Chapter 6 ALGEBRA Lesson 1 The Language of

Chapter 6: ALGEBRA Lesson 1 - The Language of Algebra THEORY

Number Symbols in Algebra Numbers Definition Examples Whole Counting Numbers 0, 1, 2, 3, 4… Integers Positive and Negative Whole Numbers. -2, -1, 0, 1, 2… Rational A number that CAN be expressed as a quotient of two integers. Fractions, Mixed Numbers, and Decimals are Rational Numbers Irrational A number that CANNOT be written as the quotient of two numbers. 10 = 10 1 1. 12 = 1 12 100 √ 2 = 1. 4142… ∏ = 3. 14159…

Operation Symbols in Algebra OPERATOR MEANING + x or • ÷ or / ≠ = < and > ≤ and ≥ Add or Positive Subtract or Negative Multiply Divide Does not equal Equals Greater than, Less than Greater or equal to, Less than or equal to

The Language of Algebra has a language of its own. Vocabulary Translation Example Variable A letter that represents a number. It is called a variable because it varies. x, y, z Expression A mathematical phrase made up of variables and/or numbers along with operations 3 x +4 y -5 z -8 Terms ‘family’ A single number and/or variable along with its operation. -3 x, +2 y, -1 Coefficient The number that appears before the variable. 3, 4, -5 Constant The term that has one number and NO variable. -8

Expressions vs. Equations An expression is like a phrase. An equation is like a sentence. EXPRESSION NUMERICAL VARIABLE EQUATION 5(3) – 4 5(3) - 4 = 11 5 x - 4 =11

Translation of English Sentence Algebra Equation Understanding how to write an algebra expression requires you to know the synonyms for mathematical operations. ADDITION SUBTRACTION Increase More than Sum Greater than Minus Reduced Decreased (by) Difference MULTIPLICATION DIVISION Times Product Into Divided by Quotient

Translation of English Sentence Algebra Equation More Tools for your Toolbox… The words… ‘what’ ‘what number’ ‘a number’ Usually represents a variable (letter) such as x or n. The words… ‘is’ ‘is equal to’ Represents the = sign.

Using a Verbal Model English Phrase The product of 6 and a number The sum of 5 and a number Expression 6 • x or 6 x 5 + x English Sentence Equation or Inequality The product of 6 and a number is 18. 6 x = 18 The sum of 5 and a number is greater than or equal to 23. 5 + x ≥ 23

Expression: -5 x + 2 y -3 z +9 Example 1: Identify the following Variable(s) Term(s) Coeffiencient(s) Constant(s)

Which are Equations? circle I. 2 x + 3 = 15 II. 11 a = 22 III. -3 x + 2 y -4 z IV. x 2 + 3 xy = 10 V. 5 n + 5 m = -6 m +2 V. 2(x + 3)

Translating from… English Algebra Expressions The sum of a number and seven. Nine less than a number. A number less than nine. Two times a number. The quotient of six and a number.

TRICKY Translations from English Algebra Twice the sum of a number and 4. Twice means 2 • BOTH the x + 4 vs. The sum of twice a number and 4 The addition of 2 • an x and 4

Translating from… English Algebra Equations A number increased by 9 is 22. Half a number is reduced by 10, the answer is equal to 14. Four is subtracted from a number to give 7. Three less than a number is 6. 20 divided by some number is four.