Tips to Solve Simple Arithmetic Problems

From primary to high school and beyond, maths is present at every point in an academic year, but also every stage in life. However, for many, topics in hard sciences like science and maths can prove challenging at one time or another. Basic arithmetic operations are one of the things that run the world and today’s economy. They play an increasingly important role even outside of academia.

In South Africa, the population is below the global average when it comes to easy arithmetic. This has created a skills crisis that has resulted in unemployment and a need for adult training.

If you are wondering how to know arithmetic sequence, you are on the right track, remember that it could contribute to your job security and help you to make empowering decisions in your life.

From politics to housing, the fundamental theorem of arithmetic is entrenched in every aspect of life, which is why so many are turning to extra arithmetic lessons for support.

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Arithmetic Laws and Definitions

There’s no doubt that the roots of mathematics like within the fundamental theorem of arithmetic. Basic arithmetic operations, which date back to 18 000 BCE are derived from arithmos, which in Greek means numbers.

Fundamental arithmetic focuses on four basic operations: addition, multiplication, subtraction and division.

While it may seem that this branch of maths only offers lessons for lower grade students, the fact is that even simple arithmetic problems can begin in first grade with counting, but are important for grade 7 pre-calculus and university level calculus.

Mastering how to know arithmetic sequence includes more than just a beginner’s guide to easy arithmetic. The following three basic laws govern both advanced and basic arithmetic operations.

Commutative Law

Essentially, the commutative law states that the order of the operation is irrelevant when multiplying or adding. For example:

• a x b = b x a
• a + b = b + a

The word “commute” is one way to remember this law, because regardless of the combination of numbers, groups of numbers will commute to the same place, or result. For instance:

• 2 + 4 = 4 + 2
• 6 x 3 = 3 x 6

The law also applies to creating percentages. As an example, a % of b should always equal to the b% of a. Here’s an example of the rule reflected in numbers:

• 3% of 60 = 60% of 3

Associative Law

The associative law means that, regardless of how you choose to group your multiplication or addition of numbers, the result is the same. For example:   

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

Considering this example, you can see that when we group or “associate” two numbers in a big addition or multiplication operation the result is always the same.

• (2 + 4) + 3 = 2 + (4+3) which leads to 6 + 3 = 2 + 7
• (3 x 3) x 4 = 3 x (3 x 4) which leads to 9 x 4 = 3 x 12

Confidence in how to know arithmetic sequence comes with learning these laws and then practising them. For instance, one of the reasons why this law is important is that it can sometimes be necessary to arrange these numbers in a different order.

Distributive Law

The distributive law is slightly more complicated but is probably the law that is used most often. It states that when adding or multiplying numbers, you are allowed to distribute the multiplier to the number that is added first. As an example:

• a x (b + c) = a x b + a x c

As shown above, the a is actually “distributed” to both the b and the c before both numbers are added. Again, operations like this can certainly make an operation easier. Here is an example of how to do it:

• 3 x (8 + 9) is easy to solve when it is rearranged as 3 x 8 +3 x 9

Here is another way where you can use the same law, only in reverse:

• Instead of solving 13 x 6 + 13 x 4 you could solve it as 13 x (6 + 4)

Having a grip on arithmetic sequence is a good way to solve both advanced and simple arithmetic problems.

Examples of Basic Arithmetic Operations at Different Levels   

From concepts like linear equations and inequalities, arithmetic is vital for maths classes at every level.

Whether you are looking for help on how to know arithmetic sequence, or just how to solve simple arithmetic problems, understanding the bases of arithmetic is essential. Remember that every student who can confidently master primary school or basic arithmetic operations will have a better chance when it comes to achieving more complex maths goals.

Easy arithmetic at its core contains many basic concepts that will be needed to build more advanced maths. One example of this is seen through the use of decimals which have many practical uses. Decimals are mainly learnt through the understanding of fractions. For example:

• 0.2 = 2/10 = 1/5
• 0.25 = 2/10 + 50/100 = 25/100 = 1/4

By understanding the fundamental theorem of arithmetic through these rules it is easy to see that how decimals are formed.

Two of the four most important arithmetic operations, addition and division, can be used to solve problems. Bear in mind that in the above example, the decimal number is in the tens position while the 5 is in the hundreds position.

In senior primary, children move on from simple arithmetic problems to more advanced concepts to include linear equations, roots, inequalities, polynomial equations, systems of equations and quadratic equations. In addition, senior primary also deals with pre-algebra, geometry and more.

For instance, learning how to simplify algebraic expressions is one of the topics covered in these grades. As an example:

• 3x + 5(x - 6)

The first step in this maths problem is to use the distributive law to work out:

• 3x + 5x - 30

Next, add 3x and 5x together. Now consider the distributive law again, you can see why:

• x(3+5) is the same as 3x + 5x

By combing all of these concepts above, you get the final answer:

• 8x -30

At high school maths can vary substantially depending on what level maths is taken. Examples of arithmetic include maths with logarithms, rational expressions, rational functions, polynomials, trigonometric concepts and exponents. A common example of arithmetic at this level is seen through matrices.

A matrix arranges numbers in columns and rows which offers many practical applications for statistics, computer science and project management. Here’s an example of how to figure out the determinant of a matrix.

A =   [a b

c d]

To work out the determinant of a 2x2 matrix in this example, we have used the following equation: det A = ad – bc. Practise finding out the determinant in the following example:

A =    [2 4

  6 3]

Naturally, at university level arithmetic can get more complex and involves everything from probability to differential equations. One example of the kind of arithmetic you are likely to use is that you will need to find the probability of two events A and B.

For instance, the probability that you will read this article up to this point is 1/16 (event A). Event B could be that the probability of you winning the national lottery is 1/45,057,474. You could also ask yourself: what is the probability of reading the article up to this point and winning the national lottery?

• Probability (events A and B) = Probability A * Probability B

Online Arithmetic Resources and Private Tutors

If you are hoping to find more arithmetic tools and resources, be sure to check out this guide for finding maths resources online.

If you’re looking for a mathematics teacher there are many options in South  Africa. Start by asking your regular teacher, or check out the local community advertising boards. Alternatively, head straight to Superprof where you can enjoy many important benefits. Amongst these, is that you could receive your first lesson for free which is helpful in determining whether you and your tutor are a good personality-fit or not.

Never underestimate the value of being able to get on well with your online math tutor. In fact, it can make all the difference when it comes to the subject of maths.  In addition, Superprof provides peace of mind by verifying the credentials of all of its tutors on your behalf.