What is Arithmetic?

Arithmetic is often used as a synonym for math, but there is a difference between arithmetic math and mathematics. In general, arithmetic math is math that deals with the numbers themselves, whereas mathematics is more about the theories of numbers. When a person starts learning math, they’ll begin with arithmetic math and then go on to learn more about more advanced mathematics. It’s crucial to have this foundation and to understand what arithmetic math is before moving on to more advanced topics.

Arithmetic Pronunciation

Arithmetic is pronounced similar to how it’s spelled, which makes sounding out the word easy to do. Typically, it’s pronounced as ar-ith-MET-ic with emphasis on the “met” part of the word. Pronunciation can vary by location; however, this is the most common pronunciation for the word. Other pronunciations will have more of an emphasis on the “th” sound, and this is also correct.

Arithmetic Definition and the Difference From Mathematics

Arithmetic is working with the numbers themselves. This includes counting, adding, subtracting, multiplying, and dividing. It also includes fractions, positive and negative numbers, the order of operations, sequencing, and more. Basically, arithmetic math is how the numbers work together to get an answer to a problem.

Learning arithmetic math is usually the beginning of a person’s math education starting with the basics, although there are far more advanced components to arithmetic a person can delve into later. According to the arithmetic definition, arithmetic starts with learning how to count, then progresses through adding, subtracting, multiplying, dividing, sequences, and more detailed topics. As a huge area of math, it is the foundation for more advanced mathematics.

Mathematics, on the other hand, includes more advanced problems like those found in algebra, geometry, trigonometry, and calculus. They are based on the same topics a person learns when they’re learning arithmetic math, but go further into the theories involved and not just how the numbers work together to get an answer.

Knowing the Arithmetic Math Definition is Important

Most people aren’t sure why they need to know the difference between the types of math. However, there are important distinctions between them. When a person understands the basic definition of what type of math they’ll be doing, such as arithmetic math, they can then understand how to solve the problem before them. With more complex problems, knowing if they’ll be using arithmetic or another type of math can help them determine what they need to do to solve the problem, such as whether they should use the sequencing formula or a geometric formula. Once they understand the definition, however, this isn’t something they’ll think about. It will just be something they automatically do.

Arithmetic Examples – Basic Examples

Viewing some examples of arithmetic can make it easier to understand exactly what arithmetic math is compared to mathematics. Simply counting whole numbers is the most basic example of arithmetic and the first thing a person learns to do. Other simple examples include 2+4=4 and 17+27=44. Multiplying numbers like 4 times 7 or 23 times 59 as well as dividing numbers like 14 divided by 2 or 330 divided by 10 are other examples of basic arithmetic.

Mathematics, on the other hand, can include the radius of a circle, the formula for determining the sides and angles in a triangle, or understanding how to do mathematical proofs. These are more advanced and often use a variety of symbols and formulas instead of just the numbers.

Arithmetic Problems and the Beginnings of Learning Arithmetic

Students initially learning arithmetic will start out with basic problems once they’ve learned how to count. These problems include adding and subtracting numbers under 10 and then will progress to adding and subtracting higher numbers. Later, multiplying and dividing are added to repertoire. They’ll learn how to add or subtract smaller numbers on paper and will then progress to being able to mentally add, subtract, multiply or divide. The more they focus on learning arithmetic, the more they can do difficult problems without added help from a calculator.

Arithmetic Formulas – The Basic Formulas Everyone Will Use

As mentioned above, the most basic formulas for arithmetic include adding, subtracting, multiplying, and dividing. These are usually taught in the beginning of a person’s journey to learn math and are the most basic formulas necessary to truly understand not only arithmetic but more advanced topics like algebra or calculus. Knowing how the numbers interact and how they can work together to get to the answer is vital throughout a person’s education.

Once the person the student has conquered the basics, they’ll learn what order to do problems to find the answer to a question involving two or more of these basic formulas. This is more complex and the problems need to be done in the proper order, called the “order of operations,” for a person to get the right answer. This provides a foundation for learning how to do problems that include adding and multiplication, subtraction and division, or all four.

From there, individuals will learn a great deal of other types of arithmetic math, such as what a square root is or how to solve other types of problems, like determining the median of a group of numbers. This foundation covers all of what they’ll need to know before they move on to more advanced topics and ensures they have an understanding of many of the ways numbers can work together as well as what formulas they can use to arrive at the answer.

