Download - 7.1 Multiplying and Dividing Monomials
7.1 Multiplying and Dividing MonomialsMath 9
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
5x
Coefficient should go first
Must square the coefficient and
the variable
Area of square:
= l2
= (10x)2
= 100x2
5x
5x 5x
That means the length of the square is 10x.
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
Example 1. Determine the following product
a) (3x) (2x)i) Using a model
x x x
x
x x2x2
x2 x2
x2
x2
x2
6x2
ii) Algebraically
(3x) (2x) = = = 6x2
b) (3x) (2y )
i) Using a model
x x x
y
y
xy
xyxyxy
xy
xy
xy
You should notice that • y is smaller than x• xy is rectangular
shaped
6xy
ii) Algebraically
(3x) (2y )
= 6xy
Example 2. Determine the following quotients
a) 12x2
4x
i) Using algebra tiles
= 3x
ii)Algebraically 12x2
4x
= 3x
b) 20xy 5xi) Using algebra tiles
= 4y
ii) Algebraically
b) 20xy 5x
= 4y
Example 3. Determine the following products or quotients:
a) (5x ) (2.4 x )
= 5 2.4 x x
= 12x2
b) (3a ) ( ⅚ a )
= 3 ⅚ a a
= 15/6 a2
= 2 ½ a2 or 5/2 a2
Multiply numbers first
Multiply variables together
c) (2 x ) (1.4 y ) (1.2w)
= 3.36 wxy
d) (-2 x3 )(7 x2 )
= -14 x5
e)
=-2x
f)
g) (-18k 2 ) ÷ (-24k 2 )= -18 ÷ (-24)= 3/4 or 0.75
h)(120 mr p ) ÷ (20 m p)= 120r ÷ 20= 6r
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
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
2.6y cm
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.
Jigsaw - p. 260#3abc, 5abcd, 7abcde, 11abc
Practice – p. 261-2629, 10, 13, 15, 17, 18