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Mental Math Tricks for the SAT and ACT Math Sections
Everyone knows the SAT and ACT are timed tests, and time is of the essence as you make your way through the ACT’s Section 2: Math or the SAT’s Section 3: No-Calculator Math (which is only 25 minutes!) and Section 4: Calculator Math (which is 55 minutes). If you’re getting everything (or most of everything) you attempt correct, you might benefit from these mental math tricks for quicker arithmetic on the SAT and ACT math sections. Let’s take a look!
Adding Big Numbers
Trying to add up big numbers using only your head is rather tough! A cool trick you can use to make the process simpler is to turn the numbers into multiples of ten. Here’s an example of this trick in action:
Let’s say we’re trying to add 592 and 383.
First, let’s round the numbers up until we reach a multiple of ten.
So 592 will become 600 and 383 will become 390.
Then add the new numbers together. 600 + 390 = 990.
Then subtract what you added from each when you rounded up.
We added 8 to 592 and 7 to 383 for a total of 15, so let’s subtract 15 from 990 to get our final answer:
592 + 383 = 975!
Subtracting Any Number from 1000
Looking to subtract a number from 1000 quickly? Here’s a cool mental math trick that might help you if you need to do so on the SAT Math test. All you need to do is subtract each number except the last number from 9 and then subtract the last number from 10. Let’s take a look at this trick in action:
1000 - 348
Step 1: 9 – 3 = 6
Step 2: 9 – 4 = 5
Step 3: 10 – 8 = 2
Those three numbers form your answer! In this case, 100 – 348 = 652!
Multiplying a Number by 5
If you’re looking to multiply an EVEN number by the number 5 on the SAT Math test, there’s quite an easy way to do so!
For example, 5 x 8.
First, take the even number you’re multiplying by 5 and divide it by 2.
Then, add a 0 to what you get.
8/2 = 4.
Adding a 0 gives 40.
So 5 x 8 = 40!
When you need to multiply an odd number by the number 5, the mental math will be a little more tricky.
Let’s take a look at 5 times 17, for example.
First, subtract one from whatever number you’re multiplying by 5. In this case, 17 will become 16.
Then divide what you get by 2, so in this case, 16 becomes 8.
Then tack a 5 on as the last digit, so 8 becomes 85. And there’s your answer!
You could also just multiply a number by 10 and then divide by 2.
How to Know if a Number is Divisible by Another Number
Looking for a fast way to judge whether or not a number on the SAT math section is divisible by a certain number? Here’s a list of tricks you can use.
If the number ends in 0, it’s divisible by 10.
If the number’s digits add up to a number divisible by 9, the number is divisible by 9.
If the final three digits of the number are divisible by 8 or are 000, the number is divisible by 8.
If it’s an even number whose digits, when added together, are divisible by 3, the number is divisible by 6.
If it ends in 0 or 5, it’s divisible by 5.
If it ends in 00 or any two digit number that’s divisible by 4, it’s divisible by 4.
If you add the digits together and the answer is divisible by 3, the number is divisible by 3.
If it ends in an even number, it’s divisible by 2.
Multiplying a Number by 10
Easy! Add a 0.
Dividing a Number by 10
Move the decimal place to the left one digit.
Multiplying a Number by 100
Add two zeroes.
Dividing a Number by 100
Move the decimal point two places to the left.
You can use this trick for any power of ten! Just add the corresponding number of zeroes for multiplication or move the decimal point the corresponding number of zeroes for division.
Multiplying a Two-Digit Number by 11
To multiply a two-digit number by 11 on the SAT math section, use this simple trick. Let’s consider the example of 11 x 14.
First, take your two-digit number and add an extra space between those digits. So 14 becomes 1_4.
Then add the numbers together and make the blank space be their sum. So the answer is 154.
If the numbers on either side add up to a number that’s two digits, insert the second digit into the blank space and then add 1 to the first digit. Let’s consider the example of 11 x 91.
91 becomes 9_1
9+1 = 10, which is two digits. So we’ll insert 0, giving us 901. Then we’ll add 1 to the first digit, giving us 1001.
Quickly Calculating a Percentage
If you need to find a certain percentage of a number quickly on the SAT math test, you might be in for a headache. However, you can make it easier for yourself if you think about the question in the proper way. For example, let’s consider what we’d do if we wanted to figure out what 5% of 196 is, it would be half of 10% of 196. So we could move the decimal place to the left once to get 19.6, which is 10% of 196, but we want 5%, so we would divide 19.6 by two to get 9.8
How to Square a Two-Digit Number Ending in 5
If you need to square a two digit number that ends in 5, here’s a quick SAT math trick:
Let’s try to square 65.
First, multiply the first digit by whatever 1+ that digit is.
So 6 will be multiplied by 7, giving us 42.
Then add the digits 25 to your answer.
65 squared is 4225!
Multiplying Numbers That End in 0
To multiply numbers that end in 0 on the SAT Math test, simply multiply the digits that aren’t 0 and then add the total number of zeroes in the two numbers to your answer.
For example, 150 * 30
15 * 3 = 45
Add on two zeroes, and you have your answer of 4500.
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