Basic Mathematics for College Students

 

 

 

Caution! We cannot remove common factors “across” an = symbol. When

this is done, the true proportion from Example 3 part a, , is changed

into the false proportion.

3

1

7



9

21

7

1

7 

9

7

3

7 

9

21

5.2 Proportions 431

b.

One cross product is 40 and the other is 39.

Since the cross products are not equal, the proportion is false.

8

3



13

5

8  5  40 3  13  39

EXAMPLE (^4) Determine whether each proportion is true or false.
a. b.
StrategyWe will check to see whether the cross products are equal (the product
of the extremes is equal to the product of the means).
WHYIf the cross products are equal, the proportion is true. If the cross products
are not equal, the proportion is false.
Solution
a.
One cross product is 1.35 and the other is 1.44.
Since the cross products are not equal, the proportion is not true.
b.
Each cross product is.
Since the cross products are equal, the proportion is true.
49
3

49
2 1 3
3
3

1

2



4

2

3

7



49

3

^7 ^2

1

 7

2

1

 3

2 1

3

 7 ^7

3

^7

1

3

1

2 ^4

2

3 

7

2 

14

3

0.9

0.6



2.4

1.5

2.4

0.6

1.44

1.5

0.9

1.35

2

1

3

3

1

2



4

2

3

7

0.9

0.6



2.4

1.5

Self Check 4

Determine whether each

proportion is true or false.

a.

b.

Now TryProblems 31 and 35

3

3

16

2

1

2



4

1

4

3

1

3

9.9

13.2



1.125

1.5

When two pairs of numbers such as 2, 3 and 8, 12 form a true proportion, we say
that they are proportional.To show that 2, 3 and 8, 12 are proportional, we check to
see whether the equation

is a true proportion. To do so, we find the cross products.

Since the cross products are equal, the proportion is true, and the numbers are
proportional.

2 # 12  24 3 # 8  24

2

3



8

12