You will learn
- Divide a decimal by a whole number.
- Divide by 0.1, 0.5.
- Use multiplication to check.
- Solve simple problems.
Version 0.2 · expanded edition · expert review pending Standards alignment: pending verification. Written in the style of common primary school assessments. No exam result is promised.
Student lesson
- Divide a decimal by a whole number place by place.
- Dividing by 0.1 multiplies by 10.
- Dividing by 0.5 doubles.
- Check by multiplying.
Words to know
Number divided.
Number divided by.
Answer.
Same amount each.
1. Discover: sharing money
7.5 litres of juice are shared equally among 5 jugs. How much per jug?
2. Understand: dividing decimals
- 7.5 ÷ 5 = 1.5.
- 12.6 ÷ 3 = 4.2.
- 0.9 ÷ 3 = 0.3.
- 4.5 ÷ 0.5 = how many halves in 4.5? 9.
- 2 ÷ 0.4 = 5.
Idea 1: By whole
9.6 ÷ 4 = 2.4 because 4 × 2.4 = 9.6. 10.5 ÷ 5 = 2.1.
Idea 2: Tenths
0.9 ÷ 3: 9 tenths ÷ 3 = 3 tenths = 0.3.
Idea 3: By decimal
4.5 ÷ 0.5 = 9: how many halves in 4.5? 2 ÷ 0.4 = 20 ÷ 4 = 5.
Why bigger? Dividing by less than 1 gives more pieces.
3. Worked examples
Example 1 (I show you): Divide
9.6 ÷ 4
- 96 tenths ÷ 4.
Answer: 2.4
Example 2 (We do it together): Divide
4.5 ÷ 0.5
- How many halves?
Answer: 9
Example 3 (You try): Divide
2 ÷ 0.4
Show the steps and answer
- 20 ÷ 4.
Answer: 5
Did you know?
Dividing 4.5 by 0.5 is the same as multiplying by 2.
Why this matters
Dividing decimals shares money and measures equally.
4. Explore: share
You need paper.
- Write 7.5 ÷ 5.
- Divide 75 ÷ 5.
- Place the point.
- Check by multiplying.
Think about it: what did you notice?
1.5.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I divide ___ by ___.
- The quotient is ___.
- Check: ___ × ___ = ___.
- It makes sense because ___.
Guided practice
Question 1. 7.5 ÷ 5?
1.5.
Question 2. 12.6 ÷ 3?
4.2.
Question 3. 4.5 ÷ 0.5?
9.
Independent practice
Level 1: Start
- 9.6 ÷ 4
- 0.9 ÷ 3
- 4.5 ÷ 0.5
- 2 ÷ 0.4
- 10.5 ÷ 5
Level 2: Grow
- 6.4 ÷ 4
- 0.6 ÷ 2
- 3.5 ÷ 0.5
Level 3: Stretch
- 4.8 ÷ 0.6
- 12.6 ÷ 6
- Ben says 0.8 ÷ 4 = 2. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
7.5 L shared among 5 jugs. How much each?
Show a sample answer
1.5 L.
Another one. A ribbon of 7.5 m is cut into 5 equal pieces. How long is each piece?
Show a sample answer
7.5 ÷ 5 = 1.5 m
7. Common mistakes
Fix: Check by multiplying.
Fix: Check by multiplying.
Fix: Dividing by less than 1 gives a bigger answer.
8. Lesson summary and revision card
- I can divide a decimal by a whole number.
- I can divide by 0.1 and 0.5.
- I can check by multiplying.
- I can solve simple problems.
9. Check and master
Answer all 14 questions. You will see feedback after each one.
Your result appears here after you answer every question.
10. Key takeaways
- Divide as whole numbers.
- Check by multiplying.
- How many tenths fit.
11. Next lesson
Next lesson: Decimal applications. Keep going with the next idea in this course.
Exam practice
These questions are written in the style of common school and international primary assessments. Try them on your own, without looking back. Then check your answers in the marking guide. The marks are shown in brackets.
- Find 9.6 ÷ 4. [2 marks]
- Find 0.9 ÷ 3. [2 marks]
- Find 4.5 ÷ 0.5. [3 marks]
- Find 2 ÷ 0.4. [3 marks]
- Ali says 10.5 ÷ 5 = 21. Is he right? Explain. [3 marks]
Total: 13 marks.
Marking guide and model answers
- 96 tenths ÷ 4 = 24 tenths [1]; 2.4 [1]
- 9 tenths ÷ 3 = 3 tenths [1]; 0.3 [1]
- How many halves in 4.5 [1]; × 2 [1]; 9 [1]
- 2 ÷ 0.4 = 20 ÷ 4 [1]; 5 [1]; check 5 × 0.4 = 2 [1]
- No [1]. 10.5 ÷ 5 should be about 2 [1]. The answer is 2.1 [1].
Score guide: 12 to 13 = secure. 8 to 11 = nearly there, revise the parts you missed. Under 8 = work through the lesson again with a grown-up.
