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# Algebra Terms

Question | Answer |
---|---|

Absolute Value | "Absolute value makes a negative number positive. Positive numbers and 0 are left unchanged. The absolute value of x is written |x|. We write |–6| |

Formally, the absolute value of a number is the distance between the number and the origin. This is a much more powerful definition than the ""makes a negative number positive"" idea. It connects the notion of absolute value to the absolute value of a com | |

Real Numbers | The numbers we use to measure real-world quantities, such as length, temperature, or volume, are called real numbers. All the rational and irrational numbers make up the set of real numbers. The number line is a model of the set of real numbers. |

Rational Number | A number that can be expressed as the quotient of two integers. Fractions, mixed numbers, decimals and integers are all rational numbers, because they may be expressed as a quotient of two integers. Ex: 3 1/4 |

Irrational Number | Some numbers cannot be written as a quotient of two integers, and these are called irrational numbers. |

Variable | A letter that stands for a number in a mathematical expression is called a 'var'iable, because its value can vary. In the expression 4n + 7, n is a variable |

Expression | A mathematical phrase made up of variables and/or numbers and operations is called an expression. Ex: 2ab + 3ab - a |

Terms | in an expression, the terms are the elements separated by the plus or minus signs. In the expression 2ab + 3ab - a, the terms are 2ab, 3 ab, and a |

Coefficient | A number that appears before a letter in a term. For example in the term 2ab, 2 is the coefficient. |

Constant | A term that has only one number and no variables is called a constant, because its value doesn't vary. In the expression 2ab + 3b + 6, the number 6 is a constant |

Algebraic Expressions | An algebraic expression is one or more algebraic terms in a phrase. It can include variables, constants, and operating symbols, such as plus and minus signs. It's only a phrase, not the whole sentence, so it doesn't include an equal sign. |

the sum of three times a number and eight | "3x + 8 |

The words ""the sum of"" tell us we need a plus sign because we're going to add three times a number to eight. The words ""three times"" tell us the first term is a number multiplied by three. | |

In this expression, we don't need a multiplication sign or parenthesis. Phrases like ""a number"" or ""the number"" tell us our expression has an unknown quantity, called a variable. In algebra, we use letters to represent variables. | |

" | |

the product of a number and the same number less 3 | "x(x – 3) |

The words ""the product of"" tell us we're going to multiply a number times the number less 3. In this case, we'll use parentheses to represent the multiplication. The words ""less 3"" tell us to subtract three from the unknown number. " | |

a number divided by the same number less five | "x/x-5 |

The words ""divided by"" tell us we're going to divide a number by the difference of the number and 5. In this case, we'll use a fraction to represent the division. The words ""less 5"" tell us we need a minus sign because we're going to subtract five." | |

A number n times 3 is equal to 120. | "A number n times 3 is equal to 120. |

This is an easy one. The word ""times"" tells you that you must multiply the variable n by 3, and that the result is equal to 120. Here's how to write this equation: " | |

Commutative properties | "Commutative Properties |

Addition: a+b | b+a Multiplication: ab |

Associative Properties | "Associative Properties |

Addition: (a+b) + c | a + (b+c) Multiplication: (ab) c |

Distributive Property | "Distributive Property |

a(b+c) | ab+ac" |

Density Property | Between any two real numbers, there is always another real number. |

Identity Properties | "Identity Properties |

Addition: a + 0 | a multiplication: a x 1 |

Like Terms | |

≥ | greater than or equal to |

≤ | less than or equal to |

> | greater than |

< | less than |

Solving addition and subtraction equations | To solve an equation means to find a value for the variable that makes the equation true. Whatever you do to one side of the equation, you must also do to the other side. (Balance the scale) |

Solving multiplication equations | To solve a multiplication equation, use the inverse operation of division. Divide both sides by the same non-zero number. |

Solving division equations | To solve a division equation, use the inverse operation of multiplication. Multiply both sides by the same number. |

Inequalities | A mathematical sentence built from expressions using one or more of the symbols <, >, ≤, or ≥. |

Exponent | The number (written in superscript) used to express how many times a base is multiplied by itself |

Base | The number directly preceeding an exponent |

polynomial | is a series of one or more terms that are added or subtracted, such as 3x + 2y - 4 |

To change from percent to decimal | you move the decimal point two places to the right |

equations for the Perimeter | (P |

equation of Area | A |

Perimeter | P |

Area of a triangle | A |

Area of a rectangle | A |

Area of a parallelogram | A |

Area of a trapezoid | A |

Area of a circle | A |

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