Download numerator The first number. denominator The second number

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A ratio is the quotient of two numbers.
In other words, a ratio is the result of dividing one number or by another.
5
3
5:3
5 to 3
5÷3
numerator
The first number.
denominator
The second number.
Unless you are told otherwise, a ratio is given in lowest terms
(reduced form).
A proportion is an equation stating that two or more ratios are equal.
5 10
=
3 6
5 : 3 = 15 : 9
The first term.
The second term.
The third term.
The fourth term.
5 to 3 = 20 to 12
5 ÷ 3 = 25 ÷ 15
The extremes are far away from each
other in the proportion.
The means are close to each other in the
proportion.
extreme
mean
=
mean
extreme
1
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In a proportion, the product of the means is equal to the product of
the extremes.
If
a c
= , then ad = bc.
b d
In other words, when you do the Means-Extremes Products
Theorem, you are cross multiplying.
If the product of a pair of nonzero numbers is equal to the product
of another pair of nonzero numbers, then either pair of numbers
can be made the means, and the other pair made the extremes.
2(10) = 4(5)
means extremes
4 = 2
10 5
5 = 10
2
4
2(10) = 4(5)
extremes means
2 = 5 10 = 4
4 10 5
2
This is the Means-Extremes Ratio Theorem.
If the means position in both ratios are the same, then you are finding the
geometric mean.
The idea of geometric mean comes from what happens when looking at
geometric figures. If a rectangle is formed with side lengths a, and b, the
geometric mean of a and b gives the side length of a square with the same
area. In a similar way the geometric mean of three numbers gives the side
length of a cube with the same volume as a rectangular parallelepiped
(box) with sides of lengths a, b, and c.
Find the geometric and arithmetic means between 4 and 9.
Arithmetic Mean
Geometric Mean
4 + 9 13
=
= 6.5
2
2
4 x
=
x 9
x2 = 36
x=!6
Find the geometric and arithmetic means between 4, 6, and 9.
4 x 9
= =
! x3 = 216 ! x = 6
x 6 x
2
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Similar figures have the same shape, but their sizes may differ.
If polygons are similar then:
a) The ratios of the measures of corresponding sides are equal.
b) Corresponding angles are congruent.
c) The ratio of the perimeters equals the ratio of any pair of
corresponding sides.
D
A
B
C
E
F
AB BC AC
=
and
If !ABC ~ !DEF then =
DE EF DF
m!A = m!D, m!B = m!E, m!C = m!F
3