Operations of Arithmetic

The first thing to note is that in algebra we use letters as well as numbers. But the letters represent numbers. We imitate the rules of arithmetic with letters, because we mean that the rule will be true for any numbers.

Here, for example, is the rule for adding fractions:

a/c + b/c = a/c + b/c

The letters a and b mean: The numbers that are in the numerators. The letter c means: The number in the denominator. The rule means:

"Whatever those numbers are, add the numerators
and write their sum over the common denominator."

Algebra is telling us how to do any problem that looks like that. That is one reason why we use letters.

(The symbols for numbers, after all, are nothing but written marks. And so are lettersexclamation As the student will see, algebra depends only on the patterns that the symbols make.)

The numbers are the numerical symbols, while the letters are called literal symbols.

The four operations of arithmetic

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1. Addition:  a + b.   The operation sign is + , and is called the plus sign.  Read a + b as "a plus b. For example, if a represents 3, and b represents 4, then a + b represents 7.
2. Subtraction:  a − b.   The operation sign is − , and is called the minus sign.  Read a − b as "a minus b." If a represents 8, for example, and b represents 2, then a − b represents 6.
3. Multiplication:  a· b.  Read a· b as "a times b." The multiplication sign in algebra is a centered dot.  We do not use the multiplication cross ×, because we do not want to confuse it with the letter x. And so if a represents 2, and b represents 5, then a· b = 2· 5 = 10. "2 times 5 equals 10." Do not confuse the centered dot -- 2·5, which in the United States means multiplication -- with the decimal point:  2.5. However, we often omit the multiplication dot and simply write ab.  Read "a, b."  In other words, when there is no operation sign between two letters, or between a letter and a number, it always means multiplication.  2x  means  2 times x.
4. Division:  a/b. Read as "a divided by b." In algebra, we use the horizontal division bar.  If a represents 10, for example and b represents 2, then a/b  =   10/ 2   =  5. "10 divided by 2 is 5."

Note:  In algebra we call  a + b  a "sum" even though we do not name an answer.  As the student will see, we name something in algebra simply by how it looks.  In fact, you will see that you do algebra with your eyes, and then what you write on the paper, follows.

Similarly, we call  a − b  a difference,  ab

 a product, and  a
b  a quotient.
This sign = of course is the equal sign, and we read this --

a = b

-- as "a equals (or is equal to) b."

That means that the number on the left that a represents, is equal to the number on the right that b represents.  If we write

a + b = c,

and if a represents 5, and b represents 6, then c must represent 11.



This article was originally published on The Math Page. Read the original article.

Source:

https://www.themathpage.com/alg/algebraic-expressions.htm#parentheses