Basic arithmetic forms the foundation of students’ mathematical knowledge, and it is traditionally the first mathematical concept taught that involves performing operations on numbers to solve simple equations that involve no unknown variables.

To understand basic arithmetic, students must already understand rudimentary concepts of number theory, i.e. how to count. The first basic arithmetic concept that students learn is addition, or how to combine the values of two numbers together to calculate their sum. Subtraction is also introduced as the opposite operation of addition; students learn that by subtracting a number from another number, they calculate the remainder after the number subtracted is removed from the total quantity represented. Students initially learn these concepts with single-digit whole numbers, but are later taught to add and subtract numbers with two, three, or more digits by hand; this introduces the concept of numerical places and provides a solid foundation for later learning about decimals.

After mastering basic addition and subtraction, students are introduced to multiplication and division as another pair of opposite operations. Students may begin learning about multiplication using visual representations of groups of objects; this is done in order to help them comprehend that multiplication duplicates a number a number of given times. For instance, students might learn that having a pair of socks is equivalent to having one group of two socks, but multiplying 2 x 3 yields a total of 6, or the equivalent of having three pairs of socks.

After learning basic multiplication, students learn basic division. Visual groupings of objects may also be utilized when teaching students division, as well as analogies such as the idea that division splits large groups into smaller groups of a certain number of objects and counts the number of smaller groups.

Once students have mastered simple single-digit multiplication and division, they will be challenged to incorporate the same concepts into more difficult problems involving larger numbers. Multiplying and dividing large numbers by hand is a skill that many students find difficult to learn, but is very rewarding.

Once students have mastered addition, subtraction, multiplication, and division, they move on to other mathematical concepts such as how to work with decimals, fractions, and percents, as well as negative numbers and absolute value; however, a great number of all of the other mathematical concepts they will learn in the rest of their academic careers all depend on a solid foundational understanding of basic arithmetic, so it is absolutely crucial that students clearly understand the concepts and do not unwittingly misunderstand them, as such misunderstandings can derail later attempts to learn about more difficult math.

If you want to make sure that you or your student has a solid understanding of basic arithmetic, Varsity Tutors’ free Basic Arithmetic Practice Tests can help you do so. Each Practice Test consists of around a dozen basic arithmetic problems that ask students to put a variety of their skills into practice. After completing a practice test, you gain access to your score and data about how it compares to other test takers who answered the exact same problems, as well as detailed explanations to each problem, to help you learn how to do the problem correctly if you made a mistake. Reviewing basic arithmetic can help you ensure that you or your student is well-prepared for more advanced mathematical concepts, and Varsity Tutors’ free Basic Arithmetic Practice Tests can help you do that for free whenever you want to study.