Fractions: Practice Set 4
Fractions: Practice Set 4 is a further practice set that pushes fraction skills beyond earlier practice sets, focusing on multi-step fraction word problems, fractions of a remaining amount, and converting between fractions, decimals and percentages, all without a calculator, since 11+ papers commonly wrap a fraction calculation inside a real-life context rather than asking for it in isolation.
Before you start
Make sure you're comfortable with these topics first:
Method
- Read a fraction word problem twice, noting the total amount and each fraction mentioned, since a wrong total is the most common cause of a wrong final answer.
- Work out one fraction operation at a time, in the order the problem describes events, rather than trying to combine several fractions in your head at once.
- When a fraction is taken 'of the remainder' or 'of what is left', calculate the amount left first, then apply the next fraction to that new, smaller amount, not to the original total.
- To convert a fraction to a decimal, divide the numerator by the denominator; to convert to a percentage, multiply the decimal by 100.
- Where amounts stay as fractions throughout, find a common denominator once at the start of the problem and use it for every step, rather than converting back and forth.
- At the end, check your final answer makes sense: an amount 'left over' must always be smaller than the total you started with.
Worked example
A charity shop receives 90 books. 2/5 of the books are fiction. Of the remaining books, 1/3 are children's books. How many books are neither fiction nor children's books?
- Find the number of fiction books: 2/5 x 90 = 36.
- Find the books remaining after fiction: 90 - 36 = 54.
- Find the children's books from the remainder: 1/3 x 54 = 18.
- Find the books that are neither: 54 - 18 = 36.
- The final answer is 36 books.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1Convert 3/8 to a decimal.Show answer
Answer: 0.375
Q2Convert 0.6 to a fraction in its simplest form.Show answer
Answer: 3/5
Q3Write 7/20 as a percentage.Show answer
Answer: 35%
Q4A jar has 72 sweets. 1/4 are red. Of the remaining sweets, 1/2 are green. How many sweets are green?Show answer
Answer: 27 (red = 18, remaining = 54, green = 27)
Q5Work out 5/6 - 3/8, giving your answer in its simplest form.Show answer
Answer: 11/24
Q6Find 2/7 of 84.Show answer
Answer: 24
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
Write 9/40 as a decimal, then as a percentage.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 2 available
A school raises 150 pounds at a fete. 2/5 of the money is spent on new library books. Of what remains, 1/3 is spent on sports equipment. How much money is left after both purchases?
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 4 available
A ribbon of length 3/4 m is cut into pieces each 1/8 m long. How many whole pieces can be cut, and is there any ribbon left over?
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 3 available
Free printable worksheet
Want more practice on paper? Download the fractions: practice set 4 worksheet pack - 9 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 35 of 11+ Maths Workbook 1, the whole course as one free printable PDF.
Next topics
Not quite what you needed?
Tell us what is missing on fractions: practice set 4, or which topic to write up next. Every request is read, and we reply to every one.
Build a full practice pack.
This topic is one of hundreds in the library - pick the ones a student needs and generate a printable PDF in minutes.