Functional Skills Practice

🔢 Maths: Fractions, Decimals and Percentages

Fractions, Decimals and Percentages (Functional Skills Level 2)

At Level 2 you must work fluently with fractions, decimals and percentages and recognise the equivalence between all three forms (DfE subject content statement 4, reference FM L2.4). The same value can be written three ways, so being able to convert quickly is essential for everyday contexts such as money, discounts, recipes and probability, where 0 (or 0%) means impossible and 1 (or 100%) means certain.

Learn the common equivalences by heart so you can compare and order values at a glance:

Converting between forms. To turn a decimal into a percentage, multiply by 100 (move the point two places right) and add the % sign; to turn a percentage into a decimal, divide by 100 (move the point two places left). To turn a fraction into a decimal, divide the numerator by the denominator, then multiply by 100 for the percentage. To turn a percentage into a fraction, write it over 100 and simplify to its lowest terms.

Working with percentages (statement 5 / FM L2.5). You must find percentages of amounts and express one amount as a percentage of another. Without a calculator, find 1% by dividing the amount by 100, or 10% by dividing by 10, then multiply by the percent you need. Statement 6 (FM L2.6) requires calculating percentage change (any size of increase or decrease) and finding the original value after a change: use a reverse percentage, dividing the new value by the multiplier (e.g. by 1.20 after a 20% increase, or by 0.80 after a 20% decrease).

Working with fractions (statement 7 / FM L2.7). You must order, add, subtract and compare proper fractions, improper fractions and mixed numbers; use a common denominator before adding or subtracting, and always simplify your answer. You must also express one number as a fraction of another (statement 8). To find a fraction of a quantity, divide by the denominator and multiply by the numerator.

Working with decimals (statements 9 and 10). Order, approximate and compare decimals, and add, subtract, multiply and divide decimals to 3 decimal places, keeping place value aligned.

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Sample questions (35)

1. To compare a fraction, a decimal and a percentage with each other, what is the most reliable first step?

  1. Convert them all into the same form, such as decimals or percentages
  2. Add the three values together and divide by three
  3. Round each value to the nearest whole number
  4. Ignore any value that is written as a percentage

Values can only be ordered safely once they are in the same form, so converting all to decimals or percentages is the standard method. (DfE 'Subject content functional skills: mathematics' (GOV.UK), Level 2 statement 4 (equivalence between fractions, decimals and percentages).)

2. Which of these correctly states a common equivalence?

  1. One half equals 0.5 equals 50%
  2. One quarter equals 0.5 equals 25%
  3. Three quarters equals 0.7 equals 75%
  4. One fifth equals 0.5 equals 20%

One half is 0.5 as a decimal and 50% as a percentage; this is a standard equivalence. (Standard fraction-decimal-percentage equivalence table; underpins DfE Level 2 statement 4.)

3. Which of these three values is the largest: 0.6, three fifths, or 65%?

  1. 65%
  2. 0.6
  3. Three fifths
  4. They are all exactly equal

As percentages these are 60%, 60% and 65%, so 65% is the largest. (DfE Level 2 statement 4 (equivalence) and statement 9 (compare values).)

4. Which value is the smallest: 0.35, three eighths, or 33%?

  1. 33%
  2. 0.35
  3. Three eighths
  4. 0.35 and three eighths are equal smallest

As decimals these are 0.35, 0.375 and 0.33, so 33% (0.33) is the smallest. (DfE Level 2 statement 9 (order and compare decimals) and statement 4.)

5. To convert a decimal to a percentage, what should you do?

  1. Multiply the decimal by 100 and add the percent sign
  2. Divide the decimal by 100
  3. Subtract the decimal from 1
  4. Move the decimal point one place to the right

Multiplying a decimal by 100 (moving the point two places right) converts it to a percentage. (Standard conversion procedure underpinning DfE Level 2 statement 4.)

6. Which value is the largest: four fifths, 0.78, or 82%?

  1. 82%
  2. Four fifths
  3. 0.78
  4. Four fifths and 0.78 are equal largest

As decimals these are 0.8, 0.78 and 0.82, so 82% is the largest. (DfE Level 2 statement 4 (equivalence) and statement 9.)

7. What is one fifth written as a decimal and a percentage?

  1. 0.2 and 20%
  2. 0.5 and 50%
  3. 0.15 and 15%
  4. 0.25 and 25%

One fifth equals 0.2, which is 20%. (Standard equivalence table; underpins DfE Level 2 statement 4.)

8. Three offers give the same product different discount labels: Offer A is 0.45 off the price, Offer B is two fifths off, and Offer C is 42% off. Which offer gives the biggest discount?

  1. Offer A
  2. Offer B
  3. Offer C
  4. All three are the same

As percentages these are 45%, 40% and 42%, so Offer A (0.45 = 45%) gives the biggest discount. (DfE Level 2 statement 4 (equivalence) and statement 9 (compare values).)

