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Click the mouse button or press the Space Bar to display the answers. Translating Expression Chapter 1, Lesson 1 Objectives • Translate verbal expressions into numerical expressions. • Write numerical expressions from verbal expressions. • Translate numerical expressions into verbal expressions. • Write verbal expressions from numerical expressions. Numerical Expressions • Two or more numbers joined by operations such as addition, subtraction, multiplication and division. • NO EQUALS SIGN IS USED!!!!!! • Constants—Terms used in mathematics for any number without a variable. • Parentheses can also be used. Variable Expressions • Variable—a letter of the alphabet that represents unknown values. • Coefficient—Number attached to variable. • Variable Expressions— mathematical statements that contains one or more variables and/or numbers. • Like Terms—terms that have identical variable parts. • Unlike Terms—terms that have different variable parts • NO EQUALS SIGN IS USED!!!! Addition • More Than – Three more than a number • Sum of – Two minus the sum of a number and 20 – “of” with an operation BEFORE it means parentheses. – 2 – (n + 20) • Increased by – A number increased by negative eight – y + (-8) – Quantity of – What is the quantity of the boxes? • Total of • What is the total of the sale? • Plus – Six plus a number Subtraction • Difference Of – Three plus the difference of a number and 20. (x – 20) • Decreased by – Negative two decreased by a number -2 - n • Less than – Seven less than a number p–7 • Minus – Three minus a negative number. 3 – (-n) Multiplication • Times • Two times a number » 2n • The Product Of • Three plus the product of 6 and a number x. » 3 + (6n) • Multiplied By • A number multiplied by negative eleven » -11n Multiplication Sign Change • We no longer use “x” for multiplication. • Since “x” is a variable and “x” means multiplication, it will get confusing. • Therefore we represent multiplication with: – • – Putting everything side by side (separating numbers with parentheses. 3(4)xyz Division • The quotient of… • The quotient of six times a number and three plus a number • Divided by • Seven divided by a number Just So You Know… Write an algebraic expression for five less than a number c. The words less than suggest subtraction. a number c less five c – 5 Answer: Thus, the algebraic expression is . Write an algebraic expression for the sum of 9 and 2 times the number d. Sum implies add, and times implies multiply. Answer: The expression can be written as . Write an algebraic expression for two thirds of the original volume v. The word of implies multiply. Answer: The expression can be written as Write an algebraic expression for each verbal expression. a. nine more than a number h Answer: b. the difference of 6 and 4 times a number x Answer: c. one half the size of the original perimeter p Answer: Exponents Write the product of algebraically. Answer: to the seventh power Write the sum of 11 and x to the third power algebraically. Answer: Write each expression algebraically. a. the difference of 12 and x squared Answer: b. the quotient of 6 and x to the fifth power Answer: Write a verbal expression for . Answer: the quotient of 8 times x squared and 5 Write a verbal expression for . Answer: the difference of y to the fifth power and 16 times y Write a verbal expression for each algebraic expression. a. Answer: 7 times a to the fourth power b. Answer: the sum of x squared and 3 Click the mouse button or press the Space Bar to display the answers. Order of Operations Chapter 1, Lesson 2 Objectives 1. Evaluate and simplify expressions using substitution and order of operations. 2. Evaluate powers and exponents. 3. Learn how to convert decimals to fractions and fractions to decimals using a Casio calculator. Order of Operations WHEN TO USE 1. To simplify numerical expressions • Parentheses 2. To simplify verbal expressions • Multiply/Divide from left to right 3. To simplify same-side like terms • Add/Subtract from left to right • Exponents Parentheses • In Algebra I, parentheses is ALWAYS first!!!!!!!!!!! • (3 + 4) = 7 (order of operations) • 3(x + 2) = 3x + 6 (distributive property) Exponents Evaluate . Use 3 as a factor 4 times. Answer: Multiply. Evaluate . Use 8 as a factor 2 times. Answer: Multiply. Evaluate each expression. a. Answer: 625 b. Answer: 32 Other Operations • Multiply/Divide FROM LEFT TO RIGHT!!! • Add/Subtract FROM LEFT TO RIGHT!!! Evaluate . Multiply 2 and 3. Add 6 and 4. Answer: Subtract 10 and 6. Evaluate Evaluate powers. Divide 48 by 8. Multiply 6 and 3. Answer: Add 18 and 5. Evaluate