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.”

SAT Math - Percents

Practice: Solve these problems using the technique I described above. Try my thought process as well and see if it helps!

 

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Borrow/Lend

Borrow- Borrowed – Borrowed

Lend – Lent- Lent

There is a very simple difference between borrow and lend, however it is a difference that many people find hard to understand. To make it simple, borrow is the action of taking something from someone for a short period of time and lend is the opposite, the action of giving something to someone again, for a short period of time.

Here are a few examples:

Can I borrow your pen?

I will lend you my pen.

 

Can she borrow your bag?

I will lend her my bag.

 

Can I borrow your phone?

I will lend you my phone.

 

Could you lend me some money?

Ask Laura to lend you some as I don’t have any.

Laura, could I borrow some money please?

 

Can she borrow your laptop?

I am sorry I have already lent it to someone! Doesn’t she have one?

 

Personal pronouns always come after the word lend: I will lend you some money

 

Take a look at the table below to help you understand the concept.

 

 

When you think you are ready have a go at the word choice exercise which is followed by a true or false task!

Good luck!

Borrow/Lend - Fill in the Blank

Read the text below and choose the correct verb.

Borrow/Lend - True or False

Indicate which sentences are true and which ones are false.

 

How Questions

One way to use the question word “how” is to ask about numbers or quantities.

It can be used with adjectives like big, much, many, tall, long, or old.

Here are some examples:

How much does that bicycle cost? It costs 100 €.
How many apples do you have? I have 6 apples.
How big is the house? It is really big!
How old is he? He is 35 years old.

Try the quiz!

How Questions Quiz

Choose the missing word in the following questions: