Aiden had some stickers. He gave 1/3 of them to his brother. He then gave 2/5 of the remainder to his sister. He had 36 stickers left. How many stickers did he have at first?
Aiden had 90 stickers at first.
Ans: 90
How to solve it
Draw all the stickers as one bar. Cut it into 3 equal parts: one third goes to his brother.
The two fifths is of the remainder, the 2 parts left. Cut every part into 5, so the remainder has 10 small units.
Find the sister's share: two fifths of the 10 units is 4 units.
What is left is 6 units, and that is 36 stickers, so 1 unit is 36 shared into 6, which is 6.
The whole bar is 15 units: 15 times 6 is 90 stickers at first.
The one third is of the whole bar. The two fifths is of the remainder. Two different wholes, so the two fractions can't just be added.
Practice questions with worked solutions
Question 1 is free to try. The other 15 open in the free trial, each with its full working.
Question 1 of 16 · Basic · free to tryPriya had some packets of biscuits. She gave 1/2 of them to her neighbours…Priya had some packets of…
Priya had some packets of biscuits. She gave 1/2 of them to her neighbours and 2/5 of the remainder to her cousins. She had 27 packets left. How many packets did she have at first?
take the denominators of the two fractions, 2 and 5
the bar = 2 × 5 = 10 units
fraction remaining after her neighbours = 1 − 1/2 = 1/2
1/2 × 10 = 5, so 5 units are left after her neighbours
fraction of that remainder left = 1 − 2/5 = 3/5
3/5 × 5 = 3, so 3 units are left after her cousins
3 units = 27
1 unit = 27 ÷ 3 = 9
10 units = 10 × 9 = 90
Answer: 90
For parents
How do you solve fraction of a remainder questions in P6?
In these word problems a fraction is spent or given away, then a fraction of what is left.
What your child learns here
In these word problems a fraction is spent or given away, then a fraction of what is left. Your child learns to treat the remainder as a new whole and to cut it into units the bar model can count.
Find the remainder after a first fraction is taken.
Take a second fraction of the remainder, not of the original whole.
Cut the units smaller so both fractions are whole numbers of units.
Work back from a final amount to the amount at the start. Applies multiplying fractions to multi-step word problems.
Does the answer make sense?
When your child works back to the amount at the start, it must be larger than any single amount given away or left at the end, such as Mrs Lim's 56 notebooks. A fraction of the remainder is always smaller than the same fraction of the starting amount, since part was used or given first.
How to practise these questions
The Basic questions train drawing a fraction of what is left, not of the whole. Intermediate questions add asking for one particular stage, or the value of one amount spent. Challenge questions add a fixed extra amount at each stage, end with equal shares, or anchor the chain on the gap between two amounts spent. When the remainder chain loses its way, read the written step-by-step solution.
Questions parents ask
What does 'remainder' mean in fraction questions? It means what is left after the first fraction is taken. In these questions it has nothing to do with the remainder in long division.
Why can't my child just add the two fractions? Only fractions of the same whole can be added. The second fraction is of the remainder, which is a smaller whole, so it is not the same size of fraction.
Which syllabus outcome is fraction of a remainder? It applies multiplying a proper fraction by a proper or improper fraction, taught the year before Primary 6, to multi-step word problems. The bar model makes each new whole visible.