each expression. a. Answer: 23 b. Answer: 7 Evaluate . Evaluate inside grouping symbols. Multiply. Answer: Multiply. Evaluate . Evaluate innermost expression first. Evaluate expression in grouping symbol. Evaluate power. Answer: Multiply. Evaluate each expression. a. Answer: 88 b. Answer: 3 Evaluate Evaluate the power in the numerator. Multiply 6 and 2 in the numerator. Subtract 32 and 12 in the numerator. Evaluate the power in the denominator. Multiply 5 and 3 in the denominator. Answer: Subtract from left to right in the denominator. Then simplify. Evaluate Answer: 1 Solve Original equation Add 8 and 2 in the numerator. Subtract 5 and 3 in the denominator. Evaluate the power in the denominator. Simplify. Answer: Divide. Answer: 6 Simplify The fraction bar indicates division. However, you cannot combine -39b and 65 (Unlike terms) Therefore, you have to split the fraction ONLY when there is ADDITION OR SUBTRACTION on top!!! -3b + 5 Simplify Answer: Substitution • When a variable stands alone and is equal to a constant, another variable or expression, then wherever I see the variable that stands alone, I can substitute whatever it is equal to in for the variable that stands alone. Evaluate Replace x with 4, y with 3 and z with 2. Evaluate . Subtract 16 and 3. Evaluate . Multiply 2 and 13. Answer: Add. Replace y with 12. Answer: Simplify. Answer: 10 Evaluate Answer: 28 . Architecture Each of the four sides of the Great Pyramid at Giza, Egypt, is a triangle. The base of each triangle originally measured 230 meters. The height of each triangle originally measured 187 meters. The area of any triangle is one-half the product of the length of the base b and the height h. Write an expression that represents the area of one side of the Great Pyramid. one half of the product of length of base and height Answer: Find the area of one side of the Great Pyramid. Evaluate Multiply 230 by 187. . Divide 43,010 by 2. Answer: The area of one side of the Great Pyramid is 21,505 . Find the area of a triangle with a base of 123 feet and a height of 62 feet. Answer: Click the mouse button or press the Space Bar to display the answers. Distributive Property Objectives • Use the distributive property to simplify expressions. • Simplify expressions by combining like terms. • Determine if expressions are simplified or not. Distributive Property If the value of a is positive, then the following can be done. If the value of “a” is negative, then the following can be done. – If a(b + c), then ab + ac. – If –a(b – c), then –ab + ac. – If a(b – c), then ab – ac. – If –a(-b + c), then ab – ac. – If a(-b + c), then –ab + ac. – If –a(-b – c), then ab + ac – If a(-b – c), then –ab - ac. – -a(b + c), then –ab – ac using the Distributive Property. Then evaluate. Distributive Property. Multiply. Answer: Add. using the Distributive Property. Then evaluate. Answer: using the Distributive Property. Then evaluate. Distributive Property. Multiply. Answer: Subtract. using the Distributive Property. Then evaluate. Answer: Terms Like & Unlike Terms Like Terms Unlike Terms Simplify & Simplified • Simplify – Combine Your Like Terms • Perform as many of the indicated operations as possible • Simplified • Your are done when only unlike terms remain Rewrite Then simplify. using the Distributive Property. Distributive Property Answer: Multiply. Rewrite Then simplify. using the Distributive Property. Distributive Property Answer: Multiply. Rewrite each product using the Distributive Property. Then simplify. a. Answer: b. Answer: Simplify . Distributive Property Answer: Substitution Simplify . Distributive Property Answer: Substitution Simplify each expression. a. Answer: 5x b. Answer: Distributive Property Multiply. Commutative (+) Associative (+) Distributive Property Answer: Substitution Answer: Use the expression three times the sum of 3x and 2y added to five times the sum of x and 4y. Write an algebraic expression for the verbal expression. three times the sum of 3x and 2y Answer: added to five times the sum of x and 4y Cars Find what the total cost of the Morris family operating two cars would have been in 1985, if they drove the first car 18,000 miles and the second car 16,000 miles. USA TODAY Snapshots® Use the Distributive Property to write and evaluate an expression. Distributive Property Multiply. Add. Answer: It would have cost them $7820. Cars Find what the total cost of the Morris family operating two cars would have been in 1995, if they drove the first car 18,000 miles and the second car 16,000 miles. USA TODAY Snapshots® Answer: $13,940 Click the mouse button or press the Space Bar to display the answers.