MathematicsExam code: 0580

Working with Fractions, Decimals and Percentages

Number

PractiseFlashcards

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
  • Give the answer 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 tenths digits show that 0.66… is the largest, and the hundredths digits 0, 1, 2 and 3 then order the other four
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%

Build on this topic

Check your understanding17 exam questions, marked instantlyTest your recall19 flashcards on the key facts