Courseversity

Subtracting fractions

Primary EducationGrade 6MathematicsCV-PRI-G06-MATH-FRA-U01-L0545–60 min

You will learn

  • Find a common denominator.
  • Subtract numerators.
  • Simplify.
  • Solve take-away problems.

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

The lesson in 60 seconds

  1. Make the denominators the same.
  2. Subtract the numerators only.
  3. Simplify the difference.
  4. Rename 1 as a fraction when needed.

Words to know

difference
Result of subtracting.
common denominator
Same bottom.
regroup
Rename to subtract.
simplify
Lowest terms.

1. Discover: what is left?

A jug holds 3/4 litre. You pour out 1/3 litre. How much is left?

2. Understand: subtracting fractions

  • 3/4 − 1/3 = 9/12 − 4/12 = 5/12.
  • 5/6 − 1/2 = 5/6 − 3/6 = 2/6 = 1/3.
  • 7/8 − 1/4 = 7/8 − 2/8 = 5/8.
  • 1 − 3/7 = 7/7 − 3/7 = 4/7.

Idea 1: Same bottom

2/3 − 1/5: denominator 15. 10/15 − 3/15 = 7/15.

Idea 2: More

7/8 − 1/4 = 7/8 − 2/8 = 5/8. 5/6 − 1/3 = 5/6 − 2/6 = 3/6 = 1/2. 3/4 − 1/2 = 1/4.

Idea 3: Whole

1 − 2/5 = 5/5 − 2/5 = 3/5.

Why rename 1? Writing 1 as 5/5 gives parts we can take away.

Remember: Common denominator, subtract tops.

3. Worked examples

Example 1 (I show you): Subtract

2/3 − 1/5

  1. Denominator 15.
  2. 10/15 − 3/15.

Answer: 7/15

Example 2 (We do it together): Subtract

1 − 2/5

  1. 1 = 5/5.
  2. 5/5 − 2/5.

Answer: 3/5

Example 3 (You try): Subtract

5/6 − 1/3

Show the steps and answer
  1. 5/6 − 2/6 = 3/6.
  2. Simplify.

Answer: 1/2

Did you know?

Subtracting fractions uses the same common-denominator idea as adding.

Why this matters

Subtracting fractions finds what is left of a share or length.

4. Explore: subtract

You need paper.

  1. Find the LCM.
  2. Convert.
  3. Subtract numerators.
  4. Simplify.
Think about it: what did you notice?

5/12.

5. Practise

Say it in a sentence

Use these starters when you talk about the lesson. Say them out loud.

  • The common denominator is ___.
  • ___ − ___ = ___.
  • Simplified: ___.
  • So ___ is left.

Guided practice

Question 1. 3/4 − 1/3?

5/12.

Question 2. 5/6 − 1/2?

1/3.

Question 3. 1 − 3/7?

4/7.

Independent practice

Level 1: Start

  1. 2/3 − 1/5
  2. 7/8 − 1/4
  3. 1 − 2/5
  4. 5/6 − 1/3
  5. 3/4 − 1/2

Level 2: Grow

  1. 3/5 − 1/5
  2. 1/2 − 1/4
  3. 1 − 1/3

Level 3: Stretch

  1. 5/6 − 1/4
  2. 3/4 − 1/3 − 1/6
  3. Ben says 3/4 − 1/2 = 2/2. What is wrong?

Answers are in the answer key below. Try first, then check.

6. Apply: everyday mathematics

A jug holds 3/4 L and 1/3 L is poured out. How much is left?

Show a sample answer

5/12 L.

Another one. A jug is 7/10 full. Ama pours out 1/5. How much is left?

Show a sample answer

1/2 of the jug

7. Common mistakes

Mistake: Subtracting denominators too.
Fix: Keep the common denominator.
Another mistake: Subtracting the denominators.
Fix: Keep the common denominator.
Another mistake: Forgetting to simplify.
Fix: Check for a common factor.

8. Lesson summary and revision card

I can…

  • I can find a common denominator.
  • I can subtract fractions.
  • I can simplify the difference.
  • I can solve take-away problems.

