Algebra PDF
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This document is a set of notes on algebra, covering topics such as algebraic expressions, equations, variables and constants. It also includes examples and exercises on performing basic arithmetic operations with integers, and translating verbal phrases into algebraic expressions.
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**ALGEBRA** **-comes from Arabic word al jebr, meaning \"reunion of broken parts,\" which appeared in the title of mathematician al-Khwarizmi\'s famous book on equations.** **- is the branch of mathematics that helps in the representation of problems or situations in the form of mathematical expre...
**ALGEBRA** **-comes from Arabic word al jebr, meaning \"reunion of broken parts,\" which appeared in the title of mathematician al-Khwarizmi\'s famous book on equations.** **- is the branch of mathematics that helps in the representation of problems or situations in the form of mathematical expressions.** - - ALGEBRAIC EQUATION **Algebraic expressions are made up of variables, operators, and constants.** **EXAMPLE:**  **An algebraic expression in algebra is formed using [integer](https://www.cuemath.com/numbers/integers/) constants, variables, and basic arithmetic operations of addition(+), [subtraction](https://www.cuemath.com/numbers/subtraction/)(-), multiplication(×), and [division](https://www.cuemath.com/numbers/division/)(/).** **[Integers]** **- a whole number that are positive, negative and zero.** a. b. c. **[FOUR BASIC OPERATIONS OF INTEGERS]** 1. - - **For examples:** **ADDITION WITH [SAME SIGN]** **RULE 1:** If the integers have the **[same sign]**, **ADD** the numbers and keep the sign 1. 2. 3. 4. **ADDITION WITH [DIFFERENT SIGN]** **RULE 2:** If the integers have the **[different signs],** **SUBTRACT** and **[use the sign]** of the **LARGER number.** 1. 2. 3. - - - - - For examples: 1. Solution : 36 + (-13) = 23 2. Solution: 12 + (13)= 25 3. Solution : -23 + -13 = -36 4. - - **For examples:** 1. 2. 3. 4. **Division** - -  **For examples:** 1. 2. 3. 4. **[MONOMIALS]** - **are algebraic expressions with a single term and can be [used in a variety of operations, including addition, subtraction, multiplication, and division.]** **Example:** **2xy** **ADDING and SUBTRACTING MONOMIALS** - For examples: 1. 2. **3. -3x + 9x = 6x** **4. -11xy + (-12xy ) = -23 xy** **5. 12b - 7b = 5b** **6. -18m - 2m = -16m** **MULTIPLYING MONOMIALS** - For examples: **DIVIDING MONOMIALS** - For examples:  **[TRANSLATING VERBAL PHRASES TO ALGEBRAIC EXPRESSIONS]** +-----------------+-----------------+-----------------+-----------------+ | **ADDITION** | **SUBTRACTION** | **MULTIPLICATIO | **DIVISION** | | | | N** | | +=================+=================+=================+=================+ | \- plus | \- minus | \- times | \- divided by | | | | | | | \- more than | \- less than | \- multiplied | \- the ratio of | | | | by | | | \- increased by | \- decreased by | | \- the quotient | | | | \- the product | of | | \- the sum of | \- the | of | | | | difference of | | | | \- the total of | | | | | | \- subtracted | | | | \- added to | from | | | +-----------------+-----------------+-----------------+-----------------+ For examples: Note : Let X = to a number. 1. 2. 3. 4. 5. 6. **[NUMBER PROBLEM EXAMPLES]** 1. v  **[DISTANCE PROBLEM EXAMPLES]** **Distance = Rate (Speed) x Time** 1. **[AGE PROBLEM EXAMPLES]** 1. NOW 3 years ago ------ ----- ------------- Phil 35 32 Tom T T - 3
