A fraction of the remainder is in the Primary 5 Four Operations of Fractions chapter. The lesson film is the one Mathweave teaches this skill with in Primary 6, and the practice set below is written for Primary 5.
Lesson video, with the working
Fraction of the remainder
2 min 56 s
The question shows first; its working is written as the film explains it.
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, each with its full working.
Question 1 of 1 · Intermediate · free to try2/3 of the beads in a box are red and the rest are blue. Siti uses 3/4 of…2/3 of the beads in a box are…
2/3 of the beads in a box are red and the rest are blue. Siti uses 3/4 of the red beads and 2/5 of the blue beads. She has 66 beads left. (a) What fraction of all the beads does she use? Give your answer in simplest form. (b) How many beads were in the box at first?
How do you solve fraction of the remainder questions in P5?
A fraction of the remainder question takes one fraction of a whole, then another fraction of what is left.
What your child learns here
A fraction of the remainder question takes one fraction of a whole, then another fraction of what is left. This page teaches it with a bar model, applying the Primary 5 outcome on multiplying a proper fraction by a proper fraction.
The first fraction is of the whole; the second fraction is of the remainder.
Every part of the bar is cut into the same number of units, so both fractions can be counted on one bar.
A fraction of the remainder is a fraction of a fraction: one half of two thirds is one third of the whole.
The amount left at the end is matched to its number to find one unit, and then the whole.
Does the answer make sense?
The fraction of beads used must be less than 1, so your child's number of beads at first must be more than the 66 left. With 19/30 used, a little over one third is left, so the box must have held a little under three times 66 beads.
How to practise these questions
The questions here split one collection into two parts, use a different fraction of each part, and give the number left. Your child first finds what fraction of the whole collection was used, then turns the fraction left into a count to reach the total. Drawing both parts as one bar keeps both fractions on the same whole. If it stalls, watch the solution film for that question, then try it again later from Revision.
Questions parents ask
What is a fraction of the remainder? It is a fraction of what is left after a first part has gone, not a fraction of the whole. One third of the remainder after one quarter has gone is one quarter of the whole.
Should my child use the bar model or multiply fractions? Both reach the same answer. The bar shows each fraction as equal units, and multiplying works it out as a fraction of a fraction, which is the Primary 5 outcome this page applies.
Is fraction of the remainder taught in Primary 5? Multiplying a proper fraction by a proper fraction is a Primary 5 outcome, and fraction of the remainder questions use it. This page teaches it with a bar, a lesson film and a worked example.
