Bellwork – 1/6/15. Unit 6: Section 6.1 Ratios, Proportions, and the Geometric Mean (Starts on Page...
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Transcript of Bellwork – 1/6/15. Unit 6: Section 6.1 Ratios, Proportions, and the Geometric Mean (Starts on Page...
Bellwork – 1/6/15
Unit 6: Section 6.1Ratios, Proportions, and the
Geometric Mean(Starts on Page 356)
Learning Target: Learn to solve problems by writing and solving proportions
Ratios
If a and b are two numbers or quantities, and b ≠ 0, then the ratio of a to b is ________
A ratio can also be written as ______________ We want to express ratios in their simplest form
(lowest terms).
a:b
14 72 1
Simplify ratios
Example 1:Simplify the ratio.
a. 76 cm : 8 cm b.
c. 3 yd : 36 ft d.
24
4
6
150
Use a ratio to find a Dimension
Example 2:
The perimeter of a rectangular table is 28 feet and the ratio of its length to its width is 5:2. Find the length and width of the table.
5:2Length = 5xWidth = 2x
2 L + 2 W = p
2 (5x) + 2 (2x) = 2810x + 4x = 28
14x = 28x = 2
Length 5x = 5(2) = 10 ft
Width 2x = 2(2) = 4 ft
Use extended ratios
Example 3:
The measures of the angles in ∆ BCD are in the extended ratio of 2:3:4. Find the measures of the angles.
2:3:42x:3x:4x
Sum of angles = 180
2x + 3x + 4x = 180
9x = 180
X = 20
Angle measurements = 40 , 60, 80 degrees
Proportion
• A equation that states that two ratios are equal
extreme
mean
d
c
b
a
mean
extreme
Cross product property
• In a proportion, the product of the extremes equals the product of the means
• If where and , then
0b 0dd
c
b
a
Proportions
Example 4:Solve the proportion.
a. b. c.
1610
5 x
8
5
7
2x
yy 3
2
1
1
5 (16) = 10 x
80 = 10 x
X = 8
2 ( 8) = 5 (7x)
16 = 35x
X = 16/35
3y = 2(y+1)
3y = 2y +2
Y = 2
Example 5:
As part of an environmental study, you need to estimate the number of trees in a 150 acre area. You count 270 trees in a 2 acre area and you notice that the trees seem to be evenly distributed. Estimate the total number of trees.
Set up a proportion:
40500 = 2xX = 20250 trees
• The geometric mean of two positive numbers a and b is the positive number x that satisfies .
So, and b
x
x
a
abx 2 abx
Geometric Mean
• Find the Geometric Mean of 12 and 27
abx
Geometric Mean
Homework – Geometry
Page 360: Exercises: 4, 5, 11, 13, 18 – 30 Even