Ordering Fractions, Decimals & Percentages (Cambridge International IGCSE Maths)

Ordering FDP

How do I put fractions in order of size?

• When comparing only fractions, write them over a lowest common denominator

  • For $\frac{3}{5},\frac{1}{2},\frac{13}{20},\frac{7}{12}$, the lowest common denominator is 60
  • So change them to $\frac{36}{60},\frac{30}{60},\frac{39}{60},\frac{35}{60}$ and then order them by their numerators
  • From smallest to largest: $\frac{30}{60},\frac{35}{60},\frac{36}{60},\frac{39}{60}$
  • Rewrite in their original form: $\frac{1}{2},\frac{7}{12},\frac{3}{5},\frac{13}{20}$

How do I put fractions, decimals and percentages in order of size?

• When comparing a mixture of fractions, decimals and percentages, change everything into decimals

Which symbols can I use?

• Rather than just listing values in order, symbols can be used to compare them

  • For example, $\frac{1}{4}<\frac{1}{3}<\frac{1}{2}$

• Recall that $>$ means greater than and $\geq$ means greater than or equal to

  • Similarly, $<$ means less than and $\leq$ means less than or equal to

• You may also see $=$and $\neq$ (which means "not equal to")

Exam Hint A calculator can be used to quickly convert any quantities into decimals.

E.g. A fraction can be entered as a division.

Worked Example Without use of a calculator, write these numbers in order, starting with the smallest.

$\frac{1}{3}$, $\frac{2}{5}$, $\frac{9}{25}$, $\frac{4}{15}$

Answer:

As they are all fractions, write them with a common denominator The lowest common denominator is 75 Rewrite each fraction with a denominator of 75

• $\frac{1}{3}=\frac{25}{75}$ $\frac{2}{5}=\frac{30}{75}$ $\frac{9}{25}=\frac{27}{75}$ $\frac{4}{15}=\frac{20}{75}$ *

Compare and write in order from smallest to largest

$\frac{20}{75},\frac{25}{75},\frac{27}{75},\frac{30}{75}$

Rewrite in their original form

$\frac{4}{15},\frac{1}{3},\frac{9}{25},\frac{2}{5}$

Worked Example Without use of a calculator, write these numbers in the spaces below.

$\frac{7}{8}$, $\frac{5}{6}$, $0.8$, $78 \%$

..... < ..... < ..... < .....

Answer:

As there is a mixture of fractions, decimals, and percentages, rewrite each as a decimal

0.8 is already a decimal

Convert 78% to a decimal by dividing by 100

$78 \% = 0.78$

Convert $\frac{7}{8}$ to a decimal by either using short division, or halving three times

$\begin{gathered} 7 \div 2 & = 3.5 \\ 3.5 \div 2 & = 1.75 \\ 1.75 \div 2 & = 0.875 \end{gathered}$ so $\frac{7}{8}=0.875$

Convert $\frac{5}{6}$ to a decimal by using short division

equation

so $\frac{5}{6} = 0.8333... = 0.8 \dot{3}$

Write them all with 3 decimal places to determine the order

$0.875\,0.833\,0.800\,0.780$

Rewrite the decimals in order

$0.78 , 0.8 , 0.8 \dot{3} , 0.875$

Rewrite in their original form, and recall that < means "less than", so the smallest value will be first

$78 \% < 0.8 < \frac{5}{6} < \frac{7}{8}$