Download Geometry 7-1 Ratios and Proportions

Geometry 7-1 Ratios and Proportions
A ratio
is a comparison between two quantities using
division. We can write "the ratio of a to b" in multiple ways:
a to b
a:b
a
b
Regardless of which form we use, we always need to
reduce our ratios to lowest terms.
The ratio of the measures of the angles in a triangle is 3:4:5.
Find the measures of the angles.
3x + 4x + 5x = 180
3(15) = 45
12x = 180
4(15) = 60
x = 15
5(15) = 75
The ratio of the measures of the sides of a triangle is 2:2:3
and the perimeter is 392 inches. Find the lengths of the
sides. 2x + 2x + 3x = 392
2(56) = 112
7x = 392
x = 56
Solve each proportion.
x 11
-4
6
=
=
4 -6
7 2y + 5
-6x = 44
-4(2y + 5) = 42
x = -7 1/3
3(56) = 168
9
7
=
z-1 z+4
7(z + 4) = 9(z - 1)
-8y - 20 = 42
7z + 28 = 9z - 9
-8y = 62
-2z = -37
y = -7 3/4
z = 18 1/2
In a particular high school, there are 190 teachers and
2650 students. What is the approximate student-teacher
ratio at this school?
2650
= 13.94 ~
~ 14 students per teacher
190
When we need to compare more than two quantities, we
use an extended ratio
. We typically write extended
ratios in the form a:b:c.
An equation that says two ratios are equal is called a
proportion.
a c
=
a:b = c:d
b d
In these proportions, a and d are called the extremes,
and b and c are called the means.
In a true proportion, the product of the extremes is equal
to the product of the means. That is,
the cross products are equal.
If we are given a proportion, we can write several equivalent
proportions.
a c
Given:
=
b d
Then the following proportions are all equivalent:
b d
a= c
d c
=
b a
a b
=
c d