PSLE Mathematics Learning Guide · Guide 53 · Companion to Guide 17
Return to the PSLE Learning Guide · Parent guide: Whole-Number Place Value
Multiplying a whole number by 10, 100 or 1000 is often taught as “add zeros”. Dividing is often taught as “cancel zeros”. Those shortcuts can produce correct answers in familiar examples, but they hide the reason the method works and become unreliable when the factor is 30, 400 or 5000, when a quotient is not an exact whole number, or when the learner later meets decimals.
The stronger idea is place value.
When a number is multiplied by 10, every digit represents ten times its previous value. When it is divided by 10, every digit represents one tenth of its previous value. Multiplication by 100 or 1000 applies the same scaling by two or three powers of ten.
This guide is a narrow companion to Guide 17: Keep Whole-Number Place Value Stable Through Large Calculations. It does not replace that broader owner. It drills the Primary 5 syllabus skill of multiplying and dividing whole numbers by 10, 100, 1000 and their multiples without calculator.
The MOE Primary Mathematics syllabus updated October 2025 provides current curriculum context. All examples and solutions below are original eduKate teaching material.
Start with place value, not a zero rule
Take 347.
347 means:
- 3 hundreds = 300;
- 4 tens = 40;
- 7 ones = 7.
Multiply by 10:
347 × 10 = 3470.
Now the same digits represent:
- 3 thousands = 3000;
- 4 hundreds = 400;
- 7 tens = 70.
Each digit’s value became ten times as large. The zero in the ones place is a consequence of the scaling, not the mathematical cause.
Multiply by 100 and 1000 as repeated ×10 scaling
54 × 100 means 54 × 10 × 10.
54 × 10 = 540.
540 × 10 = 5400.
So 54 × 100 = 5400.
Similarly:
82 × 1000 = 82 × 10 × 10 × 10 = 82 000.
The power of ten tells you how many place-value scales occur.
Division reverses the scaling
6300 ÷ 10 = 630 because 630 × 10 = 6300.
6300 ÷ 100 = 63 because 63 × 100 = 6300.
63 000 ÷ 1000 = 63 because 63 × 1000 = 63 000.
Use multiplication as the inverse check whenever a division answer feels uncertain.
Why “cancel zeros” is incomplete
For 7200 ÷ 100, crossing out two final zeros happens to give 72. But the valid reason is that 7200 is being scaled by one hundredth.
Now consider 7250 ÷ 100. There are not two final zeros to cancel. The exact quotient is 72.5, outside a whole-number-only result. A zero-cancellation rule cannot explain the structure.
In a whole-number calculation task, the question may be chosen so the quotient is a whole number. The underlying place-value relationship should still remain correct even when a later problem crosses into decimal notation.
A multiple such as 30 can be factorised
30 = 3 × 10.
Therefore:
240 × 30 = 240 × 3 × 10.
240 × 3 = 720.
720 × 10 = 7200.
This is usually clearer than treating 30 as a mysterious special case.
Multiply by 400 as ×4 then ×100
125 × 400 = 125 × 4 × 100.
125 × 4 = 500.
500 × 100 = 50 000.
A quick estimate agrees: 100 × 400 = 40 000, so 50 000 is plausible.
Multiply by 5000 through factors
36 × 5000 = 36 × 5 × 1000.
36 × 5 = 180.
180 × 1000 = 180 000.
The factors expose a manageable mental calculation followed by place-value scaling.
Division by a product can be split into factor divisions
8400 ÷ 30.
Because 30 = 3 × 10:
8400 ÷ 30 = 8400 ÷ 10 ÷ 3.
8400 ÷ 10 = 840.
840 ÷ 3 = 280.
Check: 280 × 30 = 8400.
Choose an order that keeps the arithmetic easy
48 000 ÷ 400.
400 = 4 × 100.
48 000 ÷ 100 = 480.
480 ÷ 4 = 120.
Equally, 48 000 ÷ 4 = 12 000, then ÷100 = 120. Both are valid because division by 400 is division by the product 4×100.
Check whether a whole-number quotient is expected
750 ÷ 20 = 37.5, not 37 remainder 10 if the task allows a decimal quotient.
However, a whole-number context may ask how many complete groups of 20 can be formed from 750, in which case 37 complete groups and 10 remaining may be the relevant interpretation.
Guide 51 develops remainders in context. The current guide focuses on the scaling calculation itself.
Use distributive structure for awkward multiples
Example: 47 × 60.
60 = 6 × 10.
47 × 6 = 282.
282 × 10 = 2820.
Another route:
47 × (50 + 10) = 2350 + 470 = 2820.
Equivalent methods are useful as cross-checks, but factorising into a small whole number and a power of ten is often the most efficient route for this syllabus skill.
Build inverse pairs deliberately
If 64 × 300 = 19 200, then:
19 200 ÷ 300 = 64.
19 200 ÷ 64 = 300.
Writing the inverse relation turns a memorised product into a connected multiplication-division fact family.
Estimate before accepting a large answer
398 × 200.
Estimate 400 × 200 = 80 000.
Exact calculation: 398 × 2 × 100 = 796 × 100 = 79 600.
The exact answer lies close to the estimate. An answer such as 7960 would be ten times too small and should be rejected.
A place-value table makes the scaling visible
| Number | ×10 | ×100 | ×1000 |
|---|---|---|---|
| 23 | 230 | 2300 | 23 000 |
| 406 | 4060 | 40 600 | 406 000 |
| 7005 | 70 050 | 700 500 | 7 005 000 |
Notice 7005 × 10 = 70 050. The internal zeros stay in their structural places. A rule such as “just put a zero somewhere” is not precise enough.
