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Section 8.1Ratio and Proportion

OBJECTIVE:• To write ratios and solve proportionsBIG IDEA: ProportionalityESSENTIAL UNDERSTANDINGS:• A ratio can be written to compare two

quantities• An equation can be written stating that two

ratios are equal• If the equation contains a variable, it can be

solved to find the value of the variableMATHEMATICAL PRACTICE:• Attend to precision

Ratio of a to b: a ____________________ of two quantities by division. You can write the ratio of two numbers a and b, where , in three ways:

You usually express a and b in the same unit and write the ratio in simplest form. Students need to be comfortable with ratios written as fractions, as well as decimals and percents.

Ratio

0b

A)

B)

C)

D)

EX 1: Simplify the ratios

8

2

in

ft

1

500

km

m

25

2

cm

m

18

2

ft

yd

A) length of a tennis racket: 2 feet 4 incheslength of a table tennis paddle: 10 inches

B) diameter of table tennis ball: 40 mmdiameter of tennis ball: 6.8 cm

EX 2: Write the ratio of the first measurement to the second measurement

3. Triangle XYZ has an area of . The ratio of the base of to the height of the triangle is 2:1. Find the base and height of the triangle.

Using Ratios

225inXYZ

4. The measures of the angles in a triangle are in an extended ratio 3:4:8. Find the measures of the angles.

Using Ratios

Proportion: an ____________________ that states that _______________ ratios are equal.

The first and last numbers in a proportion are the ____________________. The middle two numbers are the ____________________.

Proportion

Cross Product Property: the product of the ____________________ equals the product of the ____________________

1) Reciprocals

2) Switch the means

3) Add the denominator to the numerator

Properties of Proportions

is equivalent to a c b d

b d a c

is equivalent to a c a b

b d c d

is equivalent to a c a b c d

b d b d

EX 5: Solve the proportion

A)

B)

C)

D)

5

8 4

x

5 5

3 6

y

4 3

4x x

3

12

x

x

A photo of a building has the following measurements: width of and height of 2.75 in

a) The actual building is wide. How tall is the actual building?

b) The door height in the photo is 0.5 inches. What is the height of the door in the actual building?

EX 6: Solve for the dimensions of the building

71

8in

126

4ft

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8.1 p. 46118, 19, 20, 22, 26 – 46 evens, 47, 56, 58, 62, 65, 66,

21 questions