎 🍎 🍎 🍎
Start with 5 apples. Take away 2 apples: 🍎 🍎 removed → 3 left.
5 − 2 = 3
0
1
2
3
4
5
6
7
8
9
10
To do 9 − 4 on the number line: start at 9, count back 4 jumps: 9 → 8 → 7 → 6 → 5. So 9 − 4 = 5.
Example: 523 − 214
523
− 214
------
309
− 214
------
309
Work: 3−4 can't do, but here each column subtracts without borrowing: 3−4 would need borrowing, so choose an example without borrowing. For 523−214: 3−4 is not valid, so choose 3−4? Correction: Example chosen should show no regrouping — use 732−214 = 518.
Correct no-regroup example:
732
− 214
------
518
Explanation: 2−4 (units) not needed because units 2 ≥ 4? (Note: in 732−214: units 2 < 4, so borrowing happens). To be clear, use 743 − 214 below (no borrow needed in any column).
− 214
------
518
743
− 214
------
529
Work: Units 3−4? (again wrong) — to avoid confusion, we present a simple no-borrow example: 865 − 423 = 442.
− 214
------
529
865
− 423
------
442
Work: 5−3 = 2 (units), 6−2 = 4 (tens), 8−4 = 4 (hundreds).
− 423
------
442
Example: 732 − 458
732
− 458
------
?
Steps:
− 458
------
?
- Start at units: 2 − 8. 2 is less than 8, so we borrow 1 ten from 3 (tens).
- Now tens: 3 becomes 2, and units become 12. Units: 12 − 8 = 4.
- Tens: now 2 − 5. 2 is less than 5, so borrow 1 hundred from 7 (hundreds).
- Hundreds: 7 becomes 6, tens become 12. Tens: 12 − 5 = 7.
- Hundreds: 6 − 4 = 2.
732
− 458
------
274
− 458
------
274
Example: 500 − 278
500
− 278
------
?
Steps:
− 278
------
?
- Units: 0 − 8 → cannot, borrow from tens; but tens is 0 → must borrow from hundreds.
- Borrow 1 hundred: 5 → 4 hundreds. Tens becomes 10, then borrow 1 ten to units: tens 10 → 9, units become 10.
- Units: 10 − 8 = 2. Tens: 9 − 7 = 2. Hundreds: 4 − 2 = 2.
- Subtract in parts: 63 − 27 = (63 − 20) − 7 = 43 − 7 = 36.
- Use addition to check subtraction: if 36 + 27 = 63 then 63 − 27 = 36.
- Round and adjust: 500 − 279 ≈ 500 − 280 = 220, then add 1 → 221.
- Wanjiru had KSh 600. She bought a school bag for KSh 265. How much money did she have left?
600 − 265 = 335. She had KSh 335 left.
- A bus carried 72 passengers. 19 got off at the first stop and 14 at the second. How many stayed on the bus?
After first stop: 72 − 19 = 53. After second: 53 − 14 = 39. So 39 passengers remained.
- At a market, Peter sold 120 oranges. He had 350 to start with. How many oranges are left?
350 − 120 = 230 oranges left.
Work out these subtraction questions (show working):
- 86 − 29 = ?
- 504 − 178 = ?
- 900 − 467 = ?
- 745 − 389 = ?
- 63 − 47 = ?
- 1,200 − 678 = ?
- 421 − 205 = ?
- 50 − 18 = ?
- 1,000 − 1 = ?
- Sandra had KSh 850. She bought shoes for KSh 299 and a book for KSh 120. How much money is left?
- 86 − 29 = 57
- 504 − 178 = 326
- 900 − 467 = 433
- 745 − 389 = 356
- 63 − 47 = 16
- 1,200 − 678 = 522
- 421 − 205 = 216
- 50 − 18 = 32
- 1,000 − 1 = 999
- 850 − 299 − 120 = 431 (After first purchase: 851? No: 850−299=551; then 551−120=431)
- Always line up the digits by place value (units under units, tens under tens).
- When borrowing, reduce the next column by 1 and add 10 to the column you borrow into.
- Check your answer by adding the difference and the subtrahend. The result should equal the minuend.
- Take care with zeros — borrow from the next non-zero column.