Basic Mathematics for College Students

Chapter 5 Summary and Review 483

When two pairs of numbers form a proportion,
we say that they are proportional.

Determine whether 0.7, 0.3 and 2.1, 0.9 are proportional.

Write two ratios and form a proportion. Then find the cross products.

0.7 0.90.63 0.3 2.10.63

Since the cross products are equal, the numbers are proportional.

0.7

0.3



2.1

0.9

Solving a proportionto find an unknown term:

1. Set the cross products equal to each other
   to form an equation.


2. Isolate the variable on one side of the
   equation by dividing both sides by the
   number that is multiplied by that variable.


3. Check by substituting the result into the
   original proportion and finding the cross
   products.

Solve the proportion:

This is the proportion to solve.

Thus,xis 15. Check this result in the original proportion by finding the

cross products.

To simplify the left side, remove the

common factor of 5. To simplify the

right side, do the division: 75 5 15.

x 15

To undo the multiplication by 5 and

isolate x, divide both sides by 5.

5 x

5



75

5

To simplify the right side of the

5 x (^75) equation, multiply: 37.5 2 75.
Set the cross products equal to each
5 x37.5 (^2) other to form an equation.

5

37.5



2

x

5

37.5



2

x

Proportions can be used to solve application
problems.It is easy to spot problems that can
be solved using a proportion. You will be given
a ratio (or rate) and asked to find the missing
part of another ratio (or rate).

It is helpful to follow the five-step problem-
solving strategyseen earlier in the text to solve
proportion problems.

PEANUT BUTTER It takes 360 peanuts to make 8 ounces of peanut

butter. How many peanuts does it take to make 12 ounces? (Source:

National Peanut Board)

Analyze

• We can express the fact that it takes 360 peanuts to make
  8 ounces of peanut butter as a rate:.


• How many peanuts does it take to make 12 ounces?
  FormWe will let the variable prepresent the unknown number of
  peanuts.
  360 peanuts is to8 ounces asppeanuts is to12 ounces.

SolveTo find the number of peanuts needed, solve the proportion

for p.

StateIt takes 540 peanuts to make 12 ounces of peanut butter.

Check16 ounces of peanut butter would require twice as many

peanuts as 8 ounces:. It seems

reasonable that 12 ounces would require 540 peanuts.

2 360 peanuts 720 peanuts

To simplify the left side, do the division:

4,320 8 540. To simplify the right side,

remove the common factor of 8.

540 p

To undo the multiplication by 8 and

isolate p, divide both sides by 8.

4,320

8



8 p

8

To simplify the left side of the equation,

4,320  8 p multiply: 360 12 4,320.

Set the cross products equal to each

360  12  8 p other to form an equation.

Number of peanuts

 Ounces of peanuts

360 

8



p

 12

Number of peanuts 

Ounces of peanuts

360 peanuts

8 ounces^