ALGEBRA READINESS

LESSON 6-5Warm Up Lesson 6-5 Warm-Up

ALGEBRA READINESS

LESSON 6-5Warm Up Lesson 6-5 Warm-Up

ALGEBRA READINESS

“Proportions” (6-5)What is a “proportion”?

What is the “extremes of the proportion”?

What is the “means of the proportion”?

What are “cross products”?

Why do “cross products” work?

proportion: equal ratios (in other words, equal fractions)

Example:

extremes of the proportion: the first cross product of a proportion. In the above proportion, the “extremes of the proportion” are a and d.

means of the proportion: the second cross product of a proportion. In the above proportion, the “extremes of the proportion” are b and c.

cross products: the product of the means equals the product of the extremes (in the above example, ad = bc).

Rule:

Example:

Work:

=ab

cd

for b ≠ 0 and d ≠ 0

60 = 60

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“Proportions” (6-5)How can you determine whether two ratios (fractions) are equal (form a proportion)?

To determine whether two ratios form a proportion (in other words, are equal), test the cross products. If the cross products are equal, then the ratios form a proportion. If the cross products aren’t equal, the two fractions aren’t equal.

Example: Do and form a proportion?:

The cross products are equal, so = .

45

1215

45

1215

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Do and form a proportion? Explain. 49

818

49

818

gallons Write as a proportion.

4 • 18 = 9 • 8 Find out if the cross products are equal.

Because the cross products are equal, = form a proportion.49

818

ProportionsLESSON 6-5

Additional Examples

72 = 72 The cross products are equal

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Use cross products to solve the proportion • - . w 4.5

65

w4.5

= - 65

w(5) = (4.5)(–6) Write cross products.

5w = –27 Simplify.

5w5

= –27 5 Divide each side by 5.

w = –5.4 Simplify.

Proportions

LESSON 6-5

Additional Examples

(-5.4)4.5 =

–6 5

Replace w with -5.4 and change both fractions into decimals by dividing bottoms into tops.

Check:

-1.2 = –1.2 True Statement (Both sides equal one another.)

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The fixed rate of conversion is 1 euro = 0.7876 Irish pounds.

How many euros would you receive for 125 Irish pounds?

You would receive 158.71 euros.

Let x = the number of euros.

=1

0.7876x

125 Write the proportion .

0.7876 • x = 1 • 125 Write the cross products.

=0.7876 • x0.7876

1250.7876

Isolate the variable. Use the Division Property of Equality.

x ≈ 158.71Simplify. Round to the nearesthundredth.

ProportionsLESSON 6-5

Additional Examples

known ratio unknown ratio

euro 1 x

Irish pounds 0.7876 125

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Solve each proportion.

2. =

3. =

4. Suppose the exchange rate for dollars to Indian rupees is 0.02. How many rupees should you receive for $100?

w12

34

20r

45

9

25

5,000 rupees

1. Is proportional to ? Explain.58

1024

No; the fractions are not equal.

ProportionsLESSON 6-5

Lesson Quiz