Fractions and Decimals: Practice Set 5
Fractions and Decimals: Practice Set 5 is a mixed practice set combining fraction and decimal skills: converting between the two, ordering a mixed list, and calculating with both. It is a repeated cross-topic combination in 11+ papers, used to check that a student can move fluently between the two representations rather than only calculating within one of them.
Method
- Recognise common fraction-decimal equivalents instantly (1/2=0.5, 1/4=0.25, 1/5=0.2, 1/10=0.1, 3/4=0.75) rather than converting from scratch each time.
- For a fraction without a memorised equivalent, divide the numerator by the denominator to get its decimal form.
- To convert a decimal to a fraction, write it over the correct power of ten (tenths or hundredths) and simplify.
- When ordering a mixed list of fractions and decimals, convert everything into the same form, usually decimals, before comparing.
- When adding or subtracting decimals, line up the decimal points before calculating, including any missing zeros.
- When adding or subtracting fractions, find a common denominator first, exactly as in a fractions-only question.
- Always check whether the question wants the answer as a fraction or a decimal, and give it in the form asked for.
Worked example
Put these in order from smallest to largest: 0.6, 3/4, 0.35, 2/5.
- Convert 3/4 to a decimal: 3/4 = 0.75.
- Convert 2/5 to a decimal: 2/5 = 0.4.
- Now compare all four decimals: 0.6, 0.75, 0.35, 0.4.
- Order them smallest to largest: 0.35, 0.4, 0.6, 0.75.
- Write the answer using the original values: 0.35, 2/5, 0.6, 3/4.
Practice questions
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Q1Convert 7/10 to a decimal.Show answer
Answer: 0.7
Q2Convert 0.85 to a fraction in its simplest form.Show answer
Answer: 85/100 = 17/20
Q3Work out 0.3 + 0.45.Show answer
Answer: 0.75
Q4Work out 1/2 + 1/4.Show answer
Answer: 3/4
Q5Which is larger, 0.6 or 5/8?Show answer
Answer: 5/8 = 0.625, which is larger than 0.6.
Q6Work out 2.5 - 0.75.Show answer
Answer: 1.75
Q7Convert 9/20 to a decimal.Show answer
Answer: 0.45
Q8Work out 3/5 as a decimal, then double it.Show answer
Answer: 3/5 = 0.6, doubled = 1.2.
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A recipe uses 0.375kg of flour. (a) Write this weight as a fraction of a kilogram in its simplest form. (b) State how many grams this is.
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Three test scores are given as 0.7, 3/4 and 0.68. (a) Write all three as decimals to 2 decimal places. (b) Which score is the highest?
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Free printable worksheet
Want more practice on paper? Download the fractions and decimals: practice set 5 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 37 of 11+ Maths Workbook 1, the whole course as one free printable PDF.
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