You will learn
- Make equivalent fractions.
- Simplify to lowest terms.
- Test whether two fractions are equal.
- Use equivalent fractions for a common denominator.
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
- Equivalent fractions have the same value.
- Multiply or divide top and bottom by the same number.
- Simplify by dividing by the greatest common factor.
- Cross-check by simplifying both fractions.
Words to know
Equal in value.
Write in lowest terms.
A factor shared by both.
Same bottom number.
1. Discover: same amount
2/3 of a cake and 8/12 of the same cake look the same size. Are they equal?
2. Understand: equivalent fractions
- 2/3 = 4/6 = 8/12 (multiply top and bottom by 2, 4).
- 3/4 = 9/12.
- Simplify 18/24: divide by 6 → 3/4.
- Test: 5/10 and 3/6. Both simplify to 1/2, so they are equal.
Idea 1: Make equivalent
3/4 = 9/12 because 3 × 3 = 9 and 4 × 3 = 12. 5/8 = 15/24.
Idea 2: Simplify
12/16 ÷ 4 = 3/4. 15/45 ÷ 15 = 1/3.
Idea 3: Test
4/6 = 2/3 and 6/9 = 2/3, so 4/6 = 6/9: yes.
Why the same number? Multiplying top and bottom by the same number is multiplying by 1.
3. Worked examples
Example 1 (I show you): Make equivalent
3/4 = ?/12
- × 3 top and bottom.
Answer: 9
Example 2 (We do it together): Simplify
12/16
- ÷ 4.
Answer: 3/4
Example 3 (You try): Test
Is 4/6 = 6/9?
Show the steps and answer
- Simplify both.
Answer: Yes, both are 2/3
Did you know?
Every fraction has endless equivalent fractions.
Why this matters
Equivalent fractions are needed to add, subtract and compare fractions.
4. Explore: match
You need paper strips.
- Make 2/3 on a strip.
- Make 8/12 on another.
- Compare.
- Simplify 18/24.
Think about it: what did you notice?
3/4.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I multiply top and bottom by ___.
- The new fraction is ___.
- I divide both by ___.
- In lowest terms it is ___.
Guided practice
Question 1. 2/3 = ?/12
8.
Question 2. Simplify 18/24.
3/4.
Question 3. Is 5/10 = 3/6?
Yes.
Independent practice
Level 1: Start
- 3/4 = ?/12
- Simplify 12/16
- Simplify 15/45
- Is 4/6 = 6/9?
- 5/8 = ?/24
Level 2: Grow
- 2/5 = ?/10
- Simplify 8/12
- Is 3/9 = 1/3?
Level 3: Stretch
- 5/6 = ?/36
- Simplify 36/48
- Ben says 1/2 = 2/3 because he added 1 to top and bottom. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
Ada ate 8/12 of a pie, Bayo ate 2/3. Who ate more?
Show a sample answer
The same amount.
Another one. Ana eats 4/8 of a pizza and Ben eats 1/2. Did they eat the same amount?
Show a sample answer
Yes: 4/8 = 1/2.
7. Common mistakes
Fix: Multiply or divide both.
Fix: Multiply or divide both.
Fix: Divide by the greatest common factor.
8. Lesson summary and revision card
- I can make equivalent fractions.
- I can simplify to lowest terms.
- I can test whether fractions are equal.
- I can use equivalent fractions for a common denominator.
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
- Same factor top and bottom.
- Simplify with the GCF.
- Test by simplifying.
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.
- Find ? in 3/4 = ?/12. [2 marks]
- Simplify 12/16. [2 marks]
- Simplify 15/45. [2 marks]
- Is 4/6 = 6/9? Explain. [3 marks]
- Find ? in 5/8 = ?/24. [2 marks]
Total: 11 marks.
Marking guide and model answers
- × 3 on top and bottom [1]; 9 [1]
- ÷ 4 on top and bottom [1]; 3/4 [1]
- ÷ 15 on top and bottom [1]; 1/3 [1]
- 4/6 = 2/3 [1]; 6/9 = 2/3 [1]; yes [1]
- × 3 on top and bottom [1]; 15 [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
- 3/4 = ?/12
- Simplify 12/16
- Simplify 15/45
- Is 4/6 = 6/9? (yes/no)
- 5/8 = ?/24
- 2/3 = ?/12
- 18/24 in lowest terms
- 3/4 = ?/12
- 12/16 in lowest terms
- 5/8 = ?/24
Homework
Write four fractions equivalent to 3/5.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 3/4 = ?/12 | 9 | 2 |
| Simplify 12/16 | 3/4 | 2 |
| Simplify 15/45 | 1/3 | 2 |
| Is 4/6 = 6/9? (yes/no) | yes | 2 |
| 5/8 = ?/24 | 15 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 9; 2 3/4; 3 1/3; 4 yes; 5 15.
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 8; 7 3/4; 8 9; 9 3/4; 10 15.
Independent practice answers. Level 1: 1 9; 2 3/4; 3 1/3; 4 yes (both equal 2/3); 5 15. Level 2: 1 4; 2 2/3; 3 Yes. Level 3: 1 30; 2 3/4; 3 Adding does not keep the value. Multiply both by 2 to get 2/4..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Make equivalent fractions | 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 Simplify to 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 |
| O3 Test whether two fractions are equal | 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 Use equivalent fractions for a common 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 |
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: Adding the same number to top and bottom. Multiply or divide both.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Compare fraction strips.
- 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 makes and simplifies equivalent fractions. You do not need to be good at mathematics to help.
- Cut a pizza or chocolate into equal parts.
- Ask: what did we multiply by?
- Compare fractions with fraction strips.
- 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: make equivalent fractions; simplify to lowest terms; test whether two fractions are equal; use equivalent fractions for a common denominator.
Prerequisite knowledge. Grade 4 equivalent fractions.
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 strips. 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 do I multiply or divide by? Is it in lowest terms?
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. Adding the same number to top and bottom. Multiply or divide both.
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. Compare fraction strips. 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 4.NF.A.1; Cambridge Primary Mathematics Stage 5 (equivalent fractions). These sources informed the lesson; no official alignment is claimed.