how to solve proportions

Propotion

A Ratio or Proportion is a name we have given to a statement that two ratios are equal. It can be written in two ways:

two equal fractions, a / b= c / d

or,

using a colon, a : b = c : d

When two ratios are equal, then the cross products of the two ratios are equal.

That is, for the ratio or proportion, a:b = c:d , a x d = b x c


solving proportions problems


Example 1:

Jane ran 100 meters in 15 seconds. How long did she take to run 1 meter?

Step 1: Think of the word problem as:

If 100 then 15. If 1 then how many?

Step 2: Write the proportional relationship:

100 .......> 15

so 1........> (1 x 15) / 100 = 0.15

Answer: She took 0.15 seconds


Example 2:


If 4/7 of a tank can be filled in 2 minutes, in how many minutes will it take to fill the whole tank?

solution:

Step 1: Think of the word problem as:

If 4/7 then 2. If 1 then how many? (Whole tank is =1)

Step 2: Write the proportional relationship:

4/7 => 2

1 => (1 x 2)/ (4/7) = (7/4)*2 = 3.5

Answer: It took 3.5 minutes


Example 3:


A car travels 125 miles in 3 hours. How far would it travel in 5 hours?

Solution:

Step 1: Think of the word problem as:

If 3 then 125. If 5 then how many?

Step 2: Write the proportional relationship:

3 =>125

5=> (5*125) / 3 = 208  1/3 miles

Answer: He traveled 208  1/3 miles. Having problem with Addition and Subtraction of Rational Numbers keep reading my upcoming posts, i will try to help you.


Inversely Proportional Problems


Inversely Proportional problems are similar to directly proportional problems, but the difference is that when x increase y will decrease and vice versa - which is the inverse proportion relationship. The most common example of inverse proportion problems will be “the more men on a job the less time taken for the job to complete”

Again, the method is to change the proportion problems into the form:

If x then y. If x is changed to a then what will be the value of y?

and then write the inverse relationship as (take note of the "inverse" form):

x => y

a = > (x/a)*y


Example 4:


It takes 4 men 6 hours to repair a road. How long will it take 7 men to do the job if they work at the same rate?

Solution:

Step 1: Think of the word problem as:

If 4 then 6. If 7 then how many?

Step 2: Write out the inverse relationship:

4 => 6

7 => (4/7)*6=3  3/7

Answer: They will take 3  3/7 hours.