Algebra is a branch of mathematics that teaches us how the laws of mathematics is applied to arithmetic. Because of a infinite number of variables letters of the English and Greek alphabet stand in for numbers. lets forget the letters for the time being using number examples. Two dollar calculators is a good help if you struggle with numbers. Or all you need is your standard computer calculator. If you like to write by hand by all means use a pad and pencil.

Take 2 plus 5 equals 7. Our mathematical instinct agrees if 2 plus 5 equals 7 it pans out 7 take away 5  equals 2. We can see if we use letters  c = b + c respectively. It doesn't matter which way done whether a plus b or  b plus a the answer is always the same.

Calculators agrees.

2 plus 5 equals 7

5 plus 2 equals 7

7 takeaway 5 equals 2

7 takeaway 2 equals 5

Our mathematical instinct agrees 2 fives equals to 5 plus 5, five doubled or 2 times 5 respectively.

If we take the same numbers your calculator  agrees if two 5's equals 10.It pans out 10 divided in half is 2.  x, y z poses a problem with x because it looks identical to the muiltiply sign. A solution is to omit it. Using letters  7 = a  b respectively.

Once again calculators agree

2 multiplied by 5 equals 10

5 multiplied 2 equals 10

10 dived 5 equals 2

10 dived 2 equals 5

Our mathematical instinct agrees 2 fives pans out to 5 plus 5, five doubled or 2 fives at the same time as 10 divided in half panning out to 5 or  2. Five and 2 are the roots of 10 divided in half at the same time. It is just a matter of witch way we look at a sum.

Algebra teaches us we start to observe a symmetrical pattern when we look up in any children's times table in the 2 times, for 2 fives. When we look up in the times5 table we find the same sum in the 5 times 2.

The times table pattern is mathematically symmetrical with every sum occurring in every other place in the entire tables. If we look up 7 threes in the times 7 table we will find 3 sevens inm the 3 times table is equally 21.

Operating on the principle we can look up any answer following back to the roots of the answers turns the times table into roots tables at the same time being a times table called inverse. The inverse of times 10 are roots 2 and 5 respectively. Every answer of the entire table.

This is were we learn about squares and square roots. If we look up in the five times table for 5 fives, using centimeters 5 centimeters long and 5 centimeters high forming a perfect square. It pans out to five plus 5 plus 5 plus five. It simply means any number in the times table multiplied by itself. The mathematical symbol for a square is a little razed 2 just to the right of any number

Operating on the principle number multiplied themselves in the entire table can be rewritten in the square form with a little razed 2 just the right of number.3 Squared equals the square root of 9

If we divide 25 by 5 we have the root of the square is back to 5 called the square root. Our mathematical instinct agrees is only a mater of the the law of mathematics revering (Inverting) any sum. It occurs with ever number multiplied by itself. The mathematical symbol for a square root is the answer of the square in the times table with a tick like sign over it.

Our mathematical instinct agrees in the times 9 table the square of 3 is 9 and the square root of 9 is 3 at the same time.

Algebra teaches a us a mathematical pattern 5 plus 2 equals 7. 9 plus 3 is 12. Seven times 12 (or 12 times 7) is 84. The 84 plus 7 pans out to 91.

It sounds like 5 plus 2 times 9 plus 3. It is not calculated the way it sounds. We do 5 plus 2 first writing down the answer for safe keeping. (Or stored in memory of your calculator).

Then we calculate 9 plus 3.Keeping the answer. We then muiltiply the two answers such as 7 by 12 (or add the answer you stored stored memory in our calculator entering the equals key pans out to 91 respectively. There is only 4 operations to math'. times the inverse divide, plus and the inverse takeaway.

Algebra teaches us sums in brackets to do first then the other sums. We can calculate a written down formulae the square root sign over 5 plus 2 in brackets followed 9 plus 3.Using a calculator  we enter the square root key getting  9 with a very long decimal fraction over.

This is were we learn about primes. Primes is any number apart from squared doesn't dived evenly. there is always a fraction over. Every answer in the times table is not a prime. The are called composites. Primes are the numbers you can at lest square but does not divide evenly any other way.

If you square 5 you are multiplying evenly. But when try to divide it by any other means does not render evenly with a fraction remaining. 5 is a prime. An example shows 5 squared is 25 divided by another number renders a number with a decimal point fraction over every time.25 is a prime

Mathematicians have found the number of primes that come up seems to be endless.