P4: Fraction of Remainder (Basic)

Fraction of a remainder is a concept similar to Fraction of a Fraction.

Student will need to know that they must not make both denominator the same if each denominator of the 2 fractions do not represent the same total.

Such questions are common in Section C of P4 exams.

More of such questions with slightly higher difficulty for P4 students here.

Jaya has some plates in green, blue and red in colour.

¹/₄ of his plates are green.

⁵/₆ of the remaining plates are blue and the rest are red.

He has 40 blue plates.

How many plates does he have altogether?

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P4P5 Math: 2 Different Totals with 2 Different Quantities of 2 Different Items

Such questions presents 2 different type of items, each of different values.

The total of 2 different quantities of 2 items are given.

Without any comparison given, students must be able to make use of the 2 totals given in order to solve.

Such questions are common in Section C and Paper 1 of P4 and P5 exams.

Calculator usage is not allowed.

Similar questions of varying difficulties can also be found here and here.

3 pots and 5 lids costs $25.

4 pots and 3 lids costs $26.

How much does 6 lids cost?

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P6 Math: Fraction of Remainder with Guess and Check

This question type requires students to be able to use part/whole models to visualize "Fraction of Total" and "Fraction of Remainder". The "Guess and Check" table will also be required here.

Such questions are common in Paper 2 of P6 exams.

Calculator usage is allowed

Teddy bought some apples from the market.

After he threw away 152 apples and gave ¹/₅ of the remaining apples to his sister, 

he was left with ⁴/₇ of the apples bought. 

He packed the apples he had left into large boxes of 12 and small boxes of 8.

All the boxes were full without any apples left over.

What was the least number of boxes used by Teddy?

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P4 Math: Simple Pie Chart

Pie Charts in P4 will require students to understand the meaning of the 90 degree and what fraction(of the total) the right-angled piece represents.

Such questions usually appear in Section C of P4 exam papers.

P5 and P6 students can use this as extra practice for Paper 1 as well (no calculator usage).

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P5/P6 Math: Before and After Fractional Decrease with Total at the End

2 values, in which one is a fraction of another, each undergoes fractional decrease and the total amount left is provided.

Such questions will need students to make use of common multiples and comparison models in order to solve.

Such questions are common in Paper 2 of P5/P6 exams.

Calculator usage is allowed.

An easier version of this question for P4 students can be found here.

Alan and Ben each have some water in their bottles.

The volume of water Alan have is ¹/₂ of the volume of water that Ben have.

After Alan drank ¹/₃ of his water and Ben drank ³/₄ of his water,

both boys have 560ml of water left altogether.

What is the total volume of water both boys have at first?

Army water bottle is also known as a water canteen

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P5/P6 Math: Different Multiples of 2 Items with Same Total Value (Individual Difference Given)

2 items of different quantities have the same total value.

The difference between each item is also given.

Such questions can appear in both P5 and P6 Paper 2.

Calculator usage is allowed.

3 bottles of soy sauce cost as much as 5 bottles of cooking oil.

A bottle of soy sauce costs $17.60 more than each bottle of cooking oil.

Find the cost of one bottle of soy sauce.

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P6 Math: Counting using Hops/Gaps instead of Objects

When questions appears to be too juvenile for P6 students, 

they usually are.

Such is this type of question which an object must traverse past several objects to reach the final destination. The focus is on the number of hops/gaps and not the number of objects.

Such questions are common in Paper 1 of P6 exams.

Calculator usage is not allowed.

A lift takes 24 seconds to travel
from the 1st floor to the 4th floor.

How much time will the lift take to travel 

from the 1st floor to the 8th floor?

Antique Elevator Iron Pointer

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P4/P5 Math: Starting Multiples and Ending Multiples After Equal Decrease in Value

"Before and After Comparison Models" are staple for P3 to P6 Math.

The folowing question type presents one party to be a multiple of another at first.

After both undergo an equal decrease in value, the ending comparison is another multiple of one another.

Such questions are common in P4 Section C and P5 Paper 1.

Calculator usage is not allowed.

Kenneth has thrice as many baseball caps as Hiroshi at first.

After each gave away 45 caps,
Kenneth still has 8 times as many baseball caps as Hiroshi.

How many caps did both have altogether at first?

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P4 Math: Two Fractions of Total given ( difference known )

In the following question type, there are 3 different items of different quantity making up the unknown total.

2 fractions of the total are given to differentiate the quantity of 2 items.

The difference between 2 items is also provided.

The concept of common multiples will be useful here since the denominator represents the same total.

Such questions appear can in P4 Papers Section B and C.

A simpler version of the question can be found here.

Harry and Albert and Thomas were given some stamps from their uncle.

¹/₃ of the stamps were given to Harry. 

Albert received ¹/₄ of the stamps.

The rest of the stamps were given to Thomas.

Thomas received 80 more stamps than Harry.

How many stamps were given to the 3 boys altogether?

Vintage Singapore Stamps "Ship Series"

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P6 Math : Buying 2 different items in Different Quantity and Different Value with known Ratio

This question type is similar to the one practiced here.

2 different items are sold in bags of different quantities and not sold individually.
Each bag of items have different value.
A ratio of the number of items bought is given and the difference between the total values of the 2 items are also known.

Such questions require the knowledge of "set method" and "common multiples" and "ratio".

As these questions appear in Paper 2 of P6 exam papers,
calculator usage is allowed.

Carnations and roses are sold in bunches at a market stall.

A bunch of 12 roses are sold at $27.

A bunch of 9 carnations are sold at $23.

The number of roses that Alexis bought to the number of carnations
that Belle bought was in the ratio of 2:3.

Belle paid $76 more for her carnations than Alexis for her roses.

a) How much did Alexis pay for her roses?

b) How many bunches of carnations did Belle buy?

Did you know?
Freshly cut carnation flowers last longer than roses

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P4/P5 Math: Cutting out Smaller Squares from Larger Rectangle (Area)

Cutting out smaller squares from a larger rectangular sheet of paper requires students to remember that there may be "wastage" involved.

Common multiples may be employed to check if there are wastage.

Such questions usually appear in P3 and P4 exams in Section C.

Plots of land divided into smaller rectangles

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