9. Check and master

Answer all 14 questions. You will see feedback after each one.

1. 3/4 − 1/3 =

2. 5/6 − 1/2 =

3. 7/8 − 1/4 =

4. 1 − 3/7 =

5. 2/3 − 1/5 =

6. 4/5 − 1/5

7. 1/2 − 1/6

8. 5/8 − 1/4

9. 1 − 3/8

10. 3/5 − 1/2

11. 7/10 − 1/5

12. A pizza is 3/4 left and 1/6 is eaten. How much is left?

Challenge 1. 5/6 − 1/3 =

Challenge 2. 3/4 − 1/3 − 1/6

Your result appears here after you answer every question.

10. Key takeaways

  • Common denominator.
  • Subtract numerators.
  • Simplify.

11. Next lesson

Next lesson: Multiplying 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.

  1. Work out 2/3 − 1/5. [3 marks]
  2. Work out 7/8 − 1/4. [2 marks]
  3. Work out 1 − 2/5. [2 marks]
  4. Work out 5/6 − 1/3. [3 marks]
  5. Ali says 3/4 − 1/2 = 2/2. Is he right? Explain. [3 marks]

Total: 13 marks.

Marking guide and model answers
  1. Common denominator 15 [1]; 10/15 − 3/15 [1]; 7/15 [1]
  2. 7/8 − 2/8 [1]; 5/8 [1]
  3. 5/5 − 2/5 [1]; 3/5 [1]
  4. Common denominator 6 [1]; 5/6 − 2/6 = 3/6 [1]; 1/2 [1]
  5. No [1]. Bottoms must stay the same [1]. 3/4 − 2/4 = 1/4 [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

  1. 2/3 − 1/5
  2. 7/8 − 1/4
  3. 1 − 2/5
  4. 5/6 − 1/3
  5. 3/4 − 1/2
  6. 2/3 − 1/5
  7. 7/8 − 1/4
  8. 1 − 2/5
  9. 5/6 − 1/3
  10. 3/4 − 1/2

Homework

Find 5/6 − 1/4 and 3/5 − 1/3.

Answer key and marking scheme

Question Expected response Marks
2/3 − 1/5 7/15 2
7/8 − 1/4 5/8 2
1 − 2/5 3/5 2
5/6 − 1/3 1/2 2
3/4 − 1/2 1/4 2
Total 10

Practice answers: Worksheet: 1 7/15; 2 5/8; 3 3/5; 4 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 7/15; 7 5/8; 8 3/5; 9 1/2; 10 1/4.

Independent practice answers. Level 1: 1 7/15; 2 5/8; 3 3/5; 4 1/2; 5 1/4. Level 2: 1 2/5; 2 1/4; 3 2/3. Level 3: 1 7/12; 2 1/4; 3 Bottoms stay the same. 3/4 − 2/4 = 1/4..

Mastery and remediation

Objective Bronze (Developing) Silver (Proficient) Gold (Advanced)
O1 Find 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
O2 Subtract numerators 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 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
O4 Solve take-away 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

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

  1. Find the misconception: Subtracting denominators too. Keep the common denominator.
  2. Explain another way: use real objects first, then pictures.
  3. Show a simpler example: Same-denominator subtraction.
  4. Guided practice: work through one example together and let the learner try the next one.
  5. Reassess: use the quiz again or the worksheet.
  6. Move on when the learner shows Silver-level evidence independently.

For parents and guardians

In this lesson your child subtracts fractions with different denominators. You do not need to be good at mathematics to help.

  • Share a bar of chocolate and take some away.
  • Ask: what is the common bottom?
  • Check by adding back.
  • 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 denominator; subtract numerators; simplify; solve take-away problems.

Prerequisite knowledge. Lesson 4.

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. Do the bottoms match? What is left?

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. Subtracting denominators too. Keep the common denominator.

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. Same-denominator subtraction. 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.A.1; Cambridge Primary Mathematics Stage 6 (subtracting fractions). These sources informed the lesson.

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