One Arithmetic Formula – Sequence Arithmetic

The sequence formula is one of the most common formulas for arithmetic and it includes how numbers work together when counting. The most basic of this is counting by ones: 1, 2, 3, 4, 5, and so on. Counting by tens is usually the next one a person will learn, with more difficult ones following. An example of a sequence is counting with a difference of 4’s between each number. So, the person will count 1, 5, 9, 13, 17, 21, and further.

The formula for a sequence is typically a, a+d, a+2d, a+3d, and so on. Using the previous example, with “a” being one and “d” being 4, it could be written as 1, 1+4, 1+(2 times 4), 1+(3 times 4). After multiplying, it would be 1, 1+4, 1+8, 1+12, etc. Once the adding is done, this becomes the original sequence of 1, 5, 9, 13 and can continue on as long as a person follows the formula.

Sequence arithmetic can be easy to do, such as the examples above, but can also be incredibly complex. Breaking it down into easier to manage portions like above can help a person determine what sequence is being used and find what the number will be at a certain point in the sequence, on top of just determining the numbers in the sequence.

Arithmetic Questions from Basics to More Advanced

When a person is first learning arithmetic math, the questions might be simply adding or subtracting numbers together to learn how the numbers work with each other to come to a final answer and how everyone will get the same answer when they’re doing the same problem. For example, 2+2=4 no matter who is adding the numbers together.

From there, the questions can get progressively more difficult and can include sequence formulas among other types of arithmetic math like square or cube roots. An example of these questions might be to add the first 15 numbers in an arithmetic sequence together. At this point, the student will need to know how to determine the numbers in the sequence based on the beginning number and the type of sequence, then how to add the first 15 together to get the same answer. There is also a special formula that can be learned to help a person do this quickly.

Learning the Various Arithmetic Topics

There are actually a large number of arithmetic topics that a person can learn. As noted, they’ll likely start with basic counting and then learn the four main types of arithmetic. From here, topics may include the following.

  • Odd/Even and Positive/Negative – Knowing when numbers are odd or even can help with sequencing as well as many of the topics listed below. Understanding positive and negative, plus what the implications are in a math problem, can help a person ensure they’ll get the right answer.
  • Order of Operations –When two or more types of arithmetic are combined in a problem, understanding what order to do them in is vital. The order of operations ensures there is a standard for determining what comes first and how to proceed from there to get the right answer.
  • Factoring – This is a way of taking apart a number to get smaller numbers that can multiple to create the larger number. This can help make a problem much easier to solve.
  • Prime Numbers – Prime numbers are those numbers that can only be divided by the number itself and the number one. For example, 13 is considered a prime number because it can’t be divided by anything other than 1 or 13. The number 10 is not a prime number because it can be divided by 1, 2, 5, and 10.
  • Powers – Powers are the small numbers to the top right of a number that tell the person how many times to multiply the larger number. For example, 3 to the third power would mean multiplying 3 times 3 times 3 to get 27.
  • Square Root – With powers, a person can find out that 6 to the 2nd power is equal to 36. The square root works the opposite way. The square root of 36 is going to be 6 because 6 is the only number that multiplies with itself to get 36. The square root is always going to be one number that multiplies with itself to get the bigger number. For example, the square root of 144 is 12 because 12 times 12 equals 144.
  • Cube Root – This is similar to the square root, except this deals with finding the number that can be multiplied by itself three times to get the larger number. For instance, the cube root of 27 is going to be 3 because 3 times 3 times 3 equals 27.
  • Mean, Median and Mode – These are all different ways of determining averages. They can be completely different depending on the numbers that are used. It’s important to understand all three of them to learn more about how averages in real world applications might be determined.

Learning Arithmetic Math

Learning this type of math is vital and needs to be done before a person can learn more advanced types of math. It’s a crucial part of anyone’s education and allows them to learn more about how numbers work together. Beyond their education, this can help a person with many real-world incidences when they’ll need to determine how much a product costs, how much money they have, how far they need to travel to get to a location, and much more.

With a thorough understanding of arithmetic math, one can do all of this without having to even think much about it. There’s no need to use a calculator to do many of the basic problems encountered and, when they do need to use a calculator, they’ll know how to use it correctly to get the right answer.

Arithmetic math is the basics for how math works and how a person can work with numbers to get the answers they need. It delves into the relationships between numbers and how those relationships can impact each other when the person is solving a problem. Learning more about arithmetic math, how it’s different from other types of math, the various topics a person will learn, and how it can be used in the real world can help anyone determine why they’ll want to learn a lot more about the subject. It can also help them know where to look when they need extra help or they’d like to learn something new. By progressively learning more arithmetic, anyone can advance their knowledge of math to the moon and beyond!