You will learn
- Multiply fractions.
- Simplify before multiplying.
- Find a fraction of a number.
- Multiply a whole number by a fraction.
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
- Multiply tops, then multiply bottoms.
- Simplify before or after.
- A fraction of a number: divide, then multiply.
- A whole number is that number over 1.
Words to know
Result of multiplying.
Top number.
Bottom number.
Means multiply.
1. Discover: a part of a part
Half of 3/4 of a cake is left. How much cake is that?
2. Understand: multiplying fractions
- Multiply tops and multiply bottoms: 1/2 × 3/4 = 3/8.
- 2/3 × 3/4 = 6/12 = 1/2.
- 3/5 × 2/3 = 6/15 = 2/5.
- 4 × 2/5 = 8/5 = 1 3/5.
Idea 1: Tops and bottoms
1/3 × 1/4 = 1/12. 2/3 × 3/5 = 6/15 = 2/5.
Idea 2: Of
3/4 of 20: 20 ÷ 4 = 5, then 5 × 3 = 15.
Idea 3: Whole
5 × 1/2 = 5/2 = 2 1/2. 5/6 × 3/10: cancel 3 and 6 to get 1/4.
Why no common bottom? Multiplying finds parts of parts, so bottoms multiply.
3. Worked examples
Example 1 (I show you): Multiply
1/3 × 1/4
- 1 × 1 = 1.
- 3 × 4 = 12.
Answer: 1/12
Example 2 (We do it together): Fraction of
3/4 of 20
- 20 ÷ 4 = 5.
- 5 × 3 = 15.
Answer: 15
Example 3 (You try): Whole times
5 × 1/2
Show the steps and answer
- 5/1 × 1/2 = 5/2.
Answer: 2 1/2
Did you know?
Multiplying by a proper fraction makes the number smaller.
Why this matters
Multiplying fractions finds parts of quantities, like a share of money.
4. Explore: multiply
You need paper.
- Multiply numerators.
- Multiply denominators.
- Simplify.
- Check size.
Think about it: what did you notice?
3/8.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I multiply the tops: ___.
- I multiply the bottoms: ___.
- Simplified: ___.
- “Of” means ___.
Guided practice
Question 1. 1/2 × 3/4?
3/8.
Question 2. 2/3 × 3/4?
1/2.
Question 3. 4 × 2/5?
1 3/5.
Independent practice
Level 1: Start
- 1/3 × 1/4
- 2/3 × 3/5
- 3/4 of 20
- 5 × 1/2
- 5/6 × 3/10
Level 2: Grow
- 1/2 × 1/3
- 1/5 of 25
- 3 × 1/4
Level 3: Stretch
- 3/8 × 4/9
- 5/6 of 18
- Ben says 1/2 × 1/2 = 1. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
Half of 3/4 of a cake remains. How much cake?
Show a sample answer
3/8 of the cake.
Another one. A bag holds 24 mangoes. Ama takes 3/8 of them. How many does she take?
Show a sample answer
9 mangoes
7. Common mistakes
Fix: Not needed to multiply.
Fix: Multiply bottoms directly.
Fix: A fraction less than 1 gives a smaller result.
8. Lesson summary and revision card
- I can multiply fractions.
- I can simplify.
- I can find a fraction of a number.
- I can multiply a whole number by a fraction.
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
- Multiply tops and bottoms.
- Simplify.
- “Of” means multiply.
11. Next lesson
Next lesson: Dividing 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.
- Work out 1/3 × 1/4. [2 marks]
- Work out 2/3 × 3/5. [3 marks]
- Work out 3/4 of 20. [2 marks]
- Work out 5 × 1/2. [2 marks]
- Ali says 1/2 × 1/2 = 1. Is he right? Explain. [3 marks]
Total: 12 marks.
Marking guide and model answers
- Multiply tops and bottoms [1]; 1/12 [1]
- 6/15 [1]; divide by the GCF 3 [1]; 2/5 [1]
- 20 ÷ 4 = 5 [1]; 5 × 3 = 15 [1]
- 5/2 [1]; 2 1/2 [1]
- No [1]. 1 × 1 = 1 and 2 × 2 = 4 [1]. The answer is 1/4 [1].
Score guide: 11 to 12 = secure. 8 to 10 = nearly there, revise the parts you missed. Under 8 = work through the lesson again with a grown-up.
Printable worksheet
- 1/3 × 1/4
- 2/3 × 3/5
- 3/4 of 20
- 5 × 1/2
- 5/6 × 3/10
- 1/3 × 1/4
- 2/3 × 3/5
- 3/4 of 20
- 5 × 1/2
- 5/6 × 3/10
Homework
Find 2/5 of 30 and 3/4 × 2/3.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 1/3 × 1/4 | 1/12 | 2 |
| 2/3 × 3/5 | 2/5 | 2 |
| 3/4 of 20 | 15 | 2 |
| 5 × 1/2 | 2 1/2 | 2 |
| 5/6 × 3/10 | 1/4 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 1/12; 2 2/5; 3 15; 4 2 1/2; 5 1/4.
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 1/12; 7 2/5; 8 15; 9 2 1/2; 10 1/4.
Independent practice answers. Level 1: 1 1/12; 2 2/5; 3 15; 4 2 1/2; 5 1/4. Level 2: 1 1/6; 2 5; 3 3/4. Level 3: 1 1/6; 2 15; 3 Tops 1 × 1 = 1 and bottoms 2 × 2 = 4, so the answer is 1/4..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Multiply 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 before multiplying | 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 Find a fraction of a 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 |
| O4 Multiply a whole number by a fraction | 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: Finding a common denominator before multiplying. Not needed to multiply.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Fraction of a number.
- 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 multiplies fractions. You do not need to be good at mathematics to help.
- Find a fraction of a number of items.
- Ask: what is one part?
- Check the answer is smaller.
- 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: multiply fractions; simplify before multiplying; find a fraction of a number; multiply a whole number by a fraction.
Prerequisite knowledge. Lesson 2.
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 is one part? How many parts?
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. Finding a common denominator before multiplying. Not needed to multiply.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 12-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. Fraction of a number. 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 6 » Ratios & Proportional Relationships; Grade 6 » The Number System. These pages list the standards that cover this topic area; read them alongside the lesson.
Research used to shape this lesson. Common Core 5.NF.B.4; Cambridge Primary Mathematics Stage 6 (multiplying fractions). These sources informed the lesson.