P5/P6 Math: 3 Item Types with Different Quantities and Values

Such questions uses fraction and multiples(ratio) to give a breakdown of the distribution of 3 different items. Each of the item have different values and the total value of all quantities of 3 items is also provided.

Such questions are common in Paper 2 of P5 exams.

Calculator usage is allowed.

Erica bought a number of durians,watermelons and jackfruits 

from the market and spent $620 altogether.

¹/₂ of all the fruits bought were durians.

The ratio of the number of watermelons to jackfruits bought was 3:2.

Each durian costs $20, each watermelon $4 and each jackfruit was $6.

How many durians did Erica buy?

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P5 Math: Percentage and Ratio to describe 3 Values

Once students are taught percentage and ratio, these 2 concepts can be presented in the same problem sum such as the one below.

Students must make use of the "repeated identity" method to solve.

Such questions are common in WA2 and SA2 of P5 exams.

Calculator usage is allowed.

There are oranges, pears and apples for sale at a fruit stall.

15% of the fruits at the stall are oranges.

The ratio of pears to apples at the stall is 12:5.

There are 150 more apples than oranges at the stall.

How many fruits are there altogether at the fruit stall?

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P5/P6 Math: Ratio of 4 Triangles in a Rectangle

A rectangle as a composite figure containing 4 triangles.

The relationship between the triangles and rectangles are given in both fractions and ratio.

A value of the area of one of the shapes is also given.

Such questions are common in P5 and P6 Paper 2.

Calculator usage is allowed.

Triangular window panes forming rectangles and squares

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P5 Math: Splitting 2 Groups to become 4

A group of items is being split into 2 using fractions.
Each of the group is being sub-divided again using another pair of fractions.

Such questions require the student to recognise the repeated identity in order to ensure that the fractional split in each group is correctly processed.

These questions often appear in Paper 2 of P5 and P6 exams.
Calculator usage is allowed. 

A similar version of this question using percentages can also be found here.

At first, ¹/₃ of the fruits in the basket are red grapes, the rest are green grapes.

¹/₂ of the red grapes and ¹/₄ of the green grapes are sold.

150 red and green grapes were sold altogether.

How many grapes were there at the basket at the start?

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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: Repeated Identity (Ratios as Fractions)

The question presents 3 unique items of different quantities and each or 2 of them are compared with the total using "fractions".
2 of such comparison statements are given and the total is also known.

Questions like these requires students to use "ratio" methods to solve a seemingly "fraction" problem sum.

Cocepts such as "total unchanged" and "repeated identity" are required to solve such questions.

These questions will usually appear in Paper 2 of P5 and P6 exam papers.

Calculator usage is allowed.

Patricia has a collection of 135 books, stickers and pens.

²/₃ of these items were not pens.

³/₅ of these items were either books or pens.

a) How many items of Patricia's collection were stickers?

b) What is the ratio of her stickers to pens?

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P5/P6 Math: Fractions and Ratio vs Repeated Identity

This following fraction/ratio question requires students to be able to identify the repeated identities in order to be able to make sense of the relationship between each ratio/fraction.

A starting ratio is given between 2 items.

Each of the item is then split again into 2 types via fractions.

The relationship between 2 of the split items are given with a comparison statement.

[eg more than, less than ]

Such questions usually appear in Paper 2 of P5 SA2 and P6 exams.

Calculator usage is allowed.

The ratio of boys to girls at the swim meet is 3:2.

¹/₄ of the boys and ¹/₃ of the girls are swimming
and the rest are not swimming.

There are 11 more boys than girls, whom are not swimming.

How many boys and girls are there altogether at the swim meet?

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P5/P6 Math : 4 Different Regions of the Rectangle

Such questions usually appears in P5 Paper 2 after students have learnt ratio and triangles.

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The diagram above may not drawn to scale.

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P5/P6 Math : Repeated Identity Ratio (Basic)

Questions of these type will start to appear in tests and exam papers once the students have been exposed to REPEATED IDENTITY and RATIO.

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

Gerald, Thomas and Brandon shared the cost of a present.

The ratio of Gerald's share to Thomas' share was 2:3.
The ratio of Thomas' share to Brandon's share was 1:2.

Brandon paid $48 more for his share than Gerald.

How much was the present?

Some history about Christmas

If you are able to solve the above question, try the one below with higher difficulty.

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P6 Math: 3 Parties Fractional Comparison (One Vs Sum of Two)

The following question is a high value 4 or 5 marks P6 Math paper 2 type questions.

Calculator usage is allowed.

Although it looks like a fraction problem sum,
this question requires the usage of two known ratio techniques in order to solve.

Abel, Benny and Carlise shared some stickers.

Half of Abel's stickers was equal to 1/4 of Benny's and Carlise's stickers combined.

1/4 of Benny's stickers was the same quantity
as 1/5 of the total of Abel's and Carlise's stickers.

What is the ratio of Abel to Benny to Carlise's stickers?

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P5/P6 Math: Repeated Identity (Advanced)

Questions of these type will start to appear in tests and exam papers once the students have been exposed to REPEATED IDENTITY and RATIO.

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

Mabel, Alice and Kate have a total of 697 beads.

The ratio of Mabel's beads to the total of Alice's and Kate's beads is 3:14.

The ratio of Alice's beads to those that belongs to both Mabel and Kate is 6:11.

How many beads does Kate have?

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