# PSLE Math Tips : Understanding Base Percentage

Percentage is a topic that often throws a few curveballs in the way of phrasing. Many students are often confused in solving percentage questions as they cannot identify the true base percentage. Here are some examples to help illustrate this concept of base percentage to your kids.

**Example 1: Percentage Increase
**Karl had a 15% salary increase in starting from January.

Which of the statements is true?

Statement 1: Karl’s salary in December is 85% and his salary in January is 100%

Statement 2: Karl’s salary in December is 100% and his salary in January is 115%.

To solve this, we need to look at the base percentage, which is his salary in December. Statement 2 is correct as the increase in salary should be computed by adding the increase to the base percentage in December.

**Example 2: Percentage Reduction
**Kenny bought a bag which was 20% cheaper than Lina’s bag.

Which of the statements is true?

Statement 1: Kenny’s bag is 80% and Lina’s bag is 100%

Statement 2: Kenny’s bag is 100% and Lina’s bag is 120%.

In this case, statement 1 is true, as the 20% discount should be subtracted from the base percentage. Thus Lina’s bag should be the base percentage, since Kenny’s bag is cheaper by 20%.

**Example 3: Percentage of a Percentage
**Daniel bought a bag which had a 50% discount. The shop owner gave him another 50% discount. Did he get his bag for free?

100% X 50% or 100% – 50% = 50%

50% X 50% = 25%

The answer is no, as since the discount was on top of another discount, Daniel still had to pay the shop owner 25% of the original selling price. Note that the base percentage has changed therefore the percentage discount is applied to different bases.

**Example 4: Comparison of 3 Quantities
**Kingston has 20% more beads that Lenny. Lenny has 50% more beads than Peter. What the ratio of Peter’s beads to Kingston’s beads?

Base Percentage: Peter –> 100%

Lenny –> Has 50% more than Peter so 100% + 50% or 100% X 150% = 150%

Kingston –> Has 20% more than Lenny so 150% X 120% = 180%

Peter : Kingston –> 100 : 180 = 5:9

Notice that in this case, we take the lowest value, Peter’s percentage as the base percentage and work out Lenny’s percentage from there. Then, we use Lenny’s percentage as the base and work out Kingston’s percentage. After calculation, the percentages of both Peter and Kingston can be put together and simplified to the lowest ratio.

I hope these tips are useful in helping your child in their final revision for the PSLE!

## You're Welcome

Thanks everyone, you’re most welcome. Can only blog when I have time though, so apologies for the infrequent entries.

## Thank you for sharing

Hi, this is great! Will share with DD as she is taking PSLE next week.

## Thanks for simplifying it for

Thanks for simplifying it for us!