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- 1. Tools for Algebra and Geometry T- 1-855-694-8886 Email- info@iTutor.com By iTutor.com
- 2. Order of Operations When a numerical expression involves 2 or more operations, there is a specific order in which these operations must be performed. In earlier grades you learned to solve numerical expressions using “order of operations” or as most of us say PEMDAS which stands for: Parenthesis, Exponents, (Multiplication/Division) then (Add/Subtract) PEMDAS The reason (multiplication & division) and (add & subtract) are grouped is when those operations are next to each other you do the math from left to right. You do not necessarily do addition first if it is written next to subtraction.
- 3. Variables and Expressions Variable – A symbol used to represent a quantity that can change. Coefficient – The number that is multiplied by the variable in an algebraic expression. Numerical expression – An expression that contains only numbers and operations. Algebraic expression – An expression that contains numbers, operations and at least one variable. Constant – A value that does not change. Evaluate – To find the value of a numerical or algebraic expression. Simplify – Perform all possible operations including combining like terms.
- 4. Numerical expression 8 – 6 + 2 Subtraction is first Remember when those operations, (multiplication & division) and (add & subtract) are grouped next to each other you do the math from left to right. When there are 2 or more operations, and we use grouping symbols such as parenthesis or brackets, you perform the inner most grouping symbol first. 2 + 3[5 +(4-1)²] 2 +3[5 + (3)²] 2 + 3[5 + 9] 2 + 3[14] 2 + 42 44
- 5. Summary of Basic Steps Simplify any grouping symbols (such as parenthesis) first, starting with the inner most group. Simplify any powers (exponents). Perform the multiplication & division in order from left to right. Do the addition & subtraction last, from left to right. Remember, if operations are written next to each other, work from left to right. It is very important to understand that it does make a difference if the order is not performed correctly!!!!!!!!! 70 – 2(5 + 3) 70 – 2(8) 68(8) 544 incorrect (subtraction was done before multiplication) 70 – 2(5 + 3) 70 – 2(8) 70 – 16 54 correct
- 6. Order of Operations is not an isolated skill. This skill applies to almost every topic in Math. Remember that “PEMDAS” is used with evaluating formulas, solving equations, evaluating algebraic expressions, simplifying monomials & polynomials, etc… Get your pencil and calculator ready and try these problems. 1) 20 + 3(5 – 1) = 2) 3 + 2²(1 + 8) = 3) (5 · 4)² = 4) 2(3 + 5) – 9 = 5) 2[13 – (1 + 6)] = 6) 48 / 3 + 5 = 7) 3(6 + 4)(5 – 3) = 8) 100 – 4(7 – 4)³ = 9) 1² + 2³ + 3³ = 10) (24 – 6)/2 =
- 7. Here is an example of an algebraic expression. 4 is the coefficient. X is the variable. 7 is the constant. Algebraic Expression 4x + 7 4 = coefficient x = variable 7 = constant
- 8. Evaluating Algebraic Expressions To evaluate an algebraic expression, substitute a given number for the variable, and find the value of the resulting numerical expression. X – 5 for x = 12 (12) – 5 = 7 2y + 1 for y = 4 2(4) + 1 = 9 6(n + 2) – 4 for n = 5, 6, 7 38, 44, 50
- 9. Evaluate each expression for t = 0, x = 1.5, y = 6, z = 23 1) y + 5 2) 3z – 3y 3) z – 2x 4) xy 5) 4(y – x) 6) 3(4 + y) 7) 3(6 + t) – 1 8) 2(y – 6) + 3 9) y(4 + t) - 5 10) x + y + z
- 10. The End Call us for more Information: www.iTutor.com 1-855-694-8886 Visit

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