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7.1 Multiplying and Dividing Monomials

7.1 Multiplying and Dividing Monomials. Math 9. Determine the area of the circle and square in the diagram. Leave π in exact form. Area of circle: = π r 2 = π (5x) 2 = π 25x 2 = 25 π x 2. Must square the coefficient and the variable. 5x. Coefficient should go first.

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7.1 Multiplying and Dividing Monomials

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  1. 7.1 Multiplying and Dividing Monomials Math 9

  2. Determine the area of the circle and square in the diagram. Leave π in exact form. Area of circle: = πr2 = π(5x)2 = π25x2 = 25πx2 Must square the coefficient and the variable 5x Coefficient should go first

  3. Area of square: = l2 = (10x)2 = 100x2 5x 5x 5x That means the length of the square is 10x.

  4. What is the ratio of the area of the circle to the area of the square? Acircle Asquare Does this ratio change as the size of the circle changes? No. When a number is doubled and both are squared the ratio will always be the same. = 25πx2 100x2 = 25π 100 = π 4

  5. Example 1. Determine the following product • (3x) (2x) • Using a model x x x x x x2 x2 x2 x2 x2 x2 x2 6x2

  6. ii) Algebraically (3x) (2x) = = = 6x2

  7. (3x) (2y ) • Using a model 6xy x x x y y xy xy xy xy xy xy xy • You should notice that • y is smaller than x • xy is rectangular shaped

  8. ii) Algebraically (3x) (2y ) = 6xy

  9. = 3x Example 2. Determine the following quotients a) 12x2 4x i) Using algebra tiles

  10. ii)Algebraically 12x2 4x = 3x

  11. = 4y b) 20xy 5x i) Using algebra tiles

  12. ii) Algebraically b) 20xy 5x = 4y

  13. Example 3. Determine the following products or quotients:

  14. Multiply numbers first Multiply variables together • (5x ) (2.4 x ) = 5 2.4 x x = 12x2 • (3a ) ( ⅚ a ) = 3 ⅚ a a = 15/6 a2 = 2 ½ a2 or 5/2 a2

  15. (2 x ) (1.4 y ) (1.2w) = 3.36 wxy d) (-2 x3 )(7 x2) = -14 x5

  16. e) =-2x f)

  17. (-18k 2 ) ÷ (-24k 2) = -18 ÷ (-24) = 3/4 or 0.75 h)(120 mr p ) ÷ (20 m p) = 120r ÷ 20 = 6r

  18. 4. A rectangle has a length of 15x cm and a width of 6.4x cm. What is the area of the rectangle? A = l * w = 15x * 6.4x = 96x2 The area of the rectangle is 96x2 cm2. 6.4x cm 15x cm

  19. 2.6y cm 5. A triangle has a base of 18y cm and a height of 2.6y cm. What is the area of the triangle? A = ½ bh or bh 2 = 23.4 y2 Area of the triangle is 23.4 y2 cm2. 18y cm

  20. 6. The area of a parallelogram is 38.2a2 m². Determine the height if the base is 4a m. A = bh 38.2a2= 4a * h ÷4a ÷4a 9.55a = h The height of the parallelogram is 9.55m.

  21. Jigsaw - p. 260 #3abc, 5abcd, 7abcde, 11abc Practice – p. 261-262 9, 10, 13, 15, 17, 18

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