Primary 5 Maths | Converting Between Fractions and Decimals Lesson-Prep Guide (for tutors) | 45-minute flow, teaching script, common errors

2026-11-15

Tutor lesson-prep guides · Primary Maths

Written as three quarters or as 0.75, the same number looks like two worlds to a pupil. This lesson does one thing: treat a fraction as an unfinished division, and the two notations join up.

Objectives — By the end of the lesson the pupil can: (1) convert a fraction to a decimal by dividing the numerator by the denominator; (2) write a decimal as a fraction over 10, 100 or 1000 and simplify it; (3) recognise a recurring decimal such as one third and mark it with a dot or an approximate sign; (4) put a fraction and a decimal into the same form before comparing them.

01 Prerequisites (3-minute check)

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

Skill	Quick check	Pass mark
Division	works out 3 divided by 4	answers 0.75
Simplifying	reduces 4 over 6 to lowest terms	answers 2 over 3
Place value in decimals	names the place of the last digit in 0.375	answers thousandths

02 Lesson flow (45 minutes)

Time	Stage	Tutor does	Student does
0-6 min	Entry check	asks 3 divided by 4, simplifying 4 over 6, and the place value in 0.375	answers aloud and names numerator, denominator and place
6-15 min	Fraction to decimal	shows 3 over 4 as 3 divided by 4 giving 0.75, then 5 over 8	converts 2 over 5 and 1 over 8
15-24 min	Decimal to fraction	shows 0.6 as 6 over 10 then 3 over 5, then 0.375	converts 0.25 and 0.45
24-33 min	Recurring decimals	shows 1 divided by 3 as 0.333 and marks the dot, explaining it never terminates	converts 1 over 3 and 2 over 3
33-41 min	Independent practice	reads questions only and checks that everything is fully simplified	works three items and one comparison
41-45 min	Exit check	marks at once and names whether the error was direction or simplification	says which of the two went wrong

03 Teaching script (read it out)

Scene 1: Act 1: a fraction is a division not yet finished

The notation 3 over 4 is really 3 divided by 4 left unfinished. Finish it and you get 0.75. So converting a fraction to a decimal takes one move: divide the numerator by the denominator. The numerator sits on top and is being shared, the denominator underneath says into how many parts, so 3 over 4 means 3 divided by 4 and not 4 divided by 3. And 1 over 8 is 1 divided by 8, which is 0.125.

To turn 3 over 4 into a decimal, which number do you divide by which?

Scene 2: Act 2: decimal to fraction, read the place then simplify

The 6 in 0.6 sits in the tenths place, so it is 6 over 10, which simplifies to 3 over 5. The 5 in 0.375 sits in the thousandths place, so it is 375 over 1000, and dividing both by 125 gives 3 over 8. The rule: one decimal place means tenths, two means hundredths, three means thousandths, and the fraction must then be simplified. Seeing 6 over 10 means the job is not finished.

Writing 0.375 as a fraction, what is the denominator, and why?

Scene 3: Act 3: when it will not divide out, it recurs

One divided by 3 gives 0.3333 and never stops, which makes it a recurring decimal. The notation is a dot above the repeating digit, or an approximate sign. There is a quick test: simplify the fraction, and if the denominator only has 2 and 5 as factors it will terminate; if the denominator carries 3, 7 or 11 it usually recurs. That is why 1 over 8 terminates at 0.125 while 1 over 3 never finishes.

Will 1 over 3 terminate as a decimal? Why or why not?

04 Question types and worked steps

Type	Example	Steps	Answer
Fraction to terminating decimal	3 over 4	divide the numerator by the denominator	0.75
Decimal to fraction	0.375	write 375 over 1000 by place value, then simplify	3 over 8
Recurring decimal	1 over 3	divide until the remainder repeats and mark it with a dot	0.3 recurring
Comparing sizes	which is larger, 3 over 5 or 0.58	put both into decimals first	3 over 5, because 0.6 is larger than 0.58

Sanity check (teach this): Three checks: a proper fraction always converts to a decimal below 1, so an answer above 1 means numerator and denominator were swapped; a decimal written as a fraction must be in lowest terms, with nothing more dividing both parts; and a recurring decimal cannot be stopped after a few places, so it needs a dot or an approximate sign.

05 Independent practice (3 questions)

Question	Answer	What to watch
What is 3 over 4 as a decimal?	0.75	whether 3 was divided by 4 and not the reverse
What is 0.25 as a fraction?	1 over 4	whether it was simplified to lowest terms
Which is larger, 3 over 5 or 0.58?	3 over 5, because 0.6 is larger than 0.58	whether both were turned into decimals first

06 Common mistakes and what to say

Mistake	Student writes	Say this
Dividing the wrong way round	turning 3 over 4 into 4 divided by 3 equals 1.33	The numerator is on top and is being shared, so it is 3 divided by 4; the other way gives an answer above 1.
Leaving the decimal fraction unsimplified	writing 0.25 as 25 over 100 and stopping	25 over 100 divides by 25 to give 1 over 4; unsimplified means unfinished.
Treating a recurring decimal as terminating	writing 1 over 3 as 0.3 and leaving it	One decimal place is not the value; 1 over 3 is 0.333 recurring and needs the dot.
Comparing by counting digits	deciding 0.85 is larger than 0.9 because 85 is larger than 9	Compare by place value: 0.9 has 9 tenths against 8 tenths, so 0.9 is larger.

07 Homework (paper, section and question numbers)

Primary 5 maths paper 1: fractions and decimals section — Section A, questions 1 to 3

08 Exit check (last 5 minutes)

Question	Answer	Decision
What is 1 over 8 as a decimal?	0.125	wrong: reteach Act 1, numerator divided by denominator
What is 0.45 as a fraction?	9 over 20	wrong: reteach Act 2, simplify to lowest terms
What is 2 over 3 as a decimal?	0.6 recurring, that is 0.666 and never ending	wrong: reteach Act 3, recurring decimals

09 Tutor FAQ

Which year group is this for?

Hong Kong primary schools treat fraction and decimal conversion as the basis for comparing values in Primary 5, after the simple tenths and hundredths work in Primary 4. Percentages and speed in Primary 6 both depend on it, so the direction should become automatic.

Is 45 minutes enough?

Yes, but Act 3 needs its full nine minutes. Pupils resist the idea that a division may never end, so contrast 1 divided by 8 with 1 divided by 3 and let them watch one stop and one not.

Is there a practice paper?

Yes. The homework line links to the Primary 5 paper with the section and question numbers, and the page carries an answer version.

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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.

Practice papers　Paper 1 (basics)　·　Paper 2 (intermediate)　·　Paper 3 (challenge)　·　Paper 4 (error clinic)