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Proportion problems are word problems where the items in the question are proportional to each other. In these lessons, we will learn the two main types of proportional problems: Directly Proportional Problems and Inversely Proportional Problems.

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Ratio or Proportion Worksheets

The question usually will not tell you that the items are directly proportional. Instead, it will give you the value of two items which are related and then asks you to figure out what will be the value of one of the item if the value of the other item changes.

Proportion problems are usually of the form:

If

xtheny. Ifxis changed toathen what will be the value ofy?

For example,

If two pencils cost $1.50, how many pencils can you buy with $9.00?

The main difficulty with this type of question is to figure out which values to divide and which values to multiply.

The following method is helpful:

Change the word problem into the form:

If

xtheny. Ifxis changed toathen what will be the value ofy?

which can then be represented as:

For example,

You can think of the sentence:

If two pencils cost $1.50, how many pencils can you buy with $9.00?

as

If

$1.50thentwopencils. If$9.00then how many pencils?

Write the proportional relationship:

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:

Answer: She took 0.15 seconds

Example 2:

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

Step 1: Think of the word problem as:

If then 2. If 1 then how many? (Whole tank is )

Step 2: Write the proportional relationship:

Answer: It took 3.5 minutes

Example 3:

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

Step 1: Think of the word problem as:

If 3 then 125. If 5 then how many?

Step 2: Write the proportional relationship:

Answer: He traveled miles.

Inversely Proportional questions 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 would be “the *more** men* on a job the *less** time* taken for the job to complete”

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

If

xtheny. Ifxis changed toathen what will be the value ofy?

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

Example:

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?

Step 1: Think of the word problem as:

If 4 then 6. If 7 then how many?

Step 2: Write out the inverse relationship:

Answer: They will take hours.

Basic Proportion Problems

Use proportions to find the missing value

1) 8 inches in 25 minutes ; 28 inches in

2) 3 gallons in 7 hours ;

Solve word problems using a proportion.

Arthur is typing a paper that is 390 words long. He can type 30 words in a minute. How long will it take for him to type the paper?

How to solve a word problem that involves inverse proportion

It takes 175 minutes to drive home at 80 km/hr. How long will it take to drive home at 100 km/hr?