With the rise of global education rankings from organizations like the UN and OECD in the past decades, countries have found themselves in a precarious position with regards to their academic national standards. The UK in particular has always struggled in the areas of math and science, lagging behind many similar economies in the subjects. In fact, after the OECD's last PISA, or Programme for International Student Assessment, results came through - many started to question whether or not the UK's students were proficient in their level's grade math on the global scale.

This has led to many changes in the national curricula, such as implementing "Shanghai-style" teaching of maths in the classroom that has led to ambiguous results. Regardless of where you stand on national academic standards and the many measures that have been passed geared towards improving overall academic performance, test taking has never been more important.

While some might be slogging through subjects like calculus and trigonometry, for most of us the problems begin with basic math. While you may not think elementary math is too important, a host of studies have suggested that achievement in early math classes is a great predictor of later academic success. Whether you want to learn more about arithmetic or simply need to brush up on some basic math concepts, this guide will give you the tools to start talking challenging math homework or courses.

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getting a maths tutor for interactive learning
If you're having trouble in arithmetic, getting a tutor in maths can give you a fun, interactive math environment

Definition of Arithmetic

While math problems and concepts have been torturing students since time immemorial, arithmetic has actually been around since long before many of us can fathom. This is the main reason why arithmetic can be a bit difficult to define. The word arithmetic is obtained from the Greek word for number, arithmos, and at its most basic can be understood as involving the computation of numbers through addition, multiplication, subtraction, division and more.

While the earliest examples of these concepts have been traced back to 18,000 BCE in Africa, they were further developed by equally as infamous mathematicians in Egypt, Greece, and Europe throughout the centuries. Because of this long and complex history, it can be helpful to start with some fundamental aspects of the discipline.

Types of Numbers

While some of these concepts may seem like they belong in elementary school math, some can be taught in math courses in high school math classes or even at the college level. Understanding the different numbers involved in the various arithmetic and algebraic expressions and operations is integral to succeeding in subjects like pre-algebra, algebra, geometry and pre-calculus.

Natural Numbers

Natural numbers are a set of numbers that you can count not including those that have decimals or negatives, such as: 1, 2, 3, 4 and so on. If the number 0 is included in this set, it is called a set of whole numbers. These are the most basic classifications of numbers.


This set of numbers includes all-natural and whole numbers with the addition of all negative numbers. Again, this set of numbers does not include decimals or fractions.

Rational Numbers

The set of rational numbers includes all integers and does include decimals and fractions. However, this classification only works if each decimal can be written as a fraction when the denominator is not 0 and if the numerator and denominator are both integers.

Irrational Numbers

This set of numbers is completely separate from those included in the set of rational numbers. Meaning, they are a set of numbers that cannot be expressed as a fraction of two integers. Some examples of this are:

  • Pi
  • E
  • Phi
  • Square roots that are not perfect squares, such as the square root of 2

Real Numbers

This set is classified as the set of all rational and irrational numbers.

examples of the distributive property
From linear equations and inequalities to inverse functions: arithmetic is involved

Basic Arithmetic Operations

While mostly everyone can get through basic arithmetic and algebraic equations without a hitch, there are some basic arithmetic operations and laws involved in solving many arithmetic problems that can haunt the rest of your mathematics career. Here are some of the most common ones your likely to find in any math program.

Arithmetic Laws

In general, there are three laws of arithmetic. While you’re unlikely to find these laws in a higher-level math class, such as those involving math logarithms, conic sections and more – these laws can help you grasp more complex rules later down the road. These three laws apply to all rational numbers.

Commutative Law

Applying to both multiplication and addition, the law states that:

a + b = b + a


ab = ba

This law can also be extended to percentages, explaining that:

a% of b = b% of a

Associative Law

Again, this law applies to both multiplication and addition:

(a + b) + c = a + (b + c)


(a x b) x c = a x (b x c)

Distributive Law

This law states that:

a x (b + c) = a x b + a x c

While the commutative and associative laws do not apply to subtraction and division, the distributive law does not apply for division. Seemingly simple, these math skills can have applications or help you understand concepts and operations such as:

  • Exponents and laws of exponents
  • System of equations
  • Word problems involving inequalities or quadratic equations

If you’re still a bit confused as to how these different laws work, try practicing some examples at home on a whiteboard or through a maths game online.

work with addition, subtraction and mental math in the library
Libraries often offer help for homework in all grade levels!

Find the Right Arithmetic Tutor

From the complex polynomial to trigonometric functions, supplemental instruction in the field of mathematics can be difficult to find. While this is by no means a definitive guide on how to find the perfect maths tutor for your needs, here are some guidelines to follow.

Mathematics Courses with a Private Tutor

Arithmetic is usually taught at the primary school level. However, issues in math courses or concepts involving arithmetic can continue well into advanced math classes. The first step you should take in deciding whether or not a private math teacher is right for you is by determining what areas of arithmetic you or your child might be struggling with.

For example, at the primary school level, you will need to find a primary grade level tutor who is not only experienced in giving maths lessons but also one who is capable of working with children. Middle school math, on the other hand, will probably necessitate an algebra tutor or general math tutor that is qualified to teach arithmetic involved in solving complex equations and inequalities, linear equations, polynomials and more.

Private tutors at the high school and college level will generally aid in solving arithmetic problems linked with subjects like high school or college algebra, physics, organic chemistry and more. These tutors should be well versed in teaching subjects like math and science and can be anything from a physics tutor to a chemistry tutor.

You can also get a maths tutor for help in the arithmetic problems involved in many common standardized tests, such as the A-levels. Test prep math courses can go through everything from concepts from 7th grade math, rational functions and rational expressions, polynomial and trigonometric functions and even matrices.

Online Math Resources

If you’re struggling with arithmetic or need some test prep help, looking online for basic math resources can often be the best solution. One website that covers extensive arithmetic concepts at the elementary school level is AAA Math. Offering lessons as well as practice problems, this is a great way to tackle some of the issues you or your child may be having in the subject.

While AAA Math also has webpages dedicated to geometry and algebra, Wolfram Alpha is a great resource for those looking for arithmetic help on a higher level. Walking you through complex problems and definitions, this website also offers many examples in subjects ranging from elementary math to calculus and complex analysis.

Free Math Help

While finding free help with math online is the easiest way to learn on a budget, you can also get one-on-one help in person throughout the UK. One of the best places to start is by checking to see if your or your child’s school has a math lab. Math labs are usually peer and teacher led programs that are developed specifically to help students solve their most difficult issues.

If this option isn’t available for you, try checking out your local library. Many libraries throughout the UK have plenty of programs aimed at assisting parents and children at no cost.

Online Arithmetic Tutors

Many tutoring companies today offer 21st century solutions to some of our basic tutoring concerns. In fact, many of the biggest tutoring platforms not only offer virtual classrooms for maths tutoring online, but also at a lower cost than in-person tutoring. Check out websites like TutorHunt and Superprof for plenty of tutoring options for all grade levels at costs that average between 12 to 70 pounds an hour.

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