Mathweave
Menu
Lessons How it works Pricing AboutSign inStart your free trialFree trial

Primary 6 · Fractions · Question type 2.3

P6 Fractions: Fraction of the Remainder Problems

The second fraction is taken from the remainder, which is a new and smaller whole, so the two fractions cannot be added. Identify what is left after the first change before finding a fraction of that amount.

Try the question yourself, or watch the lesson first.

Primary 6, on the MOE Primary Mathematics syllabus.

In the Fractions chapter7 question types · see the chapter

The lesson · 2 minutes 29 seconds

How do you solve P6 fraction-of-the-remainder problems?

Watch: 1/3 of the stickers given away, then 2/5 of what is left

Another worked example

A worked example

Kumar spent 1/3 of his money on a badminton racket. He then spent 3/8 of the remainder on a pair of shoes. The racket cost $46 more than the shoes. How much money did Kumar have left in the end?

The working · Nine lines

The step-by-step working

Written out in full, the way it should appear on paper.

  1. the bar = 3 × 8 = 24 units
  2. the racket = 1/3 of 24 units, so 8 units
  3. fraction left after the racket = 1 - 1/3 = 2/3 of 24 units, so 16 units
  4. the shoes = 3/8 of 16 units, so 6 units
  5. the racket cost 8 - 6 = 2 units more than the shoes
  6. 2 units = $46
  7. 1 unit = $46 ÷ 2 = $23
  8. he had 16 - 6 = 10 units left
  9. 10 units = 10 × $23 = $230

The answer is $230.

Practise · Modelled on top school exam questions

Try a different question

Try it yourself first. Open the solution when you want to see the steps. No sign-up is needed. These questions are written by Mathweave, not copied from school papers.

Try it yourself

Find the notebooks at first

Draw your own model and find the amount at first.

Mrs Lim had some notebooks. She gave 1/5 of them to the library and 1/3 of the remainder to her class. She had 56 notebooks left. How many notebooks did she have at first?

Show the step-by-step solution
  1. take the denominators of the two fractions, 5 and 3
  2. the bar = 5 × 3 = 15 units
  3. fraction remaining after the library = 1 - 1/5 = 4/5
  4. 4/5 × 15 = 12, so 12 units are left after the library
  5. fraction of that remainder left = 1 - 1/3 = 2/3
  6. 2/3 × 12 = 8, so 8 units are left after her class
  7. 8 units = 56
  8. 1 unit = 56 ÷ 8 = 7
  9. 15 units = 15 × 7 = 105

Ans: 105

Keep practising

The practice plan adds more questions and saved progress.

See practice plans See how practice works

Choose your next step

Next, compare equal fractions of two different wholes. Equal Fractions of Two Wholes →

← Back to the chapter: three questions and all the lessons