7.1 Ratio and Proportion

1
7.1 Ratio and Proportion

• Geometry
• Ms. Kelly

2
Objectives

• 7.1 Ratio and Proportion

• 7.2 Properties of Proportions

• Express a _____ in simplest form.

• Solve for an unknown term in a given proportion.

3
Real Life Applications

• Lets list on the board where you find ratios and
  proportions in real life. (1st block)

4
Real Life Applications

• Lets list on the board where you find ratios and
  proportions in real life. (3rd block)

5
Definitions

• Ratio

• What is looks like..

• The ratio of one number to another is the _______
  when the first number is ______ by the second.
• Its usually expressed in simplest form.

• The ratio of 8 to 12 is ______, or ______.
• If y ? 0, then the ration of x to y is _______.

6
Ex. 1 Simplifying Ratios

• Simplify the ratios
• 12 cm b. 6n2 c. 9p
• 4 cm 18n 18p

7
Example 2

• Find the ratio of OI to ZD

• Using the same trapezoid

• Find the ratio of the measure of the smallest
  angle of the trapezoid to that of the largest
  angle.

8
Ratios in Form ab

• Sometimes the ratio of a to b is written in the
  form ab. This form can also be used to compare
  three of more numbers, like abc.
• Example The measures of the three angles of a
  triangle are in the ratio 225. Find the
  measure of each angle.

9
Ex. 3 Using Extended Ratios

• The measures of the angles in ?JKL are in the
  extended ratio 123. Find the measures of the
  angles.
• Begin by sketching a triangle. Then use the
  extended ratio of 123 to label the measures of
  the angles as x, 2x, and 3x.

2x
3x
x
10
Solution

• Statement
• x 2x 3x 180
• 6x 180
• x 30

• Reason
• Triangle Sum Theorem
• Combine like terms
• Divide each side by 6

So, the angle measures are 30, 2(30) 60, and
3(30) 90.
11
More examples of ab

• Find the ratio and express in simplest form.

12
Proportion

• What it is

• What is looks like.

• A proportion is an equation stating that ____
  ratios are equal.
• When three of more ratios are equal, you can
  write an extended proportion.

13
Closure to 7.1

• Ticket to stay in class

• Answers

• Three numbers arent known but the ratio of the
  numbers is 125. Is it possible that the
  numbers are
• 10, 20 and 50?
• 3, 6, and 20?
• x, 2x, 5x

14
Classwork

• Page 243 1-4, 8-11 on mini-white boards or
  whiteboards

15
7.2

• Properties of Proportions

16
Using Proportions

• An equation that equates two ratios is called a
  proportion. For instance, if the ratio of a/b is
  equal to the ratio c/d then the following
  proportion can be written

Means
Extremes
? ?
The numbers a and d are the extremes of the
proportions. The numbers b and c are the means
of the proportion.
17
Properties of proportions

• CROSS PRODUCT PROPERTY. The product of the
  extremes equals the product of the means.
• If
• ? ?, then ad bc

18
Properties of proportions

• RECIPROCAL PROPERTY. If two ratios are equal,
  then their reciprocals are also equal.
• If ? ?, then ?

b
a
To solve the proportion, you find the value of
the variable.
19
Ex. 4 Solving Proportions
4
5
Write the original proportion. Reciprocal
prop. Multiply each side by 4 Simplify.

x
7
4
x
7
4

4
5
28
x

5
20
Ex. 5 Solving Proportions
3
2
Write the original proportion. Cross Product
prop. Distributive Property Subtract 2y from each
side.

y 2
y
3y 2(y2)
3y 2y4
y
4

21
Example 6 - Factoring
22
Example 7

• In the figure,
• If CE 2, EB 6 and AD 3, then DB ___
• If AB 10, DB 8, and CB 7.5, then EB ___

23
Homework

• Page 243-244 1-14, 21-30
• Page 247 248 9-29 odds, 33-38