Courseversity

Lesson

Subtracting fractions with like denominators

Primary EducationGrade 4MathematicsCV-PRI-G04-MATH-FRA-U01-L0745–60 min

You will learn

  • Subtract numerators only.
  • Keep the denominator.
  • Simplify the difference.
  • 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

The lesson in 60 seconds

  1. Subtract the numerators only.
  2. Keep the denominator the same.
  3. Simplify the difference.
  4. Write 1 as a fraction with the same denominator.

Words to know

difference
Answer to subtraction.
like denominators
Same bottom number.
simplify
Lowest terms.
numerator
Top number.

1. Discover: a ribbon

A ribbon is 7/10 m long. 3/10 m is cut off. How much is left?

2. Understand: subtracting like fractions

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

Subtract the numerators and keep the denominator.

Idea 1: Subtract

5/8 − 2/8 = 3/8. 4/5 − 1/5 = 3/5.

Idea 2: Simplify

9/10 − 4/10 = 5/10 = 1/2. 7/12 − 1/12 = 6/12 = 1/2.

Idea 3: From a whole

1 − 1/4: write 1 as 4/4. Then 4/4 − 1/4 = 3/4.

Why keep the denominator? The pieces stay the same size.

Remember: Subtract the tops; keep the bottom; simplify.

3. Worked examples

Example 1 (I show you): Subtract

5/8 − 2/8

  1. 5 − 2 = 3.

Answer: 3/8

Example 2 (We do it together): Simplify

9/10 − 4/10

  1. 5/10 ÷ 5.

Answer: 1/2

Example 3 (You try): Whole

1 − 1/4

Show the steps and answer
  1. 1 = 4/4.

Answer: 3/4

Did you know?

A whole can always be written as a fraction like 4/4 or 10/10.

Why this matters

Subtracting fractions tells us how much is left.

4. Explore: take away

You need fraction strips.

  1. Colour 7/10.
  2. Remove 3/10.
  3. Count what is left.
  4. Simplify.
Think about it: what did you notice?

4/10 = 2/5.

5. Practise

Say it in a sentence

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

  • The denominators are ___.
  • I subtract ___ − ___ = ___.
  • The difference is ___.
  • In lowest terms it is ___.

Guided practice

Question 1. 7/10 − 3/10?

2/5.

Question 2. 5/6 − 1/6?

2/3.

Question 3. 1 − 3/8?

5/8.

Independent practice

Level 1: Start

  1. 5/8 − 2/8
  2. 9/10 − 4/10
  3. 1 − 1/4
  4. 7/12 − 1/12
  5. 4/5 − 1/5

Level 2: Grow

  1. 5/9 − 2/9
  2. 1 − 2/5
  3. 11/12 − 5/12

Level 3: Stretch

  1. 17/20 − 9/20
  2. 1 − 7/10
  3. Ana says 1 − 1/4 = 0/4. What is wrong?

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

6. Apply: everyday mathematics

A ribbon of 7/10 m has 3/10 m cut off. How long is the rest?

Show a sample answer

2/5 m.

Another one. A ribbon is 7/8 m long. 3/8 m is cut off. How much is left?

Show a sample answer

7/8 − 3/8 = 4/8 = 1/2 m

7. Common mistakes

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

8. Lesson summary and revision card

I can…

  • I can subtract numerators only.
  • I can keep the denominator.
  • I can simplify the difference.
  • I can solve simple problems.

9. Check and master

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

1. 7/10 − 3/10 =

2. 5/8 − 2/8 =

3. 9/10 − 4/10 =

4. 1 − 1/4 =

5. 7/12 − 1/12 =

6. 6/7 − 2/7 =

7. 8/9 − 5/9 in simplest form is…

8. 1 − 3/5 =

9. 1 − 5/8 =

10. 10/11 − 4/11 =

11. 5/6 − 1/6 in simplest form is…

12. When subtracting fractions with like denominators, the denominator…

Challenge 1. 4/5 − 1/5 =

Challenge 2. A jug has 7/8 litre. Ana pours out 2/8 and then 3/8. What is left?

Your result appears here after you answer every question.

10. Key takeaways

  • Subtract numerators.
  • Keep denominator.
  • Write 1 as a fraction.

11. Next lesson

Next lesson: Mixed numbers. 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. Find 5/8 − 2/8. [2 marks]
  2. Find 9/10 − 4/10 in lowest terms. [3 marks]
  3. Find 1 − 1/4. [2 marks]
  4. Find 7/12 − 1/12 in lowest terms. [2 marks]
  5. Kofi says 4/5 − 1/5 = 3/10. Is he right? Explain. [3 marks]

Total: 12 marks.

Marking guide and model answers
  1. 5 − 2 = 3 [1]; 3/8 [1]
  2. 5/10 [1]; divide by 5 [1]; 1/2 [1]
  3. 1 = 4/4 [1]; 3/4 [1]
  4. 6/12 [1]; 1/2 [1]
  5. No [1]. The denominator stays 5 [1]. The answer is 3/5 [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. 5/8 − 2/8
  2. 9/10 − 4/10
  3. 1 − 1/4
  4. 7/12 − 1/12
  5. 4/5 − 1/5
  6. 7/10 − 3/10 =
  7. 5/8 − 2/8 =
  8. 9/10 − 4/10 =
  9. 1 − 1/4 =
  10. 7/12 − 1/12 =

Homework

Subtract four pairs of fractions.

Answer key and marking scheme

Question Expected response Marks
5/8 − 2/8 3/8 2
9/10 − 4/10 1/2 2
1 − 1/4 3/4 2
7/12 − 1/12 1/2 2
4/5 − 1/5 3/5 2
Total 10

Practice answers: Worksheet: 1 3/8; 2 1/2; 3 3/4; 4 1/2; 5 3/5.

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 2/5; 7 3/8; 8 1/2; 9 3/4; 10 1/2.

Independent practice answers. Level 1: 1 3/8; 2 5/10 = 1/2; 3 3/4; 4 6/12 = 1/2; 5 3/5. Level 2: 1 3/9 = 1/3; 2 3/5; 3 6/12 = 1/2. Level 3: 1 8/20 = 2/5; 2 3/10; 3 1 = 4/4, so 4/4 − 1/4 = 3/4..

Mastery and remediation

Objective Bronze (Developing) Silver (Proficient) Gold (Advanced)
O1 Subtract numerators only 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 Keep the 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
O3 Simplify the difference 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

  1. Find the misconception: Subtracting denominators. Keep the denominator.
  2. Explain another way: use real objects first, then pictures.
  3. Show a simpler example: Use strips to take away.
  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 the same denominator. You do not need to be good at mathematics to help.

  • Eat part of a pizza and say what is left.
  • Ask: how many pieces are left?
  • Use fraction bars.
  • 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: subtract numerators only; keep the denominator; simplify the difference; solve simple problems.

Prerequisite knowledge. Lesson 6.

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 fraction 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. Are the denominators the same? Can I simplify?

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. Keep the denominator.

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. Use strips to take away. 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.B.3 (subtract fractions with like denominators); Cambridge Primary Mathematics Stage 4 (subtracting fractions). These sources informed the lesson; no official alignment is claimed.

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