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Primary 5 Maths | Four Operations with Fractions: Tutor Lesson Guide | Common Denominators, Reciprocals
Pupils can find a common denominator, then collapse the moment a fraction appears under a division sign. They have never been asked how many thirds fit inside three quarters. This lesson turns division back into multiplication.
01 Prerequisites (3-minute check)
If any of these fails, fix it before the lesson starts.
| Skill | Quick check | Pass mark |
|---|---|---|
| Expanding and simplifying | can reduce 6/15 to 2/5 | needed before common denominators |
| Times tables | secure on 2 to 9 | simplifying depends on common factors |
02 Lesson flow (40 minutes)
| Time | Stage | Tutor does | Student does |
|---|---|---|---|
| 0-5 min | Diagnostic | what is 1/2 plus 1/4 | answer 3/4 |
| 5-15 min | Adding by common denominator | 1/2 plus 1/3, denominator 6 | 3/6 plus 2/6 is 5/6 |
| 15-23 min | Subtracting | 3/4 minus 1/6 | 9/12 minus 2/12 is 7/12 |
| 23-32 min | Simplify before multiplying | 2/3 times 3/5 | cancel the 3, answer 2/5 |
| 32-40 min | Division and exit check | 3/4 divided by 2/5 | 15/8 becomes 1 and 7/8 |
03 Teaching script (read it out)
Scene 1: Act 1: A common denominator unifies the cuts
Tutor line: “One half and one third are cut differently. Make every piece the same size first, then you can add them.”
Scene 2: Act 2: Simplify before you multiply
Tutor line: “Do not multiply yet. Is there the same number above and below that you can cancel? Cancel first, then the numbers stay small.”
Scene 3: Act 3: Dividing by a fraction means multiplying by its reciprocal
Tutor line: “Dividing by 2/5 asks how many 2/5 fit inside 3/4. One and seven eighths fit, so it is less than two. Check with the reciprocal and see if you get the same.”
04 Question types and worked steps
| Type | Example | Steps | Answer |
|---|---|---|---|
| Adding unlike denominators | find a common denominator, expand, add numerators, simplify | denominators are never added | |
| Subtracting unlike denominators | common denominator, subtract numerators, simplify | a negative answer means the order is wrong | |
| Multiplying fractions | cancel across first, then multiply across | 2/3 times 3/5 is 2/5 | |
| Dividing fractions | flip the divisor, multiply, simplify | 3/4 divided by 2/5 is 1 and 7/8 |
05 Independent practice (3 questions)
| Question | Answer | What to watch |
|---|---|---|
| 1/2 + 1/3 = ? | 5/6 | denominator 6: 3/6 + 2/6 |
| 3/4 – 1/6 = ? | 7/12 | denominator 12: 9/12 – 2/12 |
| 2/3 x 3/5 = ? | 2/5 | cancel the 3 first |
| 3/4 / (2/5) = ? | 1 7/8 | multiply by 5/2 to get 15/8 |
| 2/3 + (1/4 x 2) = ? | 1 1/6 | multiply first: 1/2 + 2/3 is 7/6 |
06 Common mistakes and what to say
| Mistake | Student writes | Say this |
|---|---|---|
| Adding the denominators | writing 1/2 + 1/3 as 2/5 | the denominator is the size of the cut, so it does not change when adding |
| Multiplying before simplifying | writing 6/15 first | cancel a matching number above and below before multiplying |
| Flipping the wrong fraction | writing 4/3 times 2/5 | only the divisor is flipped; the first fraction stays as it is |
| Multiplying mixed numbers directly | treating 1 1/2 times 2/3 as 1 times 2/3 plus something | convert to an improper fraction first, 3/2 times 2/3 |
07 Homework (paper, section and question numbers)
- Independent practice in this chapter (questions 1 to 5 above) — questions 1 to 3: adding and subtracting; 4 to 5: multiplying, dividing, mixed
- Primary Maths chapter index (related chapters at this level) — questions 6 to 8: write one question of each type
08 Exit check (last 5 minutes)
| Question | Answer | Decision |
|---|---|---|
| 5/6 – 1/3 = ? | 1/2 | if wrong: reteach common denominator 6 |
| 4/5 / 2 = ? | 2/5 | if wrong: reteach that the reciprocal of 2 is 1/2 |
| 1/2 + (1/3 x 3/4) = ? | 3/4 | if wrong: reteach multiply before adding |
09 Tutor FAQ
Why insist on a mixed number?
An improper fraction is not wrong, but school marking at this level and secondary questions use mixed numbers, and a mixed number makes the size of the value visible.
How deep should the meaning of division go?
At least once with the how-many-fit explanation. Pupils who only memorise flip and multiply fail once algebraic fractions appear.
Must the common denominator be the lowest one?
No. Multiplying the two denominators works but gives bigger numbers. Get accuracy first, then teach the lowest common multiple to cut the arithmetic.
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A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.