How to Understand Math

Co-authored by Daron Cam

Last Updated: June 30, 2024 Fact Checked

Math can be a difficult subject, but it is something that everyone is capable of mastering. Math is based on logic and rules that you can study and apply – there isn’t any special skill involved. The subject might come easier to others than you feel it does to you, but if you practice and try hard you’ll also be good at math.

Method 1

Method 1 of 5:

Learning Addition and Subtraction

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1
Use objects to count out the math visually. Take a bag of marbles and use these to visually see how addition works. For example, take five marbles out of the bag. Now take another three marbles out of the bag. Combine all the marbles together and count how many you have. You’ll have eight marbles. That means that five plus three equals eight. ^{[1]
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- Using this tactic can help you visual subtraction too. Try taking four marbles away from your pile of eight marbles. You’ll end up with four marbles left. That means that eight minus four equals four.
You can buy workbooks online or visit free websites that allow you to practice. You’ll be presented with a table filled with all sorts of problems to solve – everything from one plus one to seventeen plus fifteen and so on.^{[2]
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Start by adding the final digits of both numbers together. If you are adding numbers that have multiple digits you can set them up on top of each other to make it easier to add. Consider the problem 21 plus 14. Draw the equation so that the 21 is sitting on top of the 14. Now draw a line underneath the 14. Adding down, add the final two numbers. In this case, those numbers would be the ‘1’ from 21 and the ‘4’ from 14.^{[3]
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- One plus four equals five, so you would write a five below the line you made under those two numbers. Now add the ‘2’ from 21 and the ‘1’ from 14. Two plus one equals three. Write the three under those two numbers to the left of the five that you just wrote. You should have the numbers 3 and 5 sittings next to each other below the line you drew. That means the answer to this problem is 35. 14 + 21 = 35.
- If you add two numbers together and they make another two digit number, take the one from that two digit number and move it over to the left. For example, if the problem was 14 + 28 instead your first calculation would be 8 + 4. This would give you 12. You would still put the ‘2’ from 12 below the line underneath the 4 and the 8. However, the ‘1’ from 12 would then be moved over to the left and added to the second equation. So you would add the ‘1’ from 14, the ‘2’ from 28 and the ‘1’ from 12. That would give you the number 4 once you add all those numbers together. This means that 14 + 28 must equal 42.
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Daron Cam
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Expert Interview. 29 May 2020.} Pass the pigs is a popular game that has you roll tiny ceramic pigs on a table. Based on the way that they land, you earn a certain amount of points. You only play to 100 so the numbers never get too high, but it’s a great way to learn basic addition. It’s much better than doing addition tables for hours!

Method 2

Method 2 of 5:

Learning Multiplication and Division

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1
Understand the concept of multiplication and division. The idea behind multiplication is to shortcut adding the same things over and over again. You use multiplication when you have groups of the same size. For example, maybe you have three cups of water that you drank ten times. How many cups of water did you drink total? You could solve this problem by counting adding the amount of times you drank the water from each cup together, or you could clump them into groups to multiply. ^{[5]
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- The idea behind division is splitting equal parts into groups. If you have a pizza with eight slices and four friends, how should you split it up so that each person gets an equal amount of the pizza? In division, that problem would be written as eight divided by four. Each person gets two pieces of pizza.
For example, order doesn’t matter when you multiply. That’s one of the properties that you should learn if you want to learn multiplication. You also should learn multiplication problems that change the order of factors, which is called commutativity, problems that change the grouping of factors, which is called associativity.^{[6]
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Becoming familiars of the rules to each number will be a huge help when dividing and multiplying. For example, when you multiple numbers by five the answer will always end in a five or a zero. If you multiply a number by two, it will always end in an even number. Similar rules apply for division. Learn these rules and practice your tables.^{[7]
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Method 3

Method 3 of 5:

Being a Good Student

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You'll never learn mathematics if you don't know the basics. Make sure you pay particular attention at the start of each new unit as things are explained. Math is generally taught as a series of building blocks and if you miss a block it could be very difficult to catch up.
If you take notes in class you'll be able to look back on what you did in class that day. When you go to do your homework you’ll be able to refer back to the examples that you wrote down from class. Make sure you write down each individual step needed to solve a problem, or else you might get stuck in your work.^{[8]
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Expert Interview. 29 May 2020.}Writing as you learn also helps you learn and remember better.^{[9]
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Studying before the test is always going to be necessary, but there’s nothing wrong with taking fifteen or twenty minutes every night to study the lesson that you learned that day. You’ll find that you feel much more prepared for the following day of class and you will do less cramming the day before the test.^{[10]
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It doesn't matter if you get the answer wrong, at least you tried and don't feel ashamed by asking questions.^{[11]
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Daron Cam
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Expert Interview. 29 May 2020.} How do you know you might ask somebody else's question, they might be thankful and probably help you out on bits you don't understand.
Working on math everyday is the real key to understanding it. The more time you spend around the number and concepts the more comfortable you will be with them. Homework might seem like a drag but the daily repetition will really help you.

