P6 Math: Equal Quantity after 2 Parties undergo Fractional Decrease

The question presents 2 different items, each of different value and quantity.
After each undergo a fractional decrease, both items have the same number remaining.

The unit value of each item and the total value of the remaining items are provided.

Such questions require students to make use of "Equal Value Fractions" in order to solve.

These type of questions will usually appear in Paper 2 of P6 exams.

Calculator usage is allowed.

Craig has a stack of $2 and $10 notes.

After using ²/₉ of the $2 notes and ³/₅ of the $10 notes to buy a figurine,

he has equal number of $2 and $10 notes remaining.

He has $672 left at the end.

How much money did Craig have at first? 

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P5P6 Math: Starting Difference Given with Both ending Equal at the End

This type of question begins with a value given(usually the difference between 2 parties).

Each of the value undergo fractional decrease and both ends up to be equal in the end.

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

Calculator usage is allowed.

Rachel has $105 more than Phoebe at first.

After Rachel spent ²/₃ of her money and Phoebe spent ¹/₄ of her money,

both girls have equal amount of money left.

How much did Rachel spend?

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P5 Math: Ratio Basics (3 parties)

Ratio of 3 parties merely expresses the simplest form between 3 values and are not representing the exact value.

With one or more values given, students must make be able to derive the other values by means of multiplication or division.

Such questions usually appear in P5 Paper 1.

Calculator usage is not allowed.

Tricia, Belinda and Alicia has baked some muffins in the ratio of 4:3:1 respectively.

They baked a total of 640 muffins.

How many more muffins than Alicia did Tricia bake?

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P5 Math: Ratio (Before and After) Fractional Change

Ratio is a concept taught in P5 and it closely resembles simplified fractions.

The following question type requires student to be able to perform fractional decrease to one of the ratio numbers.

Such questions are common in Paper 1 of P5 and P6 exam papers.

Calculator usage is not allowed.

Petrina has markers and files in the ratio of 2:3 respectively.

She gave away ¹/₃ of her markers.

What is the ratio of her remaining markers to files in the end?

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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: Ratio : Difference Unchanged (Age)

Age comparison questions are common in P4 but in P5 ratio will be used(instead of fractions or multiples) to compare the ages.

These questions requires the concept of "Difference Unchanged".
Similar questions can be viewed here.

Such before and after questions will usually appear in Paper 2 of P5 exams.

Caculator usage is allowed.

The ratio of Hannah's age to Grace's age was 5:6 at first.

10 years ago, the ratio of their age was 5:8.

How old is Grace now?

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P5/P6 Math: Percentage of 2 Totals ( Equal at the End )

This question type shows that 2 unequal quantities undergo percentage decrease.

The quantity left after the percentage decrease is equal to each other.

Such question resembles "Fractions of Equal Value" and there are similar questions using "Percentage" to represent the fractions of equal value here.

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

Calculator usage is allowed.

Mr Rahim has 250 more laptops than smartphones for sale.

After selling 70% of the laptops and 20% of the smartphones,

he has the same number of laptops and smartphones left.

How many smartphones and laptops altogether does he have for sale at first?

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P6 Math: Different Percentage Discounts causing Different items to be Same Price

2 different items for sale at different discount percentages but has the same price after their respective discounts.

Such questions are common in Paper 2 of P6 Prelims and PSLE papers.
Calculator usage is allowed.

A pen was for sale at a 15% discount and a vase was selling at a 20% discount.
Both items were sold at the same price after the discount.

Lisa wanted to buy both discounted items but was short of $36.

If she only bought the pen at the discounted price, she'd have $100 left.

How much more will she need if she were to buy both items without discount?

An intricate antique Chinese vase

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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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