Primary 5 Maths | Multiplying Fractions: a Tutor Prep Guide | Fraction by fraction, whole numbers, mixed numbers and simplifying

2026-11-10

Tutor lesson-prep guides · Primary Maths

Fresh from adding fractions, students reach for a common denominator the moment they see multiplication. Say it plainly: multiplication never needs a common denominator, numerator times numerator and denominator times denominator is enough.

Objectives — By the end the student can: (1) multiply three quarters by two fifths as three tenths using numerator by numerator and denominator by denominator, simplifying on the way; (2) compute a whole number times a fraction, 4 times three eighths giving three halves, or one and a half; (3) convert two and a half into five halves and multiply by one third to get five sixths; (4) explain that the word of signals multiplication and judge whether the answer should be larger or smaller than the original.

01 Prerequisites (3-minute check)

If any of these fails, fix it before the lesson starts.

Skill	Quick check	Pass mark
Simplifying	Simplify eight twelfths	Two thirds
Mixed and improper	Write two and a half as an improper fraction	Five halves
Meaning of multiplication	What is half of a half	One quarter, which is smaller

02 Lesson flow (45 minutes)

Time	Stage	Tutor does	Student does
0-5 min	Diagnose the habit	Two questions side by side, one addition one multiplication; which needs a common denominator	Only addition and subtraction do
5-15 min	Fraction by fraction	Three quarters times two fifths, multiply then simplify	Three tenths
15-25 min	Whole numbers	Four times three eighths, writing the whole as over one	Three halves, one and a half
25-33 min	Mixed numbers	Two and a half times one third	Five halves times one third is five sixths
33-40 min	Word problems	Three fifths of a box, one third of that is chocolate	Write the product and an answer sentence
40-45 min	Exit check	Mark three questions at once	Work independently

03 Teaching script (read it out)

Scene 1: Fraction by fraction: multiply, do not common-denominator

Break the habit first: students want a common denominator because the previous chapter demanded it. Put addition and multiplication side by side; one needs it, the other does not.
Three quarters times two fifths: 3 times 2 is 6, 4 times 5 is 20, giving six twentieths, which simplifies to three tenths.
Simplifying can wait until the end or happen early: cancel the 4 with the 2 to get 2 and 1, and the multiplication is smaller. Show both routes and let students pick.

Student should do: solve one and say when they simplified.

Scene 2: Whole numbers and mixed numbers: over one, or improper

A whole number 4 is four over one. Times three eighths gives 12 over 8, which simplifies to three halves, or one and a half.
A mixed number such as two and a half must first become five halves: 2 times 2 plus 1 is 5. Times one third gives five sixths.
Insist on converting mixed numbers. Multiplying the parts separately can work mathematically, but at Primary 5 the extra steps are where errors breed.

Student should do: write out the conversion step for one mixed number product.

Scene 3: Word problems and reasonableness: of means multiply

Three fifths of a box, one third of which is chocolate, gives two ofs and therefore two multiplications: three fifths times one third is three fifteenths, which is one fifth.
Check plausibility: multiplying by a fraction below one always gives a smaller result; only multiplying by something above one grows the number. An answer larger than the original means a slip.
The answer sentence carries both unit and object: one fifth of a box is chocolate.

Student should do: write the product, the simplified result and the answer sentence.

04 Question types and worked steps

Type	Example	Steps	Answer
Fraction by fraction	Three quarters times two fifths	Multiply across, then simplify	Three tenths
Whole number by fraction	Four times three eighths	Write the whole over one, multiply, simplify	One and a half
Mixed numbers	Two and a half times one third	Convert to improper first, then multiply	Five sixths
Word problem	One third of three fifths	Turn of into multiplication, then simplify	One fifth

Sanity check (teach this): Sanity check: multiplying by a fraction below one always gives a smaller result, and only factors above one enlarge; multiplication never needs a common denominator, so a common denominator step means addition was confused with multiplication; answers must be fully simplified, with no common factor left; mixed numbers convert to improper fractions first, since multiplying the parts separately invites errors; the exit check allows 300 seconds for three questions.

05 Independent practice (3 questions)

Question	Answer	What to watch
Fraction by fraction	Three fifths times five ninths	Cancel first, then one third
Whole number	Six times three quarters	Four and a half
Mixed number	One and two thirds times three quarters	One and a quarter
Word problem	Three quarters of a box, two thirds of it biscuits	Half a box

06 Common mistakes and what to say

Mistake	Student writes	Say this
Using a common denominator	Three quarters times two fifths rewritten over twentieths first	Multiplication does not need it. Multiply across and simplify.
Multiplying only the whole part	Two and a half times one third using only the 2	Convert first: two and a half is five halves.
Leaving the answer unsimplified	Stopping at six twentieths	Six and twenty share a factor of two. Simplest form is the answer.
Accepting an answer bigger than the original	Multiplying by one third yet the result grows	Multiplying by less than one must shrink the number. Which step went wrong?

07 Homework (paper, section and question numbers)

Primary maths chapter index — All chapters by level
Teaching guide index — Same structure, other subjects
Redo this chapter — Questions 1 to 4 again, showing the simplification

08 Exit check (last 5 minutes)

Question	Answer	Decision
What is three quarters times two fifths	Three tenths	Answering six twentieths means it was not simplified; reteach act one
Does fraction multiplication need a common denominator	No, only addition and subtraction do	Answering yes means act one again
Is the result bigger or smaller after multiplying by one third	Smaller, since one third is below one	Answering bigger means act three again

09 Tutor FAQ

Why is no common denominator needed?

A common denominator exists so quantities share units before adding. Multiplication takes a part of a part, and multiplying across keeps the units consistent already.

Can students cancel before multiplying?

Yes, and it is faster. Be precise that the cancellation is between a numerator and a denominator, not inside one fraction.

Must mixed numbers always become improper?

Multiplying the parts separately is valid, but at Primary 5 the extra fraction addition is where mistakes appear, so converting is safer.

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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.