9. Order these from smallest to largest: 0.7, seven tenths and 72%.

  1. 0.7 = seven tenths, then 72%
  2. 72%, then 0.7, then seven tenths
  3. seven tenths, then 72%, then 0.7
  4. 72%, then seven tenths, then 0.7

0.7 and seven tenths are both 70%, and 72% is larger, so the order is 0.7 = seven tenths, then 72%. (DfE Level 2 statement 4 (equivalence) and statement 9.)

10. Which value is the largest: three fifths, 0.58, or 59%?

  1. Three fifths
  2. 0.58
  3. 59%
  4. 0.58 and 59% are equal largest

As decimals these are 0.6, 0.58 and 0.59, so three fifths (0.6) is the largest. (DfE Level 2 statement 4 and statement 9 (compare decimals).)

11. A recipe needs 0.6 litres of milk, but three different jugs are marked five eighths of a litre, 62% of a litre and 0.59 of a litre. Which jug holds the most?

  1. The jug marked five eighths of a litre
  2. The jug marked 62% of a litre
  3. The jug marked 0.59 of a litre
  4. They all hold exactly 0.6 litres

Five eighths is 0.625, which is larger than 0.62 and 0.59, so the five eighths jug holds the most. (DfE Level 2 statement 4 (equivalence) and statement 9.)

12. Order these from smallest to largest: three fifths, two thirds, thirteen twentieths and seven tenths.

  1. Three fifths, thirteen twentieths, two thirds, seven tenths
  2. Three fifths, two thirds, thirteen twentieths, seven tenths
  3. Seven tenths, two thirds, thirteen twentieths, three fifths
  4. Thirteen twentieths, three fifths, seven tenths, two thirds

As percentages these are 60%, 66.7%, 65% and 70%, giving the order 60%, 65%, 66.7%, 70%. (DfE Level 2 statement 7 (order and compare fractions) and statement 4.)

13. Why does one third NOT have an exact terminating decimal equivalent?

  1. Dividing 1 by 3 gives a recurring decimal, 0.333..., that never ends
  2. One third is larger than 1, so it cannot be a decimal
  3. Thirds can only be written as percentages, never as decimals
  4. The numerator and denominator are both odd numbers

One divided by three is 0.333... recurring, which is approximately 33.3% and has no exact terminating decimal. (Standard equivalence; relevant to DfE Level 2 statement 9 (approximate decimals) and statement 4.)

14. On a probability scale, an event is given as 'a chance of three quarters'. Which equivalent values are correct?

  1. 0.75 and 75%
  2. 0.34 and 34%
  3. 0.7 and 70%
  4. 0.075 and 7.5%

Probabilities can be written as fractions, decimals or percentages; three quarters equals 0.75 equals 75%. (DfE 'Subject content functional skills: mathematics' (GOV.UK), probability content; equivalence per statement 4.)

15. Order these four values from largest to smallest: one half, 0.45, 48% and three fifths.

  1. Three fifths, one half, 48%, 0.45
  2. One half, three fifths, 0.45, 48%
  3. Three fifths, 48%, one half, 0.45
  4. 0.45, 48%, one half, three fifths

As percentages these are 50%, 45%, 48% and 60%, so largest to smallest is 60%, 50%, 48%, 45%. (DfE Level 2 statement 4 (equivalence), statement 7 and statement 9.)

16. A bid is judged on three scores written in different forms: 0.65, seven elevenths and 64%. Which score is the highest?

  1. 0.65
  2. Seven elevenths
  3. 64%
  4. Seven elevenths and 64% are equal highest

Seven elevenths is about 63.6% and the others are 65% and 64%, so 0.65 (65%) is the highest. (DfE Level 2 statement 4 (equivalence) and statement 9 (compare values).)

17. To express one quantity as a percentage of another, what should you do?

  1. Divide the part by the whole, then multiply by 100
  2. Divide the whole by the part, then multiply by 100
  3. Subtract the part from the whole, then add 100
  4. Add the two quantities and divide by 100

You write the part over the whole as a fraction, then multiply by 100 to get the percentage. (DfE Level 2 statement 5 (express one amount as a percentage of another).)

18. A learner scores 17 marks out of 20 on a test. What is this as a percentage?

  1. 85%
  2. 17%
  3. 80%
  4. 87%

17 divided by 20 is 0.85, which multiplied by 100 is 85%. (DfE Level 2 statement 5 (express one amount as a percentage of another).)

19. In a car park there are 9 vehicles and 12 spaces. What percentage of the spaces are occupied?

  1. 75%
  2. 9%
  3. 21%
  4. 90%

9 divided by 12 is 0.75, which is 75%. (DfE Level 2 statement 5 (express one amount as a percentage of another).)

20. A shop sells 30 of its 250 jars of jam in a day. What percentage of the jars were sold?

  1. 12%
  2. 30%
  3. 8%
  4. 25%

30 divided by 250 is 0.12, which is 12%. (DfE Level 2 statement 5 (express one amount as a percentage of another).)

