Primary 6 Maths | Ratio and Proportion: a Tutor Prep Guide | Simplifying ratios, sharing in a ratio and three-part ratios

2026-11-10

Tutor lesson-prep guides · Primary Maths

Three to five is not three plus five, and it is not three divided by five either. The usual mistake is splitting the total evenly, because one part was never found first.

Objectives — By the end the student can: (1) explain a ratio as a comparison of parts, so 3 to 5 is 3 parts against 5 parts and 8 parts in all; (2) simplify a ratio by dividing both terms by the same factor, 12 to 18 becoming 2 to 3; (3) share a total in a ratio, so 240 dollars in 3 to 5 gives one part of 30 and shares of 90 and 150; (4) find the whole from one part, so 28 boys at 4 to 5 means 7 in a part, 35 girls and 63 students in all.

01 Prerequisites (3-minute check)

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

Skill	Quick check	Pass mark
Highest common factor	The highest common factor of 12 and 18	6
Division	240 divided by 8	30
Multiples	28 divided by 4	7

02 Lesson flow (45 minutes)

Time	Stage	Tutor does	Student does
0-5 min	Diagnose	Share 240 dollars in 3 to 5 and ask for each share	They say 90 and 150, or divide by 3
5-15 min	Meaning	Lay out 3 red and 5 blue blocks and count the parts	They say 8 parts in all
15-25 min	Simplify	Divide 12 and 18 both by 6	Get 2 to 3
25-33 min	One part	240 divided by 8 is 30, then multiply each part	Get 90 and 150
33-40 min	Whole from a part	Boys to girls 4 to 5 with 28 boys	35 girls, 63 in all
40-45 min	Exit check	Mark three questions at once	Work independently

03 Teaching script (read it out)

Scene 1: A ratio counts parts, not values

Start with blocks: 3 red, 5 blue, 8 in total. The ratio 3 to 5 says red holds 3 parts and blue holds 5 parts, 8 parts altogether.
Students must say “8 parts in all” out loud, because every later step depends on that number.
A ratio is not a fraction: 3 to 5 as a fraction is three fifths, but the parts in all are 8, not 5. This is where most confusion starts.

Student should do: lay out 8 blocks in the ratio 3 to 5 and say what fraction of the whole is red.

Scene 2: Simplifying multiplies or divides only

For 12 to 18, divide both terms by 6 to get 2 to 3. Both terms are always multiplied or divided by the same non-zero number, and the ratio is unchanged.
Adding or subtracting is wrong: 12 to 18 minus 2 gives 10 to 16, which is a different ratio.
With decimals or fractions, clear them first: 0.4 to 0.6 becomes 4 to 6, then 2 to 3; one half to one third becomes 3 to 2 after multiplying both by 6.

Student should do: simplify 12 to 18 and 0.4 to 0.6 and name the number used.

Scene 3: Find one part, then multiply

Sharing in a ratio is one move: add the parts, divide the total by the parts, then multiply each term.
For 3 to 5 with 240 dollars: 3 plus 5 is 8 parts, 240 divided by 8 is 30, so the shares are 30 times 3, which is 90, and 30 times 5, which is 150.
The check is instant: 90 plus 150 is 240. Three-part ratios work the same way, 2 to 3 to 5 of 200 giving 10 parts of 20, so 40, 60 and 100.

Student should do: share 200 in the ratio 2 to 3 to 5 and check by adding the shares.

04 Question types and worked steps

Type	Example	Steps	Answer
Simplify	12 to 18	Divide both terms by the highest common factor, 6	2 to 3
Share in a ratio	240 dollars in 3 to 5	3 plus 5 is 8 parts, 240 over 8 is 30, multiply each	90 and 150 dollars
Three-part ratio	200 dollars in 2 to 3 to 5	2 plus 3 plus 5 is 10 parts of 20	40, 60 and 100 dollars
Whole from a part	Boys to girls 4 to 5, 28 boys	28 over 4 is 7 in a part, girls are 5 times 7	35 girls, 63 in all

Sanity check (teach this): Sanity check: both terms of a ratio are only ever multiplied or divided, and a simplified ratio has whole numbers with no common factor left; sharing always adds the parts first, and the shares must add back to the original total, as 90 and 150 make 240; a ratio is never written as a decimal and never carries units inside it, the unit belongs to the answer; a three-part ratio adds all three terms, 2 plus 3 plus 5 is 10; finding the whole from one part must give a whole number of items in a part, so a fraction means a wrong divisor; the exit check allows 300 seconds for three questions at Primary 6.

05 Independent practice (3 questions)

Question	Answer	What to watch
Simplify	Simplify 12 to 18	2 to 3
Share	240 dollars in 3 to 5	90 and 150 dollars
Three-part	200 dollars in 2 to 3 to 5	40, 60 and 100 dollars
From a part	Boys to girls 4 to 5 with 28 boys	35 girls, 63 in all

06 Common mistakes and what to say

Mistake	Student writes	Say this
Counting terms instead of parts	240 dollars in 3 to 5 solved as 240 over 3, giving 80	Three to five is 8 parts, not 3. Add 3 and 5, then divide 240 by 8.
Subtracting when simplifying	12 to 18 simplified to 10 to 16	Simplifying only divides. Divide 12 and 18 both by 6 and you get 2 to 3.
Mismatched units	40 minutes to 1 hour answered as 40 to 1	Units must match before comparing. One hour is 60 minutes, so 40 to 60, which is 2 to 3.
Stopping at half the question	Boys to girls 4 to 5 with 28 boys, answered as 28 girls	Four parts is 28, so one part is 7. Girls are 5 parts, and 5 times 7 is 35.

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, writing the value of one part each time

08 Exit check (last 5 minutes)

Question	Answer	Decision
Simplify 12 to 18	2 to 3	Answering 4 to 6 means the factor was not taken all the way; reteach act two
240 dollars in 3 to 5; the two shares	90 and 150 dollars	Answering 80 and 160 means 3 parts were used; reteach act three
Boys to girls 4 to 5 with 28 boys; how many girls	35	Answering 28 means only one number was read; act three again

09 Tutor FAQ

How is a ratio different from a fraction?

A ratio compares parts and the parts in all are the two terms added; a fraction gives one part of the whole. Three to five has 8 parts in all and is three fifths as a fraction, and the two must not be mixed up.

Can a ratio contain decimals?

Yes, but the answer is normally a whole-number ratio: 0.4 to 0.6 becomes 4 to 6, then 2 to 3.

Do three-part ratios need teaching?

Primary 6 includes them, for example 2 to 3 to 5 when sharing money. The method is identical: add all three terms, then divide the total.

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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 review)