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Ratio and Proportion
8.1-8.2
Unit IIA Day 1
Do Now
 Simplify each fraction
 12/15
 14/56
 21/6
 90/450
Computing Ratios
 If a and b are two quantities that are measured in the
same units, then the ratio of a to b is a/b.
Can also be written as _____.
 Because a ratio is a quotient, its denominator cannot be
________.
 Ratios are usually expressed in simplified form. For instance,
the ratio of 6:8 is usually simplified to _____

Ex. 1: Simplifying Ratios

a.
Simplify the ratios (be careful of units!):
12 cm
b. 6 ft
c. 9 in.
4m
18 in.
18 in.
Ex. 2: Using Ratios
 The perimeter of rectangle ABCD is 60 centimeters.
The ratio of AB:BC is 3:2.
 Find the length and the width of the rectangle.
Ex. 3: Using Extended Ratios
 The measures of the angles in ∆JKL are in the
extended ratio 1:2:3.
 Find the measures of the angles.
Properties of proportions
 An equation that equates (sets equal) two ratios is
called a __________________


The numbers a and d are called the extremes of the
proportions.
The numbers b and c are called the means of the proportion.
Means
Extremes
=
Properties of proportions
 Cross product property: The product of the
“extremes” equals the product of the “means”.

If  = , then ________.
 Reciprocal property: If two ratios are equal, then
their reciprocals are also equal.

If  = , then ________.
Ex. 5: Solving Proportions
 Solve the proportion.
a)
b)
4 5
=
x 7
3
2
=
y +2 y
Geometric Mean
 The geometric mean of two positive numbers a
and b is the positive number x such that
a
x

=
x
b
If you solve this proportion for x, you find that x = _____
which is a ______ number.
Homework #46
 The ratio of the width to the length for each rectangle
is given. Solve for the variable.
Homework #57
 The ratios of the side lengths of ΔPQR to the
corresponding side lengths of ΔSTU are 1:3. Find the
unknown lengths.
Comparing Arithmetic and Geometric Means
 If x is the arithmetic mean of a and b, then x is the
same ___________ from a and b.

Find it by __________ a and b and then _____________.
 If x is the geometric mean of a and b, then x is the
same ___________ from a and b.

Find it by __________ a and b and then _____________.
Ex. 7: Using a Geometric Mean
 International standard paper sizes all have the same
width-to-length ratios.
 Two sizes of paper are shown. The distance labeled x
is the geometric mean of 210 mm and 420 mm. Find
the value of x.
Closure
 What distinguishes a ratio from a quotient?