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Write and Solve Proportions

Introduction

Two equivalent ratios form a proportion when they are put together into a single equation. 

W__S_Proportions_vis_1

 

W__S_Proportions_vis_2

When you are determining whether two fractions for a proportion, first see if one numerator and/or denominator is a multiple of the other.  The proportion to the right can be shown to be true by multiplying each of the numbers in the first fraction by 5 to change them into the second fraction.

 

W__S_Proportions_vis_3In the second proportion above, there is no number that can be used to change the first fraction into the second.  An observant student will notice that both fractions can be reduced.  A second way to show two fractions are equal is to reduce them to lowest terms.  Reducing each fraction changes them into four-fifths.  Since they are equal to each other in lowest terms, the fractions are equal.

 

Lesson

The easiest ways to determine whether two fractions make a proportion are to:

  • see if one fraction is a multiple of the other
  • reduce each fraction to lowest terms and then compare them

W__S_Proportions_vis_4

When you are faced with smaller fractions like the ones above, those two methods are your best options.  However, for larger fractions there is a “catch all” method that can save a lot of time.  One thing that all proportions have in common is that cross multiplication always yields the same answer.

 

W__S_Proportions_vis_5 

Example 1:  Use cross multiplication to see if the fractions form a proportion.

W__S_Proportions_vis_6

 

Solution:

W__S_Proportions_vis_7 

The cross product is a method that always works, but an observant math student will notice when a simpler method can be used.  In part c above, the numerator of 3 can easily be changed into a 9.  In instances like this, it is easier to use simple multiplication rather than cross multiplication to see if the fractions are equivalent.

 

Write and Solve Proportions

When a builder constructs a new building, it is a common practice to make a smaller scale model of the new building before beginning construction.  Since the scale model is an exact replica of the building, the size of the scale model is proportional to the size of the building.