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Primary 5 Maths | Multiplying and Dividing Decimals: a Tutor Prep Guide | Place counts, scaling and rounding
The long multiplication is right but the decimal point lands anywhere: 0.4 times 3 becomes 0.12 and 3.6 divided by 0.4 becomes 0.9. The fault is in counting places, not in the tables.
Objectives — By the end the student can: (1) multiply a decimal by a whole number and say the product takes its place count from the decimal, so 0.4 times 3 is 1.2; (2) multiply two decimals by working as whole numbers, 25 times 4 is 100, and two decimal places make it 1.00, so 2.5 times 0.4 is 1; (3) divide a decimal by a whole number, 12.6 over 3 giving 4.2 with the point aligned; (4) divide by a decimal by scaling both numbers by ten, 3.6 over 0.4 becoming 36 over 4, which is 9; (5) round only at the end, 4.37 to one decimal place being 4.4.
01 Prerequisites (3-minute check)
If any of these fails, fix it before the lesson starts.
| Skill | Quick check | Pass mark |
|---|---|---|
| Whole-number multiplication | 25 times 4 | 100 |
| Decimal place value | How many tenths are in 0.4 | 4 tenths |
| Rounding | 4.37 to one decimal place | 4.4 |
02 Lesson flow (45 minutes)
| Time | Stage | Tutor does | Student does |
|---|---|---|---|
| 0-5 min | Diagnose | Ask for 0.4 times 3 | They say 1.2 or 0.12 |
| 5-15 min | Decimal times whole | Treat 4 times 3 as 12, then place one decimal | Get 1.2 |
| 15-25 min | Decimal times decimal | 25 times 4 is 100, two places gives 1.00 | Get 1 |
| 25-33 min | Decimal divisor | Scale 3.6 and 0.4 both by ten | Get 9 |
| 33-40 min | Rounding | Round 4.37 to one decimal place | Get 4.4 |
| 40-45 min | Exit check | Mark three questions at once | Work independently |
03 Teaching script (read it out)
Scene 1: The product takes the place count of both factors
Do not mention the point at first. Read 0.4 as 4 tenths, so 4 tenths times 3 is 12 tenths, which is 1.2.
The rule is not “put the point somewhere”, it is “count the decimal places in both factors and give the product that many”. 0.4 has one place and 3 has none, so the product has one: 1.2.
For 2.5 times 0.4 the factors carry two places together, so work 25 times 4 as 100 and place two: 1.00, which is 1.
The rule is not “put the point somewhere”, it is “count the decimal places in both factors and give the product that many”. 0.4 has one place and 3 has none, so the product has one: 1.2.
For 2.5 times 0.4 the factors carry two places together, so work 25 times 4 as 100 and place two: 1.00, which is 1.
Student should do: work 0.4 times 3 and 2.5 times 0.4, saying the total place count before writing the answer.
Scene 2: A decimal divisor is cleared by scaling both numbers
Division asks how many of one fit inside the other. How many 0.4 fit in 3.6 is hard to see, so multiply both numbers by 10: 36 over 4, which is 9, and the quotient is unchanged.
Why it works: scaling both is the same as multiplying numerator and denominator by 10, so the value stays. Students only need “both sides grow together”, never one side alone.
With two decimal places scale by 100: 8.4 over 1.2 becomes 84 over 12, which is 7.
Why it works: scaling both is the same as multiplying numerator and denominator by 10, so the value stays. Students only need “both sides grow together”, never one side alone.
With two decimal places scale by 100: 8.4 over 1.2 becomes 84 over 12, which is 7.
Student should do: rewrite 3.6 over 0.4 and 8.4 over 1.2 as whole-number divisions and say what each side was multiplied by.
Scene 3: Round at the very end, looking one place further
If the question asks for one decimal place, work to the second place and then decide. For 4.37 the second place is 7, which is 5 or more, so 4.3 becomes 4.4.
Rounding is the last step and is never done midway, or the error grows with every later operation.
Keep the number of places asked for: 4.4 is the answer, and 4.40 only when two places are requested.
Rounding is the last step and is never done midway, or the error grows with every later operation.
Keep the number of places asked for: 4.4 is the answer, and 4.40 only when two places are requested.
Student should do: round 4.37 to one decimal place and to the nearest whole number, naming the digit inspected.
04 Question types and worked steps
| Type | Example | Steps | Answer |
|---|---|---|---|
| Decimal times whole | 0.4 times 3 | Work 4 times 3 as 12 and place one decimal | 1.2 |
| Decimal times decimal | 2.5 times 0.4 | Work 25 times 4 as 100 and place two | 1 |
| Decimal over whole | 12.6 over 3 | 126 over 3 is 42, point aligned | 4.2 |
| Decimal divisor | 3.6 over 0.4 | Scale both by ten: 36 over 4 | 9 |
Sanity check (teach this): Sanity check: the decimal places in a product equal the places in the two factors combined, so 0.4 times 3 giving one place makes 1.2 right and 0.12 wrong; 2.5 times 0.4 carries two places, so 100 becomes 1.00; when the divisor is scaled the dividend must be scaled too, otherwise the quotient is out by ten and 3.6 over 0.4 becomes 0.9; an estimate catches this fast, since 3.6 over 0.4 is near 36 over 4, close to 9; 7.25 times 4 is near 7 times 4, so 29 is reasonable; rounding happens only at the end; the exit check allows 300 seconds for three questions at Primary 5.
05 Independent practice (3 questions)
| Question | Answer | What to watch |
|---|---|---|
| Multiply | 0.4 times 3 | 1.2 |
| Multiply | 7.25 times 4 | 29 |
| Divide | 3.6 over 0.4 | 9 |
| Divide | 5.6 over 0.7 | 8 |
06 Common mistakes and what to say
| Mistake | Student writes | Say this |
|---|---|---|
| Wrong place count | 0.4 times 3 answered as 0.12 | Both factors carry one decimal place in total, so the product has one. 0.4 is four tenths, and three lots is twelve tenths, which is 1.2. |
| Scaling only the divisor | 3.6 over 0.4 answered as 0.9 | Scale the dividend too. 36 over 4 is 9, not 0.9. |
| Point not aligned in division | 12.6 over 3 answered as 0.42 | Work 126 over 3 as 42, then put the point in line with the dividend: 4.2. |
| Rounding too early | 4.37 rounded to the whole number first | Rounding is the last move. Work to the second place, see the 7, and the answer is 4.4. |
07 Homework (paper, section and question numbers)
- Primary maths chapter index — All chapters by level
- Teaching guide index — Same structure, other subjects
- Redo this chapter — Questions 1 to 4 again, writing the total place count each time
08 Exit check (last 5 minutes)
| Question | Answer | Decision |
|---|---|---|
| 0.4 times 3 | 1.2 | Answering 0.12 means the place count is not secure; reteach act one |
| 3.6 over 0.4 | 9 | Answering 0.9 means only one side was scaled; reteach act two |
| 4.37 to one decimal place | 4.4 | Answering 4.3 means the wrong digit was read; reteach act three |
09 Tutor FAQ
Why scale the divisor at all?
Because “how many 0.4 fit in 3.6” is impossible to see. Multiplying both by ten gives 36 over 4, and the quotient is the same.
Do decimals in multiplication line up their points?
No. Multiplication lines up the last digits and counts places at the end; only division needs the point lined up with the dividend.
Why does rounding go wrong so often?
Make the student write down which digit is being inspected, then decide 0 to 4 or 5 to 9. Naming the place removes most errors.
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A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.