P6 Math: 3 Different Fractions of 3 Different Totals

This question type shows 2 fractions of 2 different totals.

The 3rd fraction shows the relationship between the 2 numerators above.

Such questions are common in Paper 1 of P6 Exams(Mid Year and Prelims)

Calculator usage is not allowed.

Mr Teo owns an aquarium that sells goldfish and guppies.

On a particular day, he sold ¹/₃ of the goldfish and ⁵/₁₁ of the guppies.

⁸/₁₃ of the fish sold that day were goldfish.

What fraction of all his fish were sold that day?

                                                1)    ²⁶/₃₃

                                                2)    ²⁶/₃₅

                                                3)    ¹³/₃₅

                                                4)    ⁶/₁₁

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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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P5/P6 Math: Percentage of Remaining

The question first presents a "percentage of a total" used.

Followed by another "percentage of remaining" used.

A value is given for the amount "left"

Such questions are similar to "fraction of remaining" and 

usually appear in Paper 2 of P5 or P6 exams.

Calculator usage is allowed.

Wendy has a a full tank of petrol in her car at first.

30% of the petrol was used when she drove from home to her aunt's place.

She used 20% of the remaining petrol to ferry her aunt to the city.

She has has 28 litres of fuel remaining in the car.

How much fuel did she have at first?

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P6 Math: Fractions with Different Values

Such "fraction" questions are further complicated by having different values tagged to each group. Each of the "fraction of total" and "fraction of remaining" and "left" groups have different values/scores/points.

These questions often appear in Paper 2.

Calculator usage is allowed.

During a carnival, a total of 1748 play tokens were given out free to children whom visited.

¹/₄ of the children received 5 tokens each and 

²/₅ of the remaining children received 4 tokens each.

The rest of the children each received 3 tokens.

How many children visited the carnival?

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P6 Math: Fractions with incomplete sets

With a known quantity expressed as a fraction, smaller (equal)quantities in fraction are being removed until the last remaining quantity is left. 

Such questions often appear in Paper 1 of P6 papers.

Calculator usage is not allowed.

Tracy has ⁷/₅ kg of sugar. 

She packed them into as many packets of ¹/₈ kg as possible
and had some sugar left unpacked.

How many packets of sugar was she able to get?

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P6 Math: Starting Ratio and Ending Fraction and Ending Value

This question begins with a ratio between 2 parties.

Both will share to spend on an item [ unequal shares ].

One of the parties will have a fraction of its amount left and the other party will have a certain value remaining after the spending.

Matt and his brother has money in the ratio of 5:3 at first.

They shared to buy a handbag for their mother.

Matt paid for 60% of the handbag and his brother paid for the rest.

After paying for the handbag, Matt has ¹/₄ of his money left and his brother has $316 left.

How much was the handbag?

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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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P3/P4 Math: Two Fractions of Total Given

Fraction problem sums are common in Section C of P3 and P4 exams.

A "fraction of the total" representing one item and another "fraction of the total" representing another item. 

The third information given is usually the value of the first item, second item or the amount left.

A slightly more complex version of this question can be found here.

Bala have some books.

¹/₃ of his books are about cars.

¹/₉ of the books are about planes.

The rest of the books are about dinosaurs.

He has 55 books about dinosaurs.

How many books does Bala have altogether?

A Stegosaurus from the Jurassic Period

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