Reasoning Practice Paper 8
Reasoning Practice Paper 8 is another full-length mock of a Year 6 SATs Mathematics Reasoning paper, this time weighted towards fractions and ratio alongside the usual mix of number, calculation, measurement, geometry, statistics and algebra questions.
Before you start
Make sure you're comfortable with these topics first:
Method
- Skim the paper first to see how the questions are spread across topics, then work through them in order.
- For any ratio question, add the parts of the ratio together first to find the total number of equal parts before dividing anything.
- For any fraction question, check whether the denominators already match; if not, convert to a common denominator before adding, subtracting or comparing.
- Show every step of a ratio or fraction calculation clearly, since method marks are awarded even if a later step contains a small slip.
- Watch the wording carefully: 'how many more' or 'the difference between' means subtraction, while 'in the ratio' or 'shared between' means the amount must be split proportionally.
- Check any fraction answer is given in its simplest form if the question asks for this, and check any ratio answer adds back up to the original total.
Worked example
A necklace is made using blue and white beads in the ratio 3:5. If there are 40 beads in total, how many blue beads are there?
- Add the parts of the ratio to find the total number of equal parts: 3 + 5 = 8 parts.
- Divide the total number of beads by the number of parts to find the value of one part: 40 divided by 8 = 5 beads per part.
- Multiply the number of blue parts by the value of one part: 3 x 5 = 15.
- Check by finding the white beads too: 5 x 5 = 25, and 15 + 25 = 40, which matches the original total.
- There are 15 blue beads.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1Share 45 pounds in the ratio 2:3.Show answer
Answer: 18 pounds and 27 pounds (5 parts total, each part = 9 pounds, so 2 x 9 = 18 and 3 x 9 = 27)
Q2Work out 5/6 - 1/3.Show answer
Answer: 1/2 (5/6 - 2/6 = 3/6, which simplifies to 1/2)
Q3A ribbon is cut in the ratio 1:4. If the ribbon is 30 cm long, how long is the shorter piece?Show answer
Answer: 6 cm (5 parts total, each part = 6 cm, and the shorter piece is 1 part)
Q4Work out 2/5 x 15.Show answer
Answer: 6
Q5A model car is built to a scale of 1:20. If the model is 8 cm long, how long is the real car in metres?Show answer
Answer: 1.6 m (8 x 20 = 160 cm, which is 1.6 m)
Q6Work out 3 and 1/4 + 2 and 1/2.Show answer
Answer: 5 and 3/4 (3 + 2 = 5, and 1/4 + 2/4 = 3/4)
Exam-style questions
Written in the style of a KS2 Maths exam paper, with a full mark scheme.
In a fruit bowl, apples and oranges are in the ratio 4:3. There are 12 apples. How many oranges are there?
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Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 2 available
A recipe uses flour and sugar in the ratio 5:2. Josh has 250 g of flour and wants to use all of it. How much sugar does he need?
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Tick each line you got. Your score builds from the marks on the scheme.
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Work out 7/8 - 1/4, giving your answer in its simplest form. Show your working.
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Free printable worksheet
Want more practice on paper? Download the reasoning practice paper 8 worksheet pack - 10 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.
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