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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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/P5 Math: Spend and Left after buying 2 items (multiples of each other)

This question type requires students to draw comparison models and also a part/whole model to visualize the problem sum.

Such questions are common in WA2 in P4 exams and also Paper 1 in P5 exams.

Calculator usage is not allowed.

Steffi has $77 to spend at the mall.

After she bought a book and a camera, she has $14 left.

The camera costs thrice as much as the book.

How much was the book?

Vintage camera

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P4P5 Math: Fraction of Remaining(Simpler)

"Fraction of remaining" is a concept that requires students to be able to understand that in the 2 fractions given, one represents "Fraction of Total" and the other represents "Fraction of Remaining".

The denominators of both fractions need not be made to be the same as both represents a different value.

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

Calculator is not allowed. (for P5 students attempting this question)

Similar question for P4 can be found here.

A tougher version for P5 can be found here.

Calvin has a collection of precious gemstones.

¹/₄ of his gemstones are green in colour.

¹/₃ of his remaining gemstones are red and the rest are blue.

He has 24 blue gemstones.

How many gemstones does Calvin have altogether?

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P4/P5 Math: Difference between 2 Fractions of Total

Fraction of Totals where the problem sum provides 2 of such fractions and the total is not known.

Model Drawing should be employed here to demonstrate the understanding of the "total parts".

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

Calculator usage is not allowed.

Sally was given her weekly allowance on Monday.

She spent ¹/₃ of her allowance on Monday 

and spent $45 on Tuesday.

She had already spent ³/₄ of her allowance by Tuesday.

How much was her allowance?

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P4 Math: Fraction of a number

Fractions in P4 can be expressed using models.
The practice question below aims to let students use part/whole models to solve "fraction" based questions.

Such questions will appear in Section B of P4 exam papers.

³/₄ of a number is 12.

What is the number? 

Paper shredded into small pieces of itself

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P5/P6 Math: Fraction of Remaining with Additional Value at the End

Fraction of remaining question types like this requires students to use "Part/Whole Models" to represent the numerators and denominators represented in each of the fractions. 

There is usually a value (of what's left) that is given at the end for students to use it to find the total at first. But this question instead changes what is left by adding a new value to the "left" and compares it with the original total value at the end.

Such questions usually appear in Paper 2 of P5 and P6 exams.

Calculator usage is allowed.

Timmy made some lemonade for his school's open house event.

³/₈ of the lemonade were given out in the morning and ²/₅ of the remaining lemonade were given out in the afternoon.
He made another 33 litres of lemonade in the evening and had 8 more litres of lemonade than what he had at first.

How much lemonade did Timmy make 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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P4 Math: First fraction of total given

Questions like these require students to be able to draw model to represent the first fraction of total before processing the rest of the numerical values to represent the remainder.

A part whole model will allow students to be able to process the remaining using the given numerical values.

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

Gianna drank ¹/₅ of the milk in the carton.

Her father drank 115ml and her brother finished drinking the remaining 81ml.

What is the volume of milk in the carton at first in millilitres?

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P4/P5 Math: Fraction with units and without units

P4 and P5 Fractions is a relatively large topic.

One of the type of question requires student to be able to tell the difference between the following fraction problem sum.

Malcolm has 3/5 kg of sugar.	Malcolm has 3/5 kg of sugar.
He gave away 1/2 kg of the sugar.	He gave away 1/2 of the sugar.
What is the mass of sugar he has left?	What is the mass of sugar he has left?

Can you spot the difference between the 2 fraction problem sums above?

Both will produce different answers due to this subtle difference.

Such questions often appear in Section B or P4 Papers or Paper 1 of P5 Papers.
Calculator usage will not be allowed.

A more advanced version of this question can also be found here.
An expert version of this question can be found here.

Spot the difference arcade game

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P5/P6 Math: The Gap between Fraction of Total and Fraction of Total Left

Fraction problem sums like these do not provide the value of the total (at the start) nor the left (at the end) but provides a value that fills up the gap between 2 fractions [ fraction of total and fraction of total that is left ].

Model drawing is the preferred method to solve such questions.

Such questions usually appear in P5 and P6 Paper 2.
Calculator usage is allowed.

Bebe made some lollipops.

She gave ¹/₃ of her lollipops to her classmates.

She gave 60 lollipops to her cousins.

She was left with ²/₅ of her lollipops.

How many lollipops did she give her classmates?

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