Printable worksheet
- 9.6 ÷ 4
- 0.9 ÷ 3
- 4.5 ÷ 0.5
- 2 ÷ 0.4
- 10.5 ÷ 5
- 7.5 ÷ 5 =
- 12.6 ÷ 3 =
- 0.9 ÷ 3 =
- 4.5 ÷ 0.5 =
- 2 ÷ 0.4 =
Homework
Divide five decimals by whole numbers.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 9.6 ÷ 4 | 2.4 | 2 |
| 0.9 ÷ 3 | 0.3 | 2 |
| 4.5 ÷ 0.5 | 9 | 2 |
| 2 ÷ 0.4 | 5 | 2 |
| 10.5 ÷ 5 | 2.1 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 2.4; 2 0.3; 3 9; 4 5; 5 2.1.
Quiz answers: 1 A, 2 B, 3 C, 4 A, 5 B, 6 A, 7 B, 8 C, 9 A, 10 B, 11 C, 12 A, Challenge 1 C, Challenge 2 C.
Extra worksheet answers (items 6 onward): 6 1.5; 7 4.2; 8 0.3; 9 9; 10 5.
Independent practice answers. Level 1: 1 2.4; 2 0.3; 3 9; 4 5; 5 2.1. Level 2: 1 1.6; 2 0.3; 3 7. Level 3: 1 8; 2 2.1; 3 4 × 2 = 8, not 0.8. The answer is 0.2..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Divide a decimal by a whole number | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O2 Divide by 0.1, 0.5 | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O3 Use multiplication to check | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O4 Solve simple problems | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
Proposed Courseversity thresholds for this page: Bronze = at least 8 of 12 core questions correct; Silver = all 12; Gold = all 12 plus both challenge questions. A badge is never a full record of progress.
If a learner struggles
- Find the misconception: Moving the point wrongly. Check by multiplying.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Divide whole numbers.
- Guided practice: work through one example together and let the learner try the next one.
- Reassess: use the quiz again or the worksheet.
- Move on when the learner shows Silver-level evidence independently.
For parents and guardians
In this lesson your child divides decimals in simple contexts. You do not need to be good at mathematics to help.
- Share a bill with decimals.
- Ask: what does the quotient mean?
- Check by multiplying.
- Ask “how do you know?” after each answer, and listen.
- Praise effort, not only right answers. Mistakes are how we learn.
- Ten to fifteen minutes a day is better than one long session.
Teacher package
1–5. Objectives, prerequisites, materials, preparation, duration
Lesson objectives. Learners will: divide a decimal by a whole number; divide by 0.1, 0.5; use multiplication to check; solve simple problems.
Prerequisite knowledge. Lesson 7.
Materials. Counters (stones, seeds or bottle tops), paper, pencils, board or chalkboard. Low-resource options: use stones, seeds, sticks, bottle tops or drawings in the sand or on the board instead of printed materials.
Preparation. Gather the counters and draw the example pictures on the board before the lesson.
Suggested duration. 45–60 minutes. It can be split into two shorter sessions.
6–9. Teaching procedure, explanation notes, guided and independent activities
Introduction (5 min). Start with the Discover situation and let learners suggest ideas before you teach.
Explanation (10 min). Teach the Understand section with real objects first, then pictures, then symbols and words.
Guided activity (10 min). You need paper. Learners follow the Explore steps in pairs.
Independent activity (10 min). Learners complete the independent practice and the worksheet.
Assessment and reflection (5 min). Ask each learner to say one thing they learned and how they know it.
Key questions. Is the answer bigger or smaller? Does it check?
Teacher explanation notes. Use the concrete, pictorial, abstract order: real objects first, then pictures, then symbols and words. Return to real objects whenever a learner needs support.
10–12. Differentiation, formative assessment, common misconceptions
Support. Use real objects and work with a partner; say each step aloud together. Extension. Ask learners to make up their own example and explain it to a partner.
Formative assessment. Listen to learner explanations, ask “how do you know?”, and check the independent work.
Misconceptions. Moving the point wrongly. Check by multiplying.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 13-mark exam practice scheme, the 10-mark scheme and all answers are in the answer sections above. Re-check every answer and the marking scheme before publication.
16–19. Remediation, enrichment, homework, teacher reflection
Remediation. Divide whole numbers. Enrichment. Invite learners to find or create three more examples at home or in the classroom and explain them. Homework. See above.
Teacher reflection. After teaching, record: which concepts learners understood; which misconceptions occurred; which activities worked; which learners need more practice; and what to improve next time.
Sources and standards
Alignment is pending verification and no external endorsement is claimed. Reference starting points named in the Courseversity standard: Common Core State Standards for Mathematics, Cambridge Primary and the IB Primary Years Programme. Specific standard codes will be added once checked against the official documents.
Research used to shape this lesson. Common Core 5.NBT.B.7; Cambridge Primary Mathematics Stage 5 and 6 (dividing decimals). These sources informed the lesson; no official alignment is claimed.