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Proportions

PART A BCD E

Multi-Part

Lesson 1

SPI 0706.1.1

Use proportional reasoning to

solve mixture/concentration

problems. SPI 0706.2.7 Use

ratios and proportions to

solve problems. Also

addresses GLE 0706.2.3,

GLE 0706.2.4.

276 Proportions and Similarity

Main Idea

Use proportions to

solve problems.

Vocabulary

equivalent ratios

proportion

cross products

Solve Proportions

SHOPPING A local department

store advertised a sale as shown at the right.

1. Write a ratio in simplest form that
   compares the cost to the number of
   bottles of nail polish.


2. Suppose Kate and some friends
   wanted to buy 6 bottles of polish.
   Write a ratio comparing the cost
   to the number of bottles of polish.


3. Is the cost proportional to the number
   of bottles of polish purchased? Explain.

The ratios of the cost to the number of bottles of polish for two and six

bottles are both equal to _^5

2

. Equivalent ratios have the same value.

__$5

2 bottles of polish

= __$15

6 bottles of polish

Proportion

Words A proportion is an equation stating that two ratios or rates

are equivalent.

Symbols Numbers Algebra

_ 68 = _^34 _a

b

= _c

d

, b ≠ 0, d ≠ 0

Consider the following proportion.

_a

b

= _c

d

(^1)
/
(^1)
_a /
b
· bd = _c
d
· bd Multiply each side by bd and divide out common factors.
1 / 1
/
ad = bc Simplify.
The products ad and bc are called the cross products of this
proportion. The cross products of any proportion are equal.

·
· =

V
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