With the growing importance of University Rankings order from organizations like the UN and OECD in the past decades, countries and major university bodies have found themselves in a tricky situation with regards to their academic national standards. Australia in particular is a place that is now struggling in the areas of math and science, falling behind similar first world countries in these domains. After the most recent result of OECD's last PISA, or Programme for International Student Assessment,  many began questioning the state of Australia's education system - where are we going wrong? Though little has been done in regards to major transformations of the nations education system, we haven't implemented the so-called "Shanghai-style" teaching of mathematical subjects in the classroom that has led to China becoming a world leader in mathematical results - though at what cost? No matter your position on academic standards and the slow but steady progress of our nations public education curricular, test taking and exams have never been more important.  While there are some reading this who might be grinding through some algebra and trigonometry work, or multiplying some crazy number, for most of us the problems can start with any basic number operation, like to add a sum, or evening counting!! While you may not believe that primary school maths lessons are important, plenty of studies have shown that success in early math classes is a predictor of ones academic success in the future. It's also place where the vital basics are taught, such as how to add a sum, counting, the English involved in learning math, or even multiplying and dividing a sum. So, whether you wish to know more about arithmetic or you are looking for a quick guide on basic math theory, ideas and concepts, this guide provides  a theory to combat challenging math homework or courses. Fantastic maths tutors can be found here.

Here is where to find the beginners guide to arithmetic

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What Is Arithmetic?

Since ancient times, any mathematical problem and operation has been tormenting young minds the world over (OK, maybe not that long, but a couple of centuries at least). The term 'arithmetic' itself has been practiced and studied perhaps longer than you would think. For this reason, providing a definition of arithmetic is not self evident. The term 'arithmetic' comes from the Greek word for number, arithmos, so as a basic theory it can be understood as the calculation of numbers through addition, multiplication, subtraction, division and more. Sounds a bit like the term 'maths' right?  18,000 BCE in Africa is the earliest period in which these concepts have been discovered, but they were famously further developed by mathematicians in the ancient times in Egypt, Greece, and Europe throughout the centuries and milennia. Let's start with the fundamental aspects of this method, as there has been a long history of it in human culture, so there is plenty to unpack. 

Types of Numbers

You probably did learn these terms as far back as in primary school, but more likely you would have discovered these terms in early high school math classes. Knowing the difference between numbers involved in the various arithmetic and algebraic operations is so important to achieving high marks in subjects like pre-algebra, algebra, geometry and pre-calculus.

Natural Numbers

Natural numbers are a group of positive numbers that you can count, but it doesn't include decimals. So think of the classics, such as: 1, 2, 3, 4 and so on. If the number 0 is added to this set, we call it a set of whole numbers. These are the most basic, I think we all have them covered! 

Integers

Integers are a group of numbers that include natural and whole numbers with the addition of all negative numbers. Still, no decimals or fractions in this one, so really we are just adding the negative numbers to the conversation. 

Rational Numbers

Rational numbers include all integers and, it does include decimals and fractions. Although, classifying them only works if each decimal can be written as a fraction if the numerator and denominator are both integers, and when the denominator is not 0. Still following?

Irrational Numbers

These are completely separate numbers from those we mentioned were in the set of rational numbers. So, they are a set of numbers that cannot be expressed as a fraction of two integers. Here are some examples:

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

Real Numbers

All rational and irrational numbers combined.

examples of the distributive property
Arithmetic has a long history. The ancient societies in Egypt and Greece played a huge role in our understanding of the world.

The Basics Of Arithmetic Operations

For most of us who made it through the math program at school (or if you're still in school), we can handle the most basic arithmetic operations such as addition and subraction. But, there are some basic arithmetic operations and laws that can still trick even seasoned mathematicians. Here are the basic arithmetic operations than anyone is likely to come across when studying mathematical based subjects. 

Arithmetic Laws

Generally speaking, we have three laws in arithmetic. You are unlikely to have to study these in a higher level math class,  but for our purpose here it's good to start with the basics, such as those involving number logarithms, conic sections and more – understanding these laws build a foundation for learning the more complicated stuff later on. These three laws apply to all rational numbers.

Commutative Law

This applies to both multiplication and addition, the law states that:

a + b = b + a

And

ab = ba

it can also be applied to forming percentages, for example:

a% of b = b% of a

Associative Law

Again, it applies to multiplication and addition:

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

And

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

Distributive Law

This law determines that:

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

The commutative and associative laws do not apply to subtraction and division, and the distributive law does not take into account division. Simple enough, these math skills build a foundation of logic to then later apply to more complex scenarios such as:

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

Still confused? Practice some examples at home on a whiteboard or through a maths game online.

work with addition, subtraction and mental math in the library
Have a look in your local or school library! You never know what gems you might find.

Finding the Perfect Arithmetic Teacher

From the complex polynomial to trigonometric functions, additional tutoring in the field of mathematics can be difficult to find. While this is not the be all and end all advice on how to find the perfect maths tutor for your needs, we can provide some tips to give you the best result possible.

Find good Maths tutor on Superprof.

Hire A Private Tutor to Help Your Arithmetic Skills

Arithmetic is more common subject than you might think, and is taught in a sequence of term units in primary school. However, it can go deeper that, and oftern we need to revisit even the most basic of theory in later education. Just as you revisit the dictionary in English class even in university. The first step of the learning sequence is to decide on the right kind of teacher for you or your childs needs. We can't just rely on wikipedia or we will be left totally uninspired. The best thing about a good idea is that they inspire us - something that wikipedia will never do. For example a good teacher will probably teach algebra or general math in a way that is interesting for a young student. They should be qualified to teach, and with a strong knowledge involved in solving complex equations and inequalities, linear equations, polynomials and more. Private tutors at the high school and univeristy level will help you in solving an arithmetic operation linked with subjects like high school or university algebra, physics, organic chemistry and more. So don't be left behind, you can also get a mathematics tutor for help in the arithmetic problems involved in many common standardized tests, like the HSC, VCE or any other year 12 exam in Australia. In high school you will need a complete know how in dividing and multiplying algebraic equations.

Math Resources Online

Your classroom teacher called. They think you need to do more outside the classroom. If you’re struggling with arithmetic, or you've been left behind in your class, basic online math resources can really be an excellent assistance. We highly recommend you check out a place online called AAA Math. They offer lessons as well as exercises, so it's a great product to do some extra study, and certainly better than wikipedia. Another place is Wolfram Alpha, a fantastic website for mathematics help. It take you through complex problems, displaystyle, frac help and definitions. It's a product that will help your basics of dividing and multiplying, but also tackles the more complicated stuff. 

Math Help For Free

Looking online for extra tutoring is the best place if you want cheaper rates, but you can also get one-on-one help in in person, through your local school or even public library. One of the best places to start is by checking to see if your or your child’s school has a mathematics centre.  If there isn't a specific place like that, have a try at your local library. There are heaps of libraries in Australia that offer support to young learners. 

Arithmetic Teachers Online

There are plenty of tutoring companies these days that offer services in academic subjects. Many of the online options end up being cheaper than in person tutoring. For example, check out websites such as Superprof where you can choose from a huge variety of teachers, so you can find one that best suits your needs. A tutor will always be better than wikipedia!

Find Maths tutor Sydney on Superprof.

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Daniel

A student by trade, Daniel spends most of his time working on that essay that's due in a couple of days' time. When he's not working, he can be found working on his salsa steps, or in bed.