P4 Math : Fraction of Total given between 2 parties

When a fraction of total is given to describe the one share between 2 parties, the remaining fraction is meant to represent the other share.

Such fraction problem sum require students to make use of both numerators to compare the difference given, so as to derive and calculate the total value.

Such questions are common in P4 exams.

Two brothers, Imann and Najip were given some money by their parents.

Imann received ²/₉ of the total amount and received $25 less than Najip.

How much money were given to them altogether?

AI generated picture of 2 brothers

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P4 Math: One Party Unchanged ( Advanced )

2 parties "Before and After" comparison questions are staple section C questions in P4 exams.

The following question is a type of "One Party Changed" question.
Such questions are similar to the ones here.

But this version poses a slight challenge when students attempt to solve it via model drawing (comparison models).

Chris has 40 more erasers than Devi at first.

After Devi bought 4 more erasers,

Chris now has 5 times as many erasers as Devi.

How many erasers did Devi have at first?

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P4 Math: Quantity Difference and Total Value Given

This is an easier version of a common P5 question shown here.

There are 2 types of items purchased and one of the items bought is slightly more than the other.

The cost of each type of item is given and the difference between the quantities of the 2 types of items bought is also know.

Such question requires students to use "set method" to solve.

These questions are common in Section C of P4 exam papers and will be more apparent in P5 exams.

Calculator usage is not allowed.

Siew Lee bought 1 more apple than pears and 

paid $69 altogether for all the apples and pears.

Each apple cost $5 and each pear cost $3.

How many apples did Siew Lee buy?

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P5/P6 Math: Starting Fraction Comparison and Ending with Difference

Fraction Comparison between 2 parties, taught in P5, will appear with many "Before and After" type problem sums.

One of such problem sums presents itself with a known starting fractional comparison between 2 parties.

After one of the party undergoes fractional decrease and the other going through an increase or decrease with a known value, the ending difference is given.

Such questions are common in P5 Paper 2.

Calculator usage is allowed.

Aaron has ⁴/₅ as many sweets as Kelvin at first.

After Aaron ate ¹/₂ of his sweets and Kelvin bought 30 more sweets,

Kelvin now has 63 more sweets than Aaron.

How many sweets did they have altogether at first?

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P4 Math: Before and After : Start with More, Ends with Equal

This question type is a "Before and After" comparison which starts with one party have more items than the other.

After one party undergo a decrease and the other having an increase, both parties ends up with the same items.

Students are required to use "before and after" comparison models to represent what they understand from the given values.

Such question often appear in Section C of P4 exams.

At first, Alan has thrice as much money as Ben.

After Alan spents $30 and Ben received $20 from his mum,

both boys have equal amount of money remaining.

How much did Alan have at first?

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P4/P5 Math: Before and After Fractional Decrease (Start Same, End with Difference)

The questions starts off with equal quantities of 2 different items.

Each item undergoes different fractional decrease.

The difference at the end is given.

Such question requires students to be able to use "Before and After" models 

and use the denominator of each fraction to show the total items of either type at first. 

Such questions usually appear in P4 SA2 papers and P5 Paper 1.

Calculator usage is not allowed.

A slightly more complex version of this question for P5 and P6 students can be found here.

Alison has the same number of red and white roses.

After giving away ¹/₄ of the red roses and ¹/₃ of the white roses,

she now has 24 more red than white roses.

How many roses does she have altogether at first?

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P6 Math: Splitting 2 groups to become 4

For questions like these, there will be a ratio to split a larger group into 2.

Each of the smaller group is divided into 2 smaller groups.
Students are required to make use of repeated identity concept in order to solve such questions.

These questions often appear in Paper 2.
Calculator usage is accepted.

The children in a dance hall are divided equally into 2 groups.

In the first group, there were 20 more girls than boys.

In the second group, there were 12 more boys than girls.

45% of all the children in the dance hall are boys.

How many children are there at the dance hall?

Vintage picture of children dancing in hall

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P5/P6 Math: Fractional Internal Transfer with Total and Ending Difference Known

The following question type starts with a known total between 2 parties.

One of the party transfers a fraction of itself to the other.
The ending difference is also known.

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

There are 234 white and black gloves.

After ²/₅ of the white gloves dyed to become black,

there were still 24 more white gloves than black gloves.

How many black gloves were there at first?

Rock climbing gloves help to prevent abrasions on skin

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P5 Math: Total of 2 items with different quantities and different values

The question type below deals with 2 different items, each with different individual values and quantity. 

One item bought has a larger quantity that the other.
The total value of both items and their individual value difference are given.

Such questions often appear in P5 mid year exam onwards.

This is a paper 2 question so calculator is allowed.

A tougher version of this question for P6 students can be found here.

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

Calista bought 6 more dolls than hairbands from a shop.

Each doll costs $11 and each hairband costs $7.

She spent a total of $156 of all the hairbands and dolls.

How many dolls did she buy?

Classic Porcelain Dolls

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P5/P6 Math: Before and After Fractional Change with Starting Difference (Advanced)

The question below require students to be able to split up 2 different quantities with the starting difference given.

Each unknown quantity is needed to split up to its corresponding fractions.
The difference between the 2 quantities at the end is given.

A similar variation of this question can also be found "here".

Such questions will appear in P5 SA2 and P6 Paper 2.
Calculator usage is allowed.

Harry has 45 more pencils than Matthew at first.

After Harry sold ¹/₃ of his pencils and Matthew gave ¹/₂ of his pencils away,

Harry has 80 more pencils than Matthew at the end.

How many pencils did both have altogether at first?

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P3/P4 Math: 3 Party Comparison Model Drawing ( within a same sentence )

Comparing 3 parties with 2 separate sentences is common in P3.

There are 13 more green than red ribbons.

There are 10 more blue than green ribbons.

In the later part of P3 and onto P4,
students are required to know how to draw comparison models with a single sentence such as one below.

Mark has 15 more cards than Reuben and 11 less cards than Bernard.
Who has the most and who has the least cards?

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P5/P6 Math: Amount of Money Spent and Left of 2 Different Parties with Comparisons

This question type deals with 2 parties with a total sum of money.

There is a comparison with multiples on the amount of money spent between the 2 parties.
The amount of money left is also compared using multiples.

Such questions are suitable for P5 and P6.
These questions will usually appear in paper 2 in P5 SA2 and P6 papers.

Calculator usage is allowed.

Karlie and Lenny had a total of $1335.50 at first.

Karlie spent 4 times as much money as Lenny.

The amount of money that Lenny had left 

was $15 more than what he had spent.

The amount of money that Karlie had left was 

half as much as what Lenny had left.

How much did both have left altogether at the end?

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