P6 Math: Before and After Ratio made Equal at the end

This question type starts with a ratio and after both values undergo some decrease, a new ratio is given.

Both values undergo another addition and that causes both values to become the same at the end.

Such questions are common in P6 Prelim Paper 2.

Calculator usage is allowed.

Benedict and Erica has erasers in the ratio of 5:7 respectively.

After Benedict gave away ³/₇ of his erasers and Erica sold some erasers,

the ratio of Benedict's to Erica's remaining erasers became 10:7.

Benedict then bought another 60 erasers and Erica bought 240 erasers.

Each have the same number of erasers at the end.

How many erasers does Erica have at first?

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P6 Math: 3 Parties Before and After with Uneven Ratio at the End

A total of 3 parties are given at first.
Each of the party undergo increase or decrease and the end ratio is given.

Some of the increase/decrease are fractional and some are numerical.

Such questions are common in Paper 2 of P6 exams

Calculator usage is allowed.

An easier version of this question can be found here.

Elizabeth, Wendy and Lindy had a total of $483 at first.

Elizabeth was given more money by her parents and had double of what she had at first.

Wendy spent $67 on a pair of ballet shoes and Lindy's brother gave her another $94.

In the end, the ratio of remaining money of Elizabeth to Wendy to Lindy was 5:4:2.

How much did Lindy have at first?

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P5/P6 Math: A Total of 3 Given with Equal Ratio at the End

This question type starts with a known total of 3 parties.

Each party undergo either a fractional decrease or value increase/decrease and all 3 parties ends with equal ratio at the end.

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

Calculator usage is allowed.

Derrick, Lawrence and Patrick had $3025 altogether at first. 

After Derrick spent ⁵/₇ of his money and Lawrence spent ¹/₄ of his money 

and Patrick spent $155, each boy have the same amount of money left. 

How much did the 3 boys have altogether at the end?

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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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P5/P6 Math: Starting Total Known with Both Parties undergoing Fractional Decrease

A total of 2 parties is given.

Each of the 2 parties undergo different fractional decrease.

The comparison between the amount left is given as multiple of another.

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

Calculator usage is allowed.

Similar questions of this type can also be found here.

Jayden and Keane have a total of $2024.

After Jayden spent ²/₅ of his money on a gaming console and

Keane spent ³/₄ of his money on a phone, 

Jayden has twice as much money left as Keane.

How much did Jayden have at first?

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P5 Fractions : Mixed numbers undergo fractional decrease

A mixed number is used to represent the mass of a substance.

This mixed number next undergo fractional decrease.
The fractional decrease may or may not include the units of measure.

Such variation will result in different method of solving and the answers will be different.

Such questions usually appear in Paper 1 of P5 Papers.
Calculator usage will not be allowed.

An easier version of this fraction problem sum can be found here.
An expert version of this question can be found here.

Sean has 2 3⁄4 litres of milk.	Melissa has 2 3⁄4 litres of apple juice.
He drank 1⁄2 litre of the milk.	She drank 1⁄2 of the apple juice.
What is the volume of milk he has left?	What is the volume of juice she has left?

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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 Math: Before and After Fractional Change and Deduction

This is a slightly more complex version of the P4 Question "here".

This question requires students to draw "Before and After" comparison models.

Calculation using long division will be impractical due to the large divisor.
Thus question shows itself again in P5 with larger numbers.

Such question will appear in P5 Exams in Paper 2.
Calculator usage is allowed.

Ken and Ryu have sum of $1040 altogether.

After Ken spent ¹/₆ of his money and Ryu spent $732 of his money,

both have the same amount of money left.

How much money did Ryu have at first?

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P6 Math: Fractional Internal Transfer and Fractional loss

The following is a popular P6 Prelim question that requires student to perform fractional internal transfer and fractional reduction.

Percentage is often thrown into the mix to represent the fraction instead.

Such questions appears in P6 Prelims and will be in Paper 2.

Calculator usage is required.

Steve and Melanie shared total of $8600 at first.

After Steve gave 50% of his money to Melanie and
Melanie spent ³/₅ of her money on a ring,
they have a total of $4730 left.

How much did Melanie have at first?

History of tradition of exchange of wedding rings

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P5/P6 Math : Before and After Fractional change to 2 parties (Advanced)

The question type below deals with 2 parties with one having more than the other undergoing fractional change.

Such questions often appear in P5 and P6 paper 2.

Calculator is allowed.

Alistair has 450 more jewels than Benedict at first.

After Alistair gave away ¹/₃ of his jewels and Benedict sold ²/₅ of his jewels, Alistair still has 360 jewels more than Benedict.

How many jewels does Alistair have at first?

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P4 Math: Before and After Fractional Change and Deduction

Such questions deals with the "Before and After" comparison models and
will commonly appear in P4 Section C in mid year SA1 or end of year SA2.

The P5 version of this question can be found "here".

Mark and Kelvin have total of $1075 altogether.
After Mark spent ⁷/₈ of his money and Kelvin spent $220 of his money,
each boy have the same amount of money left.

How much did they have left altogether at the end?

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P6 Math: Fractional Change with Ending Ratio

Questions like these appear in P6 Paper 2.

Usually 3 or 4 marks question.

Calculator usage is allowed.

Bala has $84 more than Ali at first.

After Bala spent ¹/₄ of his money and Ali spent ²/₅ of his money,

the ratio of Bala's remaining money to Ali's remaining money is 3:1.

a) How much did Ali have at first?

b) How much did Bala have at the end?

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