Main worked workshop: twenty original calculations
1.
428 × 10.
Answer: 4280.
2.
428 × 100.
Answer: 42 800.
3.
428 × 1000.
Answer: 428 000.
4.
65 000 ÷ 10.
Answer: 6500.
5.
65 000 ÷ 100.
Answer: 650.
6.
65 000 ÷ 1000.
Answer: 65.
7.
320 × 40.
Reasoning: 320×4×10 = 1280×10 = 12 800.
8.
75 × 600.
Reasoning: 75×6×100 = 450×100 = 45 000.
9.
42 × 3000.
Answer: 126 000.
10.
9600 ÷ 30.
Answer: 320.
11.
72 000 ÷ 600.
Answer: 120.
12.
450 000 ÷ 5000.
Answer: 90.
13.
A learner writes 405 × 100 = 40 5000.
Repair: each digit scales two places: 40 500.
14.
A learner writes 70 040 ÷ 10 = 704.
Repair: 70 040 ÷ 10 = 7004. The internal zero structure matters.
15.
215 × 80.
Answer: 215×8×10 = 1720×10 = 17 200.
16.
36 000 ÷ 80.
Answer: 36 000÷10÷8 = 3600÷8 = 450.
17.
999 × 1000.
Answer: 999 000.
18.
999 000 ÷ 3000.
Answer: 333.
19.
125 × 240.
Reasoning: 240=24×10; 125×24=3000; ×10=30 000.
20.
84 000 ÷ 240.
Reasoning: 240×350=84 000, so quotient 350. One route is ÷24 then ÷10 when the intermediate arithmetic is convenient.
Diagnose the type of error
Place-value error: answer differs by a factor of 10, 100 or 1000.
Factor error: learner handles ×100 correctly but calculates ×6 incorrectly in ×600.
Operation-order error: learner confuses ÷30 with ÷3×10.
Context error: numerical quotient is correct but the practical whole-group answer is interpreted incorrectly.
These are different repairs. Do not prescribe more zero-adding practice for a learner whose actual problem is division facts.
Why ÷30 is not ÷3×10
8400 ÷ 30 = 280.
But 8400 ÷ 3 × 10 = 2800 × 10 = 28 000.
Division by a product means divide by every factor:
8400 ÷ (3×10) = 8400 ÷3 ÷10, or ÷10 ÷3.
Keep the product grouped conceptually.
Numbers with internal zeros reveal true understanding
Try:
- 5006 × 100 = 500 600;
- 40 080 × 10 = 400 800;
- 700 500 ÷ 100 = 7005.
These examples prevent the learner from treating visible trailing zeros as the entire method.
Application: repeated cartons
A warehouse packs 240 pencils into one large carton. There are 300 cartons.
Total pencils = 240 × 300.
300 = 3×100.
240×3=720; ×100=72 000 pencils.
Check by estimating 200×300=60 000 and 300×300=90 000. The exact answer lies between them.
Application: number of equal batches
A printer produces 48 000 sheets. Each batch contains 400 sheets.
Number of batches = 48 000 ÷ 400 = 120 batches.
Check: 120×400=48 000.
Independent transfer check
- 706×10
- 706×1000
- 560 000÷100
- 63 000÷1000
- 125×60
- 84×700
- 36 000÷40
- 96 000÷800
- Explain why 340×300 can be treated as 340×3×100.
- Explain why 72 000÷600 can be checked using multiplication.
- A product is about 90 000. Which is more plausible: 448×200=8960 or 89 600? Explain.
- Give an example showing why “cancel zeros” is not a complete rule for division by 100.
Independent-check answers
1. 7060.
2. 706 000.
3. 5600.
4. 63.
5. 7500.
6. 58 800.
7. 900.
8. 120.
9. Because 300=3×100, so the multiplication can be factorised without changing the product.
10. If quotient is 120, then 120×600 should rebuild 72 000.
11. 89 600; 448 is near 450 and 450×200=90 000.
12. 7250÷100=72.5; there are not two trailing zeros to cancel.
Parent and tutor guide
Begin with a place-value table and ask what each digit is worth before and after ×10. Then remove the table and keep the explanation.
Introduce multiples such as 30 or 400 only after powers of ten are secure. Ask the learner to factor the multiplier or divisor aloud: “30 is 3 times 10”; “400 is 4 times 100”.
Use inverse checks routinely. If the learner calculates 72 000÷600=120, ask them to prove it by 120×600.
Include internal-zero examples such as 7005×100. They reveal whether the child understands place value or is merely attaching zeros to the written string.
The learner’s final card
What power of ten is involved? How does each digit’s place value scale? Can I factor a multiple such as 300 into 3×100? If dividing by a product, did I divide by every factor? Does the inverse operation rebuild the original number?
Continue through Batch 14
Continue with Guide 54: Fraction Multiplication, Guide 55: Decimal Powers-of-Ten Scaling, and Guide 56: Straight-Line, Point and Vertically Opposite Angles.
Return to the PSLE Learning Guide Mathematics route.
Sources and boundaries
MOE Primary Mathematics syllabus, updated October 2025; SEAB 2026 PSLE formats.
This is a subordinate companion to Guide 17. All examples and worked solutions are original eduKate teaching material and are not official examination questions.