0580

Working with Fractions, Decimals and Percentages

Number

Ordering fractions only

  • Rewrite every fraction over the lowest common denominator, then compare numerators
    • For 2/3, 5/8, 7/12 and 3/4 the lowest common denominator is 24
    • These become 16/24, 15/24, 14/24 and 18/24
    • Ascending order is therefore 7/12, 5/8, 2/3, 3/4
  • The answer must be given in the form the values were originally written in

Ordering a mixed list

  • Convert every value to a decimal, since decimals are the one form that can be compared column by column
Ordering 0.31, two thirds, the square root of 0.09, 32 per cent and 3 to the power minus 1 by first turning each into a decimal: 0.31 already is one, two thirds is 0.6 recurring, the root of 0.09 is 0.3, 32 per cent is 0.32, and 3 to the power minus 1 is a third, or 0.3 recurring
Source: Ordering FDP by Save My Exams
  • Pad the decimals to a common number of places before comparing
The same five decimals written in a column with their points lined up, then compared one digit at a time: the first digits are all zero, so the second digits 0, 1, 2, 3 and 6 settle the order
Source: Ordering FDP by Save My Exams
  • Order the decimals, then rewrite each in its original form

Comparison symbols

  • A chain of values can be joined with the inequality symbols rather than listed
    • 1/5 < 1/4 < 1/3
  • Recall that > is greater than, < is less than, ⩾ is greater than or equal to, and ⩽ is less than or equal to
Worked example

Ordering a mixed list without a calculator

Write these values in ascending order: 0.62, 5/8, 63%, 3/5

Solution:

  • Convert each to a decimal
  • 0.62 is already a decimal
  • 5/8 by repeated halving: 5, 2.5, 1.25, 0.625
  • 63% divided by 100 gives 0.63
  • 3/5 is equivalent to 60/100, so 0.6
  • Pad to three places: 0.620, 0.625, 0.630, 0.600
  • Ascending order of the decimals: 0.600, 0.620, 0.625, 0.630
  • Rewritten in their original forms: 3/5, 0.62, 5/8, 63%
Exam tip

Convert everything to decimals to decide the order, then give the answer back in the forms the question used. Answering with your decimals loses the mark, and so does giving the order the wrong way round — check whether it asked for smallest or largest first.