SAT Math – Percents | Part 1

So you want to take the SAT? This is quite the challenge for nonnative English speakers as it’s even a challenge for native speakers! Luckily, half the test is given in the universal language… MATH. Even so, I’ve noticed some of the math is taught differently in US schools and some of the questions seem to be more focused on this style of problem. I am talking about percentages specifically. I have seen many students struggle with percentages and they almost always make the same mistakes. I’m hoping the strategy that I lay out below will simplify the problems and help you solve them more quickly, but with most maths there are many different ways to approach the same problem. Some approaches will be easier for some students and the same approach will be more difficult for others. This is the technique with which I’ve had the most success.

Part 1: Increasing by a percentage

Ex: What is 180 increased by 5%?

The quickest way to solve this is to write this 180 * 1.05 = 189.
Hold up.
Why is there a 1.05?
I took a shortcut! 180 increased by 5% can be written as:

180 + 180 * 0.5 which is rewritten 180 * (1+0.5) which simplified is 180 * 1.05

I am using the distributive property of multiplication to get 180 * (1+0.5). An easy way to think of this without the steps is to use this formula when increasing Y by percentage X.

Y*(1+X)

Side note: My thought process for solving this on the exam would go something like this. “180 increased by 5%. Do I know 5% of 180? No. What is 10% of 180? Move the decimal to the left so 18, and 5% is half of 10% so 5% must be 9. 180 plus 9 is 189.”

Part 2: Decreasing by a percentage

Ex: What is 120 decreased by 10%?

The quickest way for solving this would be 120 * 0.9 = 108.
Wait.
Stop.
Where did 0.9 come from?
I took a shortcut again. 120 decreased by 10% can be written as:

120 – 120 * 0.1 which is rewritten 120 * (1-0.1) which is equal to 120 * 0.9

In short, if you have a value Y and are decreasing by percentage X use this formula:

Y*(1-X)

Side note: If you are doing this math in your head, which is necessary for the “no calculator” portion, this is my thought process. “What is 10 percent of 120? Just move the decimal point to the left so 12. Okay, so 120 minus 12 is 108.”