Fractions: Practice Set 2
Fractions: Practice Set 2 gives a fresh set of questions on simplifying, comparing, converting and calculating with fractions, including mixed numbers, without a calculator. It follows on from the first Fractions set, practising the same core skills of finding a common denominator, multiplying and dividing fractions, and finding a fraction of an amount.
Method
- To simplify a fraction, find the highest common factor of the numerator and denominator and divide both by it.
- To add or subtract fractions with different denominators, convert them to equivalent fractions with a common denominator first.
- To add or subtract mixed numbers, convert them to improper fractions first, then apply the same common-denominator method before converting back at the end.
- To multiply fractions, multiply the numerators together and the denominators together, cancelling common factors first where possible.
- To divide by a fraction, multiply by its reciprocal, found by swapping the numerator and denominator of the second fraction.
- To find a fraction of a quantity, divide by the denominator then multiply by the numerator.
Worked example
Work out 3 1/4 - 1 5/6, giving your answer as a mixed number in its simplest form.
- Convert both mixed numbers to improper fractions: 3 1/4 = 13/4 and 1 5/6 = 11/6.
- Find a common denominator for 4 and 6: the lowest common multiple is 12.
- Convert both fractions to twelfths: 13/4 = 39/12 and 11/6 = 22/12.
- Subtract the numerators, keeping the denominator the same: 39/12 - 22/12 = 17/12.
- Convert the improper fraction back to a mixed number: 17/12 = 1 5/12, and check that 5/12 cannot be simplified further, since 5 and 12 share no common factor.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1Simplify 12/18 fully.Show answer
Answer: 2/3
Q2Write 29/8 as a mixed number.Show answer
Answer: 3 5/8
Q3Work out 5/9 + 2/9, giving your answer in its simplest form.Show answer
Answer: 7/9
Q4Work out 7/8 - 1/4, giving your answer in its simplest form.Show answer
Answer: 5/8 (7/8 - 2/8 = 5/8)
Q5Work out 3/4 x 2/9, giving your answer in its simplest form.Show answer
Answer: 1/6 (6/36 simplified)
Q6Find 5/8 of 96.Show answer
Answer: 60 (96 / 8 = 12, 12 x 5 = 60)
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
Which of the following fractions is NOT equivalent to 3/4? A) 6/8 B) 9/12 C) 12/15 D) 15/20
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 2 available
A bakery in Bristol makes 210 loaves one morning. By 9am, 3/7 of the loaves have been sold. Of the loaves that remain, 1/3 are sold by midday. How many loaves are left after midday?
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 4 available
On a school trip organised from a school in Cardiff, 1/4 of the students travel by coach. Of the students who do not travel by coach, 1/3 walk and the rest cycle. Given that 30 students cycle, work out the total number of students who went on the trip.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 5 available
Free printable worksheet
Want more practice on paper? Download the fractions: practice set 2 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 26 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 2, 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.