6th Grade Math Textbook, Fundamentals

 &KDSWHU

6-3

Key Concept

Write and Solve Proportions

Objective To write proportions • To use the cross-products rule to determine whether

ratios form a proportion • To find the missing term in a proportion

Elena uses 9 gallons of gas when she drives 225 miles on the
highway. Latif uses 7 gallons of gas when he drives 175 miles
on the highway. Is the average number of miles per gallon of
gas the same for Elena’s car as for Latif’s?

To find out if the two average rates are the same, write two

ratios, and determine if they are equivalent—that is, if they

form a proportion. A is an equationstating that

two ratios are equivalent.

Two ways to determine if a proportion is true are to use the

Cross-Products Rule to determine if the cross products are

equal or to compare simplified ratios.

proportion

Method 1 Use the Cross-Products Rule

• Write the information as a proportion.

?

Latif’s miles

Latif’s gallons

175

7

225

9

Elena’s miles ?

Elena’s gallons

• Use the Cross-Products Rule.

225 • 7 9 • 175

1575  1575 Tr u e

175

7

(^225) ?
9
?
In a proportion, the order of the labels in both ratios needs to be the same.
Cross-Products Rule
Product of Means Product of Extremes
Proportion
means
a: bc: d
extremes
Think
Elena’sElena’sgallonsmiles Latif’sLatif’sgallonsmiles or Elena’sLatif’smilesmilesElena’sLatif’sgallonsgallons
The middle terms, band c, are
called the means. The end terms,
aand d, are called the extremes.
extremes means
abdc (b, d, 0) adbcadand bcare
cross products.
Since the ratios 225 : 9 and 175 : 7 are equivalent, they form a proportion.
The average number of miles per gallon of gas for Elena’s car
is the same as for Latif’s.
Method 2 Compare Simplified Ratios

• Write each ratio as a fraction in simplest form.





25

1

175

7

25

1

225

9

25

1

Latif’s miles

Latif’s gallons

Elena’s miles

Elena’s gallons

25

1

• Compare ratios.

 Tr u e

25

1

25

1