Method 4

Method 4 of 5:

Searching for Help

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Almost any teacher will go to extra help. Don’t be too proud to ask – you’ll develop a relationship with your teacher and it will help a lot. Your teacher will appreciate that you came in looking for more help and the teacher will know what you need to work on in the future. This is highly recommended.
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Daron Cam
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Expert Interview. 29 May 2020.} You have to be honest with yourself here. Is the issue that you aren’t trying hard enough, or that you really just don’t understand math? If you’re not trying hard enough, you need to work harder to practice on your own. There’s no way to understand math if you aren’t willing to put in the work. However, if you have been practicing on your own and you just can’t wrap your head around a certain subject, then it’s perfectly logical to ask for help.
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Daron Cam
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Expert Interview. 29 May 2020.} If you’re willing to spend money, hiring a professional tutor can be a huge help when it comes to understanding a subject. Professional tutors are often very expensive, but if you hire an older student the price might come down. Tutors will sit down with you one on one and work you through your problems.
If you don’t want to hire a tutor or go to extra help another good option is to ask a peer. There is bound to be someone in the math class who understands the concepts well. Find this person and develop a relationship with them. Ask them if they would be willing to sit down with you over lunch and help you with a couple of topics you are struggling with. Don’t take advantage of them and never try to copy their answers – just use them as a resource. There’s no reason to be too proud to ask for help. That’s a good skill to develop in life.

Method 5

Method 5 of 5:

Practicing

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Daron Cam
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Expert Interview. 29 May 2020.} Memorizing formulas and tables is all well and good, but it is more important to understand why the answers are what they are. Try to figure out the logic behind the problem rather than just memorizing and regurgitating.^{[15]
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When you're getting the change in the supermarket calculate how much money you should get back. If you are buying gas at a gas station, try to multiply the price by the amount of gallons it takes to fill your tank. Getting better at mental math is a great way to feel more confident, even if the subjects you are studying in school are much more complex. You will always be using addition, subtraction, and multiplication in one way or another no matter how complicated the subject gets.

EXPERT TIP

Joseph Meyer
Math Teacher
Joseph Meyer is a High School Math Teacher based in Pittsburgh, Pennsylvania. He is an educator at City Charter High School, where he has been teaching for over 7 years. Joseph is also the founder of Sandbox Math, an online learning community dedicated to helping students succeed in Algebra. His site is set apart by its focus on fostering genuine comprehension through step-by-step understanding (instead of just getting the correct final answer), enabling learners to identify and overcome misunderstandings and confidently take on any test they face. He received his MA in Physics from Case Western Reserve University and his BA in Physics from Baldwin Wallace University.

Joseph Meyer
Math Teacher

Exercise your mental math muscles. Improve your math skills by solving daily math problems without using calculators, paper, or counting aids. By solely using your mind and getting into math discussions with your classmates, you will refine your skills and discover new approaches to problem-solving.
Math is a broad field. Unless you devote your life to the studying of mathematics it is unlikely that you’ll ever understand everything. Figure out what part of math is most important for you to understand. Maybe it’s something you’re studying in school or a subject you have a personal interest in. Start with the basics and work your way up. Don’t start trying to do algebra if you aren’t comfortable with your multiplication tables yet.
You can find practice books on the Internet or in bookstores for any math topic imaginable. These practice books will have a guided curriculum to help you get better at math.
Testing yourself is a great way to figure out for sure what you understand and what you don’t understand. You might think you understand a concept but you won’t really know for sure until you test yourself. Most textbooks feature practice questions and tests.^{[16]
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Like anything else, being good at math takes a lot of practice. You wouldn’t expect to be muscular after doing twenty pushups at the gym, so you shouldn’t expect to be good at math after doing twenty practice problems. Practice everyday and you’ll start to understand math more and more.^{[17]
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How do I get help for math?

Daron Cam
Academic Tutor
Daron Cam is an Academic Tutor and the Founder of Bay Area Tutors, Inc., a San Francisco Bay Area-based tutoring service that provides tutoring in mathematics, science, and overall academic confidence building. Daron has over eight years of teaching math in classrooms and over nine years of one-on-one tutoring experience. He teaches all levels of math including calculus, pre-algebra, algebra I, geometry, and SAT/ACT math prep. Daron holds a BA from the University of California, Berkeley and a math teaching credential from St. Mary's College.

Daron Cam

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Expert Answer

Don't be afraid to ask your teacher questions. You can also ask your peers for help or organize a study group together. If you're still having trouble, consider getting a private tutor. A tutor can answer any questions you have and will work with you to build a solid foundation in math.

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How can I get better at the basics?

Donagan

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Ask someone to tutor you in the basics and do practice problems on your own.

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How do I study math when I have an exam in two days?

Community Answer

Read all of the rules and go over your notes. Then do questions from each concept to check that you understand how to do each type of problem.

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Learn about the number zero, which appears a lot in math. It represents nothing and can be complicated to understand.

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Remember, math isn't as hard as you think. Focus on understanding the concepts (instead of just memorizing), and learn all the formulas for your specific lesson plan.
If you don't understand a problem or concept, ask your teacher, tutor, or a fellow classmate for help. It's the quickest way to improve your math skills!
Try to solve a math problem independently before asking someone for help. That way, you can learn from your mistakes.

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