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