Conversion between decimals, fractions, and percentages.
Fractions as measurements VS Fractions as units.
Used 6/7 kg VS Used 6/7 of the sugar
Units in the numerators and denominators – what do each of them refer to
E.g. 2/5 of the original cookies are left VS The vanilla cookies left is 2/5 of the chocolate cookies left.
Equivalent proportion
Make numerator same
When applying the ‘Before Change After’ concept, a change involving proportion (fraction or percentage) can be written as a BCA ratio.
When there is more than 1 set of ratios recorded, look for the common base. If there is no common base, apply units and parts.
Identify unchanged group, unchanged total, unchanged difference for the common base.
PERCENTAGE
Percentage discount and percentage GST cannot be added or subtracted together.
100 units in the percentage discount refer to the original price
100 units in the percentage GST refers to the discounted price
Percentage ‘more than’ or ‘less than’ – always treat the subject at the end of the phrase as 100%.
E.g. Yenni has 40% fewer beads than John.
Percentage increase or decrease – express the increase or decrease as a fraction of the original first, then multiply by 100 to convert the fraction to a percentage.
Percentage discount – express the discount as a fraction of the original first, then multiply by 100 to convert the fraction to a percentage.
“20% decrease from July to August and 5% increase from August to September” – The first month mentioned in each phrasing is treated as 100% (100 units).
Statements containing a fraction or percentage which shows a comparison of units between two groups – use ratio to solve, then identify the common base.
E.g. John has 20% as much money as Peter.
DIVISON STATEMENTS
Division statements that produce decimals (e.g. 7.033333… or 7.5) – three types of answers to give depending on what the answer should represent.
Remainder (usually for grouping)
Fraction (for long string of digits)
Decimal (for terminating decimals)
Do not round off the answer (for decimals especially) unless required by the question.
