an in depth look at ratios and proportions and their applications
TRANSCRIPT
An in Depth Look at Ratios and Proportions and Their
Applications
Ratios
Equal Ratios
Proportions
Special Ratios
Constant Ratios
are the comparison of two or more numbers.
Which ratio shows the ratio of 2 fish to 3 bear?
A
B
C
D
E
Which ratio shows the ratio of 1 soccer ball to 3 basketball?
A
BC
D
E
Which ratio shows the ratio of 3 butterflies to 1 apple?
A
B
C
D
E
Three Ways to Write a Ratio
The ratio of 3 boys to 5 girls can be written as:
a) 3 to 5
b) 3: 53
5c)
Equal ratios are like equivalent fractions. They name the same
quantity.
Examples of Equal Ratios:
3
5
6
1 0
3
4
7 5
1 0 0
Two equal ratios form a proportion.
In a proportion the product of the means is equal to product of the
extremes.
3 : 5 = 6 : 10
Extremes
Means
3
5
6
1 0
Means Extremes
6 x 5 = 3 x 10 30 = 30
Determine if the following are proportions.
5
3
6 0
3 6
1) 8
1 5
4
82)
5
3
6 0
3 6
3 x 60 = 5 x 36180 = 180
Yes, it is a proportion.
8
1 5
4
8
4 x 15 = 8 x 8
60 64No, it is not a proportion.
Corresponding sides of Similar Triangles have the same ratio.
Corresponding Angles of Similar Triangles have congruent angles
A is similar to D
TriangleA
Triangle
D
A
B
C
D
E
F
AB
DE
BC
EF
AC
EF <A <D <C <F
<B <E
C
A
B
D
F E
4
3
x
6
y
Use a proportion to find x and y.
5
2 4
3
3
3
x
AC
DF
CB
FE
4 3
6x
4 6 3 x2 4 3 x
8 x
CB
FE
AB
DE
3
6
5y
3 5 6 y3 3 0y 3
3
3 0
3
y
y 1 0
Another type of special ratio is a constant ratio or rate.
Distance = rate x time
is an example of a constant ratio.
Time 1 2 3 4
Distance 60120
180
240
d = r x t
0
50
100
150
200
250
300
1 2 3 4
time
dist
ance