You will learn
- Find a common factor of numerator and denominator.
- Divide to simplify.
- Know when a fraction is in lowest terms.
- Simplify fully.
Version 0.2 · expanded edition · built from cited public sources Content is based on the official frameworks and sources listed under Sources and standards. No official endorsement is claimed. Written in the style of common primary school assessments. No exam result is promised.
Student lesson
- Find a common factor of the top and bottom.
- Divide both by it.
- Stop at lowest terms.
- Use the greatest common factor to finish in one step.
Words to know
Write with smaller numbers.
Cannot be simplified more.
A factor shared by both numbers.
The biggest shared factor.
1. Discover: smaller numbers
6/8 of a field is planted. Can you say the same amount with smaller numbers?
2. Understand: simplifying
Divide the numerator and denominator by a common factor.
- 6/8: divide by 2 → 3/4.
- 12/18: divide by 6 → 2/3.
- 10/25: divide by 5 → 2/5.
A fraction is in lowest terms when 1 is the only common factor. 3/4 is in lowest terms.
Idea 1: Simplify
4/8: divide top and bottom by 4: 1/2. 9/12: divide by 3: 3/4.
Idea 2: Bigger
10/25: divide by 5: 2/5. 15/20: divide by 5: 3/4.
Idea 3: Lowest terms
7/9: the only common factor of 7 and 9 is 1, so it is already in lowest terms.
Why divide both? Dividing both by the same number keeps the value.
3. Worked examples
Example 1 (I show you): Simplify
4/8
- Divide by 4.
Answer: 1/2
Example 2 (We do it together): Simplify
15/20
- Divide by 5.
Answer: 3/4
Example 3 (You try): Lowest?
7/9
Show the steps and answer
- Common factor of 7 and 9.
Answer: Already in lowest terms
Did you know?
The greatest common factor gets you to lowest terms in one step.
Why this matters
Simplest form makes fractions easy to read and compare.
4. Explore: simplify
You need paper.
- List the factors of 12 and 18.
- Find the greatest common factor.
- Divide top and bottom.
- Check that nothing else divides both.
Think about it: what did you notice?
2/3.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- A common factor of ___ and ___ is ___.
- I divide both by ___.
- I get ___.
- It is / is not in lowest terms.
Guided practice
Question 1. 6/8 simplified?
3/4.
Question 2. 12/18 simplified?
2/3.
Question 3. Is 3/4 in lowest terms?
Yes.
Independent practice
Level 1: Start
- 4/8
- 9/12
- 10/25
- 15/20
- 7/9
Level 2: Grow
- 6/10
- 12/15
- 8/20
Level 3: Stretch
- 24/36
- 45/60
- Ben simplifies 12/18 to 6/9 and stops. What should he do?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
6 of 8 pupils passed. Write the fraction in lowest terms.
Show a sample answer
3/4.
Another one. 18 of 24 pupils walk to school. Write this as a fraction in lowest terms.
Show a sample answer
18/24 = 3/4
7. Common mistakes
Fix: Check if it can be simplified again.
Fix: Check if there is a common factor left.
Fix: Divide both by the same number.
8. Lesson summary and revision card
- I can find a common factor.
- I can divide to simplify.
- I know when a fraction is in lowest terms.
- I can simplify fully.
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 by a common factor.
- Use the greatest.
- Lowest terms: only 1 divides both.
11. Next lesson
Next lesson: Comparing fractions. 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.
- Simplify 4/8. [2 marks]
- Simplify 9/12. [2 marks]
- Simplify 10/25. [2 marks]
- Simplify 15/20. [2 marks]
- Ana says 7/9 simplifies to 1/3. Is she right? Explain. [3 marks]
Total: 11 marks.
Marking guide and model answers
- Divide both by 4 [1]; 1/2 [1]
- Divide both by 3 [1]; 3/4 [1]
- Divide both by 5 [1]; 2/5 [1]
- Divide both by 5 [1]; 3/4 [1]
- No [1]. 7 and 9 share only the factor 1 [1]. It is already in lowest terms [1].
Score guide: 10 to 11 = secure. 7 to 9 = nearly there, revise the parts you missed. Under 7 = work through the lesson again with a grown-up.
Printable worksheet
- 4/8
- 9/12
- 10/25
- 15/20
- 7/9
- 6/8 in lowest terms is
- 12/18 in lowest terms is
- 10/25 in lowest terms is
- 9/12 in lowest terms is
- 7/9 is
Homework
Simplify five fractions of your own.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 4/8 | 1/2 | 2 |
| 9/12 | 3/4 | 2 |
| 10/25 | 2/5 | 2 |
| 15/20 | 3/4 | 2 |
| 7/9 | 7/9 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 1/2; 2 3/4; 3 2/5; 4 3/4; 5 7/9.
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 3/4; 7 2/3; 8 2/5; 9 3/4; 10 already in lowest terms.
Independent practice answers. Level 1: 1 1/2; 2 3/4; 3 2/5; 4 3/4; 5 7/9 is already in lowest terms. Level 2: 1 3/5; 2 4/5; 3 2/5. Level 3: 1 2/3; 2 3/4; 3 6 and 9 share the factor 3, so 6/9 = 2/3..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Find a common factor of numerator and denominator | 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 to simplify | 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 Know when a fraction is in lowest terms | 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 Simplify fully | 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 |
Courseversity badge thresholds (overall quiz score): Gold = 90–100%; Silver = 80–89.9%; Bronze = 70–79.9%. A badge is never a full record of progress.
If a learner struggles
- Find the misconception: Stopping too early, such as 12/18 = 6/9. Check if it can be simplified again.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: List factors of small 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 simplifies fractions to lowest terms. You do not need to be good at mathematics to help.
- Ask for the common factor first.
- Check if both numbers are even.
- Practise with small fractions daily.
- 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: find a common factor of numerator and denominator; divide to simplify; know when a fraction is in lowest terms; simplify fully.
Prerequisite knowledge. Lesson 2 and factors.
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. What number divides both? Is there another?
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. Stopping too early, such as 12/18 = 6/9. Check if it can be simplified again.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 11-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. List factors of small 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
This lesson is based on the sources below, and no official 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. Where a standard code is named, it points to the official framework.
Official standards for this topic area. Common Core State Standards for Mathematics (official site): Grade 4 » Number & Operations—Fractions; Grade 4 » Number & Operations in Base Ten. These pages list the standards that cover this topic area; read them alongside the lesson.
Research used to shape this lesson. Common Core 4.NF.A.1 and 5.NF.B.3; Cambridge Primary Mathematics Stage 5 (simplifying fractions). These sources informed the lesson.