Primary Maths | Fractions, Decimals and Percentages: Conversion Prep Guide (for tutors) | 3/4 = 0.75 = 75%, 8 easy denominators, 12 exercises

2026-11-13

Tutor lesson-prep guides · Primary Maths

Students can usually convert but they are slow, because every step is a separate rule they memorised. This lesson does one thing: it joins the three forms with place value, then gives a table of eight denominators so the work becomes checking rather than calculating.

Objectives — Students can: (1) state that a fraction, a decimal and a percentage are three ways of writing one number, 3/4 = 0.75 = 75%; (2) convert a fraction to a decimal by dividing the numerator by the denominator, and recognise the eight denominators that always give a finite decimal; (3) move the decimal point two places right to reach a percentage and two places left to return; (4) simplify 36% to 9/25 and compare 3/4 with 7/10 by converting both to decimals.

01 Prerequisites (3-minute check)

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

Skill	Quick check	Pass mark
Meaning of a fraction	What does 3/4 mean?	Split into 4 equal parts and take 3
Decimal place value	Where is the 7 in 0.75?	In the tenths place, seven tenths
Simplifying	Simplify 12/18	2/3, divide both by 6

02 Lesson flow (45 minutes)

Time	Stage	Tutor does	Student does
0-5 min	One number, three forms	Write 3/4, 0.75 and 75% and ask whether they are equal	Vote, then check on a number line
5-15 min	Fraction to decimal	Model numerator divided by denominator and list the 8 denominators	Check six items on a calculator
15-25 min	Decimal to percentage	Move the point two places and add the sign	Move the point on six decimals
25-35 min	Percentage to fraction	Model 36% to 36/100 to 9/25	Do four items showing the simplifying step
35-42 min	Comparing sizes	Model converting everything to decimals first	Order four sets of three values
42-45 min	Exit check	Five oral questions	Leave only with all five correct

03 Teaching script (read it out)

Scene 1: One number in three coats

Write one number in the middle of the board: 3/4 = 0.75 = 75%. Draw a number line from 0 to 1 and mark the same point three times, once in each form. Students stop treating the three as separate topics only when they see them land on the same point.

Ask one question that connects it to life: a shop sign says 25% off; which number is that? It is 0.25, which is one quarter. This is the moment percentages stop being a foreign language.

State the precondition clearly: the three forms are equal only for the same value. 3/4 equals 75%, but 3/4% is a hundred times smaller. Students should copy that line, because the comparison section is where it is most often broken.

Scene 2: Fraction to decimal and the eight denominators

One rule: divide the numerator by the denominator. 3 divided by 4 is 0.75, 1 by 8 is 0.125, 7 by 20 is 0.35, 2 by 5 is 0.4. Let them press it on a calculator once so the written answer and the machine agree.

Then give a table of eight denominators only: 2, 4, 5, 8, 10, 20, 25, 50. Fractions with these denominators always give a finite decimal, because their only prime factors are 2 and 5. Denominators with 3, 6, 7, 9 or 11 give recurring decimals, for example 1/3 is 0.333 and never stops. Knowing the boundary stops students waiting for an answer that will not arrive.

Warn about place value: 0.125 has three decimal places, and it is 12.5%, not 125%. The number is the same, the notation is not; if the question asks for a percentage, the answer must carry the sign.

Scene 3: Moving the point and simplifying to the end

Decimal to percentage: move the point two places right and add the sign. 0.75 becomes 75%, 0.4 becomes 40%, 0.125 becomes 12.5%. Percentage to decimal: two places left. Have them touch the paper twice and count aloud, one, two, so the direction is never guessed.

Percentage to fraction: write it over 100 first, then simplify. 36% becomes 36/100, divide both by 4, giving 9/25. Insist on the simplest form, because unsimplified fractions make the cross multiplication in the next step larger and the errors more frequent.

Finally comparing: convert everything to decimals and order. 3/4 against 7/10 is 0.75 against 0.7, which is immediate. Cross multiplication also works, 3 times 10 is 30 and 7 times 4 is 28. Teach both and let each student keep one as their default.

04 Question types and worked steps

Type	Example	Steps	Answer
Fraction to decimal	Write 7/20 as a decimal	Divide 7 by 20	0.35
Decimal to percentage	Write 0.125 as a percentage	Two places right, add the sign	12.5%
Percentage to fraction	Write 36% as a fraction in simplest form	Write over 100, then simplify	9/25
Comparing	Which is larger, 3/4 or 7/10?	Convert both to decimals or cross multiply	3/4, since 0.75 is greater than 0.7

Sanity check (teach this): Three checks before collecting answers. First, has the value changed? 3/4 to 75% is a change of notation, not of size; 0.075 means the point moved the wrong way. Second, is the sign there? A bare 75 is seventy five, not seventy five per cent. Third, is the fraction fully simplified? If both parts still divide by 2, it is unfinished. Students who run these three checks themselves cut their own error rate immediately.

05 Independent practice (3 questions)

Question	Answer	What to watch
1. Write 3/4, 1/8 and 2/5 as decimals.	0.75, 0.125, 0.4	0.7 or 0.12 shows a place value error
2. Write 0.35, 0.6 and 0.125 as percentages.	35%, 60%, 12.5%	A missing sign or a wrong shift must be corrected on the spot
3. Write 36%, 45% and 8% as fractions in simplest form.	9/25, 9/20, 2/25	Unsimplified answers are not accepted
4. Order 3/5, 0.55 and 58% from smallest to largest.	0.55, then 58%, then 3/5	Ordering without converting is a method error

06 Common mistakes and what to say

Mistake	Student writes	Say this
Moving the point one place	Writing 0.75 as 7.5%	It is two places, not one. Touch the paper twice, count aloud, then read the answer back as a fraction of a hundred.
Dropping the percentage sign	Answering 75	75 and 75% differ by a factor of a hundred. If the question asks for a percentage, the answer ends with the sign.
Stopping before the simplest form	Writing 36% as 18/50	Both parts still divide by 2, so the work is not finished. Ask whether a common factor remains.
Reading 3/4% as 3/4	Answering 0.75 for 3/4%	3/4% is 0.75%, which is 0.0075. Handle the sign first, then the fraction; the order cannot be reversed.

07 Homework (paper, section and question numbers)

Primary maths prep index — Open the percentage applications chapter and compare discount questions with conversion questions
Conversion exercises — Exercises 1 and 2: all twelve conversions, with the middle step written out
Comparing exercises — Exercises 3 and 4: order four sets and record the decimal value of each

08 Exit check (last 5 minutes)

Question	Answer	Decision
What are 3/4 as a decimal and as a percentage?	0.75 and 75%	Answering 7.5% means place value is unclear
Name the eight denominators that give finite decimals.	2, 4, 5, 8, 10, 20, 25, 50	Remembering only 10 and 100 is not enough
What is 0.125 as a percentage?	12.5%	Answering 125% is the wrong direction
What is 36% as a fraction in simplest form?	9/25	Answering 18/50 means it was not simplified fully
What is the quickest way to compare 3/4 and 7/10?	Convert both to decimals: 0.75 and 0.7	Deciding by feel is not a method

09 Tutor FAQ

My student reaches for the calculator. Should I stop it?

Do not ban it, but require an estimate first and a check afterwards. Conversion tests place value understanding, not arithmetic speed.

Should recurring decimals be taught?

At P5 and P6 they only need to know that some divisions never finish, written as 0.33 and so on or rounded. The recurring notation can wait.

Why insist on the simplest form?

Because the next step, comparing and solving word problems, gets harder with larger numbers. Simplifying is for the sake of the work that follows.

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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.