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ALGEBRAIC EXPRESSION

ALGEBRAIC EXPRESSION. Which one is the algebraic ?. Key Words. Algebraic Expression : Bentuk Aljabar Unknown : Tidak diketahui Term : Suku Like term : suku sejenis Unlike term : suku tidak sejenis Variable : Variabel Coefficient : Bilangan Pengali

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ALGEBRAIC EXPRESSION

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  1. ALGEBRAIC EXPRESSION

  2. Which one is the algebraic ?

  3. Key Words • Algebraic Expression : Bentuk Aljabar • Unknown : Tidak diketahui • Term : Suku • Like term : suku sejenis • Unlike term : suku tidak sejenis • Variable : Variabel • Coefficient : Bilangan Pengali • Exponent : bilangan pangkat dari variable • Constant : bilangan yg berdiri sendiri • Simplify : Sederhanakan

  4. What do you do when you want to refer a number but you do not know? Suppose you wanted to refer the number of shops in your town, but haven't counted them yet. May be “You say 'blank' number of shops, or perhaps ' ? ' number of shops. • In mathematics a letter is often used to represent the number of shops that unknown - so you could say ' x ' number of shops, or ' q ' number of shops. • In the lesson we will take for using letters to represent numbers.

  5. Terms • Term is a letter on its own or multiplied by a number. example : r is a term and 2s is a term. • When we write algebraic terms we leave the multiplication signs out. 2 x s =2s 8 x y= 8y

  6. A. Identifying an Algebraic Term

  7. Algebraic Expression • A sign of numbers and letters joined together by mathematical operations, such as + and -,is called an Algebraic Expression (forms) . Ex : r + 2s is an algebraic expression How many term does it have ? • 3a + y consists of 2 terms( 3a and y) • 3a + p - 4a Consist of 3 terms(3a, p, -4a) • 7x – 2a + b consists of 3 terms(7x, -2a, b)

  8. B. Identifying Like term and Unlike Term • Like Terms ex. 1. 7y, -6y, 1/3 y 2. x2, -3x2 3. 4. Thus, Like Terms are terms that have same variable and same exponent of variable • Unlike Terms ex. –x, 1/3 p, 4h So, Unlike Terms are terms that have different variables

  9. Simplifying Algebraic forms(Addition and Subtraction) In algebra, when like terms are added and subtracted it is called simplifying.Only like terms can be added or subtracted ex. 10y + 3x + 8y = 10y + 8y + 3x = 18y + 3x 10y + 3x = 3x + 10y Group the like terms

  10. How to simplify the algebraic expressions

  11. Answers 4x + y - 2x + 6y = 4x - 2x + y + 6y = 2x + 7y Question:Simplify ; 4x + y - 2x + 6y. EXERCISE

  12. SIMPLIFY MULTIPLICATION EXPANDING

  13. MULTIPLICATION SIMPLIFY EXPANDING Simplify • a x 2 = 2 x a = 2a p x 1 = 1 x p = p, a x b = b x a =ab Simplify • 12 x a e. -3 x (-4) x 5p • -7 x a f. 8 x (-4p) x 3q • k x 5 g. -2y x (-4x) x 6 • h x (-1) h. -7a x (-3b) x (-2a)

  14. DISTRIBUTIVE LAW EXPANDING • ab + ac = a(b+c) = (b+c)a OR a(b+c) = • ab - ac = a(b-c) = (b-c)a OR a(b-c) = ab ac + ab ac -

  15. DIVISION • Definition of Division ex , 2 : 3 = 2 x 1/3 3 : y = 3 x 1/y So, DIVISION = INVERSE OF MULTIPLICATION • FACTOR OF TERMS

  16. Division Observe the same factor 1. 2a : a = 2 2. 6xy : 2y = 3x • Simplify • 12ab : 4a • x3 : x • 6x5y2 : 2x2y • 8x4y2z : 2xy2

  17. DIVISION ….. = 3m = 3x = 4m = 4m = -7x = 3m = 1/3(x) = 2/9m ….. = 1/3m = 1/2a ….. = 3m = 1/3(ab)

  18. Exponents/Powering • b2 = b x b (-b)2 = (-b) x (-b) -(b)2 = - (b x b) (2b)2 = 2b x 2b Describe • (2a)2 • (-3a)2 • -(2ab)3 • -3(-2a2)3

  19. MATHEMATICAL EXPRESSION • Numerical expression • Verbal Expression • Algebraic expression Example: • Verbal expression The Keene family and the Norman family visit the zoo together. Because there is more than 10 people they get a special offer : 1 child goes free. • Algebraic expression Cost for the Keene family = 3g + 2k Cost for the Norman family = 5g + 4kOffer = - gTotal cost = 3g + 2k + 5g + 4k - g = 3g + 5g - g + 2k + 4k = 7g + 6k

  20. Worked example:g is the cost of child admission and k is the cost of adult admission to the zoo.What is the cost for the Keene family of 3 children and 2 adults to visit the zoo? Solution:Cost for 3 children = 3gCost for 2 adults = 2kTotal cost = 3g + 2k

  21. Sample question:Write an algebraic forms for the cost for the Norman family, 5 children and 4 adults, visiting the zoo. Answers 5g + 4k

  22. WHEN DO WE NEED ALGEBRAIC EXPRESSION

  23. WHEN DO WE NEED ALGEBRAIC EXPRESSIONS

  24. Write algebraic expressions for these word phrases • Four more than s • The product of 7 and c • Nine less than x • A number divided by the sum of 4 and 7. • Twice the sum of a number plus 4. • The sum of ¾ of a number and 7. • Ten times a number increased by 150.

  25. Write an algebraic phrase for these situations • A car was traveling 35 miles per hour for a number of hours. • Bob ran 7 times a week for a number of weeks. • The plumber added an extra $35 to her bill. • Thirty-five fewer people came than the number expected.

  26. Simple formulae A formula is another word for an expression, usually used when an expression represents a problem in real life. Formulae (plural of formula) are useful when the numbers represented by letters in the expression change according to different situations.

  27. Worked example:The size of a rectangular wedding cake changes according to the tier it sits on. The 1st tier is the largest cake and is p cm wide and q cm long: • The length of ribbon to decorate the outside of the cake is given by a formula that is the perimeter of the cake plus 1cm, so that the ribbon can overlap. • So the formula for the length of ribbon is:p + q + p + q + 1 = 2p + 2q + 1 or 2(p + q) + 1

  28. Sample question:Write a formula for the length of ribbon for the cake on the 2nd tier, if the 2nd tier cake has the same width as the 1st tier but a length that is 5cm shorter than the 1st tier cake. Now check your answer Answers The 2nd tier cake is p cm wide and q - 5 cm long:So the formula for the length of ribbon is p + q - 5 + p + q - 5 + 1Simplifying the expression: p + p + q + q - 5 - 5 + 1 = 2p + 2q - 9 or 2(p + q) - 9

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