Do you know that Percentage and the rest of the topics like Fraction, Decimal and Ratio are inter-related?! (see pic attached) They are actually one big family!! The unique thing about Percentage is ....it is a fraction OUT OF 100 (and not other numbers) and its symbol is '%'. That is why in P5, the students will be taught on how to convert percetnage into fraction and decimal! :)
The CONFUSION or common mistake Mistake 1 When comes to problem sums, most students will just add or subtract the % because they see the percentage symbol (%) just like how they see the symbol for the units of measurement, i.e. '$', 'cm', 'kg', etc. Hence, they will just add and subtract the percentages, which is WRONG;p This is because % is NOT a unit of measurement but a symbol to represent "out of 100".
Mistake 2 The whole for percentage is the same, i.e. 100% hence students thought they are the same hence proceed to add or subtract the percentages :<
THING YOU NEED TO KNOW ABOUT % Once the 100% which we called the "percentage base" is referring to different wholes or different part of the whole and there is no clue given in the question that the different wholes have the same value, then it CANNOT be added or subtracted!
E.g. 1. "In a dance club, 30% of the members are men, 25% of the members are women and the rest are children. If there are 45 more children than men, how many members are there in the club?"
30%25% 30%-> Men 25%-> Women 100%-> Total members 100%-> Total members
The percentage base (100%) for both of the percentages are referring to the same whole, i.e. Total members hence they CAN be subtracted or added!:)
E.g. 2 "In a dance club, 30% of the members are men, 25% of the REMAINING members are women and the rest are children. If there are 32 more children than men, how many members are there in the club?"
30% 25% 30%-> Men 25%-> Women 100%-> Total members 100%-> Remaining members
The percentage base (100%) for both of the percentages are referring to the DIFFERENT part of whole hence they CANNOT be subtracted or added.
DO YOU KNOW ... Percentage problem sums need not solved by using %? It can be solved by the way on how you solve when doing Fractions questions!:)
HOW IT WORKS? Once % can be converted into Fractions, the question will just look like the usual fraction question! See example below.
E.g. 3 Jolin has some money. She used 60% (60/100 = 3/5) of her money to buy a handbag. She used 25% (25/100 = 1/4) of her remaining money to buy a blouse. She paid $25 more on the handbag than the blouse. How much money did she have at first?
KEY POINT to reiterate When the denominators are referring to different wholes (or different part of the whole) and there is no clue given in the question that the different wholes have the same value, then the fractions (or Percentages) CANNOT be added or subtracted.
In this question,the denominators are referring to 2 different PART of the whole hence CANNOT be added or subtracted. Denominator '5' (or 100%) refers to the total money Denominator '4' (or 100%) refers to the REMAINING money
HOW TO SOLVE? It can be solved by either: 1) Model ("Pull down" models) or 2) Branching (see sharing on 'Branching' above)
Hope the above sharing has deepen your understanding on 'Percentage' !!:)
Common mistakes in Percentages (Part B)
Do you make the same mistake as shown in Solution A in the picutre attached? If yes, please take EXTRA note now!!:)