Practise 36 exam-style questions on Fractions, decimals and recurring decimals for Edexcel GCSE Maths (Non-calculator). Write your answer as you would in the exam and get it marked in seconds against the mark scheme, point by point, with an AI tutor on hand if you get stuck.
36 questions
1–5 marks each
Instant marking
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20 questions, marked as you go
Sample questions with model answers
Here are 4 of the questions in this topic, each with a model answer, an explanation of why it earns the marks and the mark scheme an examiner would use.
Change the improper fraction to a mixed number, then convert the fraction part. Since \(\dfrac{1}{8} = 0.125\), \(\dfrac{3}{8} = 3 \times 0.125 = 0.375\). Alternatively, divide 11.000 by 8 using short division.
Mark scheme
1 mark
M1 for a correct method, e.g. short division of 11 by 8, or \(1\frac{3}{8}\) with \(\dfrac{3}{8} = 0.375\), or \(\dfrac{1375}{1000}\)
correct answer with no working scores full marks
1 mark
A1 for 1.375
cao
Question 2
2 marks
Given that \(0.\dot{4}\dot{5} = \dfrac{5}{11}\), write \(0.0\dot{4}\dot{5}\) as a fraction in its simplest form.
Moving every digit one place to the right is dividing by 10, so \(0.0\dot{4}\dot{5}\) is one tenth of \(0.\dot{4}\dot{5}\). Dividing a fraction by 10 multiplies its denominator by 10. Using the given fact saves doing the full algebraic method.
Mark scheme
1 mark
M1 for recognising \(0.0\dot{4}\dot{5} = 0.\dot{4}\dot{5} \div 10\), e.g. \(\dfrac{5}{11} \div 10\) or \(\dfrac{5}{110}\)
or a full algebraic method, e.g. \(1000x - 10x = 45\), \(\dfrac{45}{990}\); correct answer with no working scores full marks
1 mark
A1 for \(\dfrac{1}{22}\)
cao
Question 3
3 marks
Write \(2.\dot{4}\dot{5}\) as a mixed number in its simplest form.
Separate the whole number from the recurring part, convert \(0.\dot{4}\dot{5}\) using \(100y - y\), then add the 2 back on. If you convert the whole number at once you get \(\dfrac{243}{99} = \dfrac{27}{11}\), which must still be written as a mixed number.
Mark scheme
1 mark
M1 for \(x = 2.4545\ldots\) and \(100x = 245.4545\ldots\), or for \(0.\dot{4}\dot{5}\) written as \(\dfrac{45}{99}\)
correct answer with no working scores full marks
1 mark
M1 for \(99x = 243\) or \(2 + \dfrac{45}{99}\)
oe, e.g. \(\dfrac{243}{99}\)
1 mark
A1 for \(2\frac{5}{11}\)
cao; accept \(\dfrac{27}{11}\) for M1 M1 A0
Question 4
4 marks
\(\dfrac{a}{b} = 0.\dot{3}\dot{6}\), where \(a\) and \(b\) are positive integers. \(a + b = 30\)
Find the value of \(a\) and the value of \(b\).
Model answer
Let \(x = 0.3636\ldots\), \(100x = 36.3636\ldots\), \(99x = 36\), \(x = \dfrac{36}{99} = \dfrac{4}{11}\) So \(\dfrac{a}{b} = \dfrac{4}{11}\), meaning \(a = 4k\) and \(b = 11k\) for some \(k\). \(4k + 11k = 30\), \(15k = 30\), \(k = 2\) \(a = 8\), \(b = 22\)
Explanation
First find the fraction in its simplest form, \(\dfrac{4}{11}\). Any fraction equal to it has \(a\) and \(b\) in the ratio 4 : 11, so share 30 in that ratio. Check: \(\dfrac{8}{22} = \dfrac{4}{11}\) and \(8 + 22 = 30\).
Mark scheme
1 mark
M1 for a correct method to convert \(0.\dot{3}\dot{6}\), e.g. \(100x - x = 36\)
correct answer with no working scores full marks
1 mark
A1 for \(\dfrac{36}{99}\) or \(\dfrac{4}{11}\)
1 mark
M1 for a method using \(a + b = 30\), e.g. \(a = 4k\), \(b = 11k\) with \(15k = 30\), or sharing 30 in the ratio 4 : 11
ft their fraction in its simplest form
1 mark
A1 for \(a = 8\) and \(b = 22\)
cao
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