21. A delivery driver completes 63 of the 84 drops planned for the day. What percentage of the drops were completed?

  1. 75%
  2. 63%
  3. 21%
  4. 70%

63 divided by 84 is 0.75, which is 75%. (DfE Level 2 statement 5 (express one amount as a percentage of another).)

22. A college has 130 learners enrolled and 117 of them pass their course. What is the pass rate as a percentage?

  1. 90%
  2. 87%
  3. 13%
  4. 117%

117 divided by 130 is 0.9, which is 90%. (DfE Level 2 statement 5 (express one amount as a percentage of another).)

23. Out of 64 emails received, 48 were dealt with on the same day. What percentage were dealt with that day?

  1. 75%
  2. 48%
  3. 64%
  4. 16%

48 divided by 64 is 0.75, which is 75%. (DfE Level 2 statement 5 (express one amount as a percentage of another).)

24. A warehouse holds 400 pallets and 340 of them are full. What percentage of the pallets are full?

  1. 85%
  2. 60%
  3. 34%
  4. 40%

340 divided by 400 is 0.85, which is 85%. (DfE Level 2 statement 5 (express one amount as a percentage of another).)

25. A team logs 36 faults in a month and 27 of them are repaired within 24 hours. What percentage are repaired within 24 hours?

  1. 75%
  2. 27%
  3. 36%
  4. 63%

27 divided by 36 is 0.75, which is 75%. (DfE Level 2 statement 5 (express one amount as a percentage of another).)

26. What is the percentage equivalent of the decimal 0.5?

  1. 5%
  2. 50%
  3. 0.5%
  4. 500%

To convert a decimal to a percentage you multiply by 100, so 0.5 x 100 = 50%. (Standard equivalence table; DfE 'Subject content functional skills: mathematics' (GOV.UK) Level 2 statement 4 / L2.4.)

27. Which of these is the correct equivalence for one quarter?

  1. 0.4 and 40%
  2. 0.25 and 25%
  3. 0.14 and 14%
  4. 0.75 and 75%

One quarter is 1 divided by 4, which gives 0.25, equal to 25%. (Standard fraction-decimal-percentage equivalence table; DfE Level 2 statement 4 / L2.4.)

28. A shop sign reads '0.2 off as a fraction'. Which fraction is equivalent to the decimal 0.2?

  1. One fifth
  2. One half
  3. One quarter
  4. Two thirds

0.2 equals 2/10, which simplifies to one fifth (1/5). (Standard equivalence table; DfE Level 2 statement 4 / L2.4.)

29. How do you convert a decimal into a percentage?

  1. Divide the decimal by 100
  2. Multiply the decimal by 100
  3. Add 100 to the decimal
  4. Subtract the decimal from 1

You multiply the decimal by 100 (moving the decimal point two places to the right) and add the percent sign. (Standard conversion procedure underpinning DfE Level 2 statement 4 (equivalence).)

30. How do you convert a percentage into a decimal?

  1. Multiply the percentage by 100
  2. Divide the percentage by 100
  3. Add a decimal point at the end
  4. Multiply the percentage by 10

You divide the percentage by 100 (moving the decimal point two places to the left) to get the decimal. (Standard conversion procedure underpinning DfE Level 2 statement 4 (equivalence).)

31. A weather app shows a 75% chance of rain. Written as a fraction in its lowest terms, what is 75%?

  1. Seven fifths
  2. Three quarters
  3. Three fifths
  4. One quarter

75% is 75/100, which simplifies to three quarters (3/4). (Standard equivalence table; DfE Level 2 statement 4 / L2.4.)

32. To convert the fraction 3/8 into a decimal, what calculation should you carry out?

  1. 8 divided by 3
  2. 3 multiplied by 8
  3. 3 divided by 8
  4. 3 added to 8

To turn a fraction into a decimal you divide the numerator by the denominator, so 3 divided by 8 gives 0.375. (Standard conversion procedure underpinning DfE Level 2 statement 4 (equivalence).)

33. What is the fraction 3/8 written as a decimal?

  1. 0.375
  2. 0.38
  3. 0.83
  4. 0.625

Dividing 3 by 8 gives exactly 0.375. (Standard conversion procedure underpinning DfE Level 2 statement 4 (equivalence).)

34. A test score is recorded as 7/20. What is this as a percentage?

  1. 7%
  2. 20%
  3. 35%
  4. 70%

7 divided by 20 is 0.35, and 0.35 multiplied by 100 gives 35%. (Standard conversion procedure underpinning DfE Level 2 statement 4 (equivalence).)

35. A survey states that 0.45 of customers prefer online shopping. What is this as a percentage?

  1. 4.5%
  2. 45%
  3. 0.45%
  4. 450%

Multiplying 0.45 by 100 gives 45%. (Standard conversion procedure underpinning DfE Level 2 statement 4 (equivalence).)

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