# Algebra Signs, Definitions & Notation

## Algebra Help: Section 1.1

Learn elementary algebra definitions including the concepts of quantity, mathematics, and algebra. Learn mathematical notation including plus, minus, multiplication, division, equality, inequality, parenthesis, and the radical sign. ### Definitions and Notation

1. Quantity is anything that can be measured or compared; as distance, space, motion, or time.
2. Mathematics is the science which treats of the relations of quantities.
3. Algebra is that branch of mathematics in which the operations are indicated by signs or symbols, and the quantities are represented by letters. It is universal arithmmetic.

#### The Signs

1. Addition is denoted by the perpendicular cross, +,called plus; thus, in 4 + 2 + 9 the sign indicates that 4, 2, and 9 are added.
2. Subtraction is denoted by the horizontal line, -, called minus; thus, in 10 - 7, the sign indicates the second number, 10, is to be subtracted from the first number, 7.
3. Multiplication is denoted by the asterisk, *; thus, in 5 * 4, the sign indicates that 5 and 4 are to be multiplied.
4. Division Denote division in one of three ways.
1. Division symbol with a point above and below; ÷. Write the dividend to the left and the divisor to the right. For example 8 ÷ 6.
2. Division symbol with a right slanted line. Write the dividend to the left and the divisor to the right. For example 8/6.
3. Division symbol as a horizontal line. Write the dividend above and the divisor below. For example
```8
-
6
```
5. Equality is denoted by two horizontal parallels, =, which represent the words, equal to; thus, in 4 + 8 = 7 + 5, the parallels indicate the two sets of numbers compared; and the expression is read, 4 plus 8 equals, or is equal to 7 plus 5.
6. Inequality is denoted by the angle, >, the opening always being toward the larger number or quantity; thus, in 12 + 7 > 14, the sign >, indicates that the sum of 12 plus 7 is greater than 14, and the whole expression is read 12 plus 7 is greater than 14. The expresssion 6 < 4 + 7 is read, 6 is less than 4 plus 7.
7. Parenthesis, (), denotes that several numbers or quantities included within parenthesis should be calculated together, and subjected to the same operation. Therefore (10 + 4)* 3 indicates that both 10 and 4, or their sum, should be multiplied by 3. Therefore (10 - 4) * 3 indicates that the difference of 10 and 4 is to be multiplied by 3.
8. Parenthesis, (), also denotes multiplication, when used without an operator. For example 6(5+1) represents 6 * (5+1).
9. Radical Sign, , indicates that the root of the quantity placed under it is to be taken.

7-8

7-8

#### Help with Algebra Homework

Free tutorials provide math help for math problems. Tutorials start with algebra 1. Algebra tutorials include word problems related to algebra topics, as they're introduced. See the menu, above for algebra math equations, and explanation, by section.

Windows algebra games, designed to help with classwork, coming soon! Windows games, in progress, work with this set of free tutorials, modified from the public domain text book titled, New Elementary Algebra containing the rudiments of the science for schools and academies. By Horation N Robinison, LL. D. Ivison, Blakeman & Company, Publishers, New York and Chicago.

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