How to Use
This cheat sheet was created to help you remember, and maybe even learn, basic math rules and how to use them. However, this was not created to help you cheat on tests. Use this as a tool to help you remember the rules and be the smartest kid in your elementary class. At the bottom of this article that explains the basic math operations, you can download and print the cheat sheet to practice with.
Basic Operations
Comparing numbers:
- If one number has a leftmost place that is greater than the leftmost place in another number, the first number is greater than the second number.
Example: 675 is greater than 75 because the first number has a leftmost place of hundreds. 600+70+5
- 75 is less than 675 because the leftmost place is only tens. 70+5
Here is how you write this:
675 > 75 : > = greater than < = less than. You always compare starting with the first number as if reading left to right.
Example: Six hundred seventy five is greater than seventy five, or 675>75.
Rounding Numbers:
- To round a number to a given place value, look to the number immediately to the right and round according to these rules.
- If the number is greater than 5, round up. If the number is less than 5, round down.
Example: We want to round 7427 to the nearest tens place (2). So, look at the number immediately to the right (7) and round. The number 7 is greater than 5, so round up (30). The answer is 7430.
Additional Examples: Tens place: 423=420, 25=30. Hundreds place: 565=700, 1270=1000 etc.
Rounding Rule:
- When you write a rounded number, you replace the part not used with zeros.
Examples: Round up 27 to 30. Round down the number 21 to 20.
Addition:
- The sum is the total of two numbers added together.
- The numbers that are added together are called addends.
Example: The sum of 5 + 3 is 8
5 and 3 are the addends and they equal 8 when added together.
- The order of the addends does not affect the answer as 5 + 3 is the same as 3 + 5. They both equal 8.
Subtraction:
- In subtraction, you subtract the smaller number from the bigger one.
Example: 12 – 4 = 8 This is correct. It is incorrect to try and subtract the bigger number from the smaller one in basic math. For example, the equation 4 -12 could not be performed in basic math because 4 is not big enough to have 12 taken away from it.
- Remember: Always place the larger number first.
- Remember: You cannot change the order of the equation when doing basic subtraction. The answer will be affected even if you come up with one.
There are two basic types of subtraction.
1. If you have two shoes and subtract or "take-away" one, you are left with the difference, one shoe.
Example: 2 – 1 = 1
2. The second type of subtraction is comparison subtraction.
Example: Mark is 5 feet tall. His sister is 3 feet tall. How much taller is Mark than his sister? The answer would be 2 because 5 – 3 = 2.
Multiplication:
- Multiplication is repeated addition.
Example: 2 x 3 = 6 or 2 + 2 + 2 = 6.
- The first factor (in a horizontal problem) or the top factor (in a vertical problem) is called the multiplicand.
- The other factor is called the multiplier.
Example:
10 Multiplier
x4 Multiplicand 10 x 4 = 40 ten is the multiplier and 4 is the multiplicand
40
- The idea of multiplication is to simplify adding many numbers. You could do a multiplication problem using addition, but that would take a long time because would you to have to add up many more numbers.
Example: 4 x 3 = 12 whereas in addition, it would look like this… 3 + 3 + 3 + 3 = 12
Division:
- Division is often referred to as backwards multiplication. If you take the number 7 and multiply it by 7, the answer is 49. Now you can divide this equation as well.
- Take the number 49 (or the dividend) and divide it by 7(divisor). Your answer will be 7(quotient) or 49 / 7 = 7 (The symbol "/" is the sign for division on the keyboard).
- An easy way to remember your division is to ask yourself this question: 7 will go into 49 how many times? Next, think of a multiple of 7 that is closest to 49 – 7 x 7 = 49, so there is your answer.
Beyond the Basics
Adding Vertical Numbers:
- What do you do when you have three addends like this? Treat this like two separate problems.
–3 ———-3
–4 ——- +4
+2 —–2 + 7 = 9
–9
- First, add 3 + 4 together. The answer is 7 (3 + 4 = 7). Next, add the remaining number and the answer to adding the first two together (7 + 2 or 2 + 7 = 9). The answer to the entire problem is 9.
Adding Larger Numbers:
- Adding bigger numbers together requires starting at the right and moving left. You carry over any numbers over 9 to the next set of numbers to the left until the number equation is completed.
————(1,1) (these are the carry over numbers)
Example: 456
————+256
————-712
Step 1: Add 6 + 6, which equals 12. Place the 2 in the ones column and carry over the 1.
Step 2: Move to the left one place and add 5 + 5, which equals 10. Now add the extra 1 on top (10 + 1 = 11).
Place a 1 under the tens place and carry over the other 1 again but this time over the hundreds place.
Step 3: Finally, add the hundreds column together and remember to add the carried over 1 again ( 4 + 2 = 6; 6 + 1 = 7).
The answer to this problem is easily figured out when you take it step by step: 456 + 256 = 712.
Subtraction With Larger Numbers:
- Sometimes the top digit is smaller than the bottom digit when you begin subtracting larger numbers. In this case, you will borrow from the next number to the left that is not zero.
Example:
(4)(17)
—57
-28
=29
Here is the breakdown of the problem; because 7 is smaller than 8, we need to borrow from the next place value (tens). Borrow 1 from the tens place making the 5 into a 4 and give it to the ones place making the 7 into a 17. Subtract: 17 – 8 = 9 and 4 – 2 = 2. Going right to left, the answer is 29.
A free, printable version is available to you (just click on the link in the next section). Print it out and keep it with you, and also feel free to bookmark this page for future reference.
Multiplication:
- When multiplying bigger numbers, don't forget the process because it is different than addition or subtraction.
You still work from right to left.
Renaming in multiplication is the same as in addition.
- Remember to multiply with the farthest right number on the bottom first. Then you multiply it with each number in the number above it, all the way across until you have completed the process.
Example:
432
x 3
Multiply the 3 x 2 = 6 first. Next, multiply the 3 x 3 = 9. Next multiply the 3 x 4 =12. You keep placing the answer under the problem as you get them figured out from right to left. If there is a carry over number, you add it after multiplying. For instance, if 4 x 3 was in the middle of the problem, you would carry over the 1. When you multiplied the next numbers together, you would add the 1 to the answer.
It is important to write out your carryovers as you may forget them if you don't.
–432
__x3
1,296
Multiplying Two Large Numbers Together:
- Keep in mind that this is not hard if you just follow the rules you have learned.
Remember to follow the rules above for starting out your multiplication problem.
- When you have two large numbers, remember to move over one space when you get to the next bottom number or multiplier.
Example:
—(1)-carryover number
—–23
—-x61
—–23
+1380
–1403 Answer
- Just remember your rules and you will always be ready to use even the biggest numbers in math.
Division:
- If the division problem is not a fact or a near fact, it can be solved by a method known as long division.
- Remainders are carried over by either a period or point (.) or you place an r and then the number remaining.
14 divided by 4 would be 3 with a remainder of 2 because 4 x 3 =12 and 14 -12 = 2.
140 divided by 40 would be 3 with a remainder of 20 because, 40 x 3 =120 and 140 -120 = 20.
- To see this problem on paper using long division, just do as you have learned in school already and follow these instructions to see it happen.
Author’s Note
I have included a free downloadable cheat sheet for you to print. It is a condensed version of this article and filled with examples. Be sure to print this and keep it with you, and bookmark this page so you can always refer back to it for the deeper explanations of your math problems.
I hope this elementary math operation cheat sheet helps you keep these steps of math fresh in your mind every day.
References:
Source: Atlanta Page has been a homeschool teacher for the past 13+ years. These tips are explained from years of experience teaching math to her students.
Volume Library volume 1–A modern, Authoritative Reference for Home and School Use. Copyright 2000, by the Southwestern Company. Original copyright 1917, by Educators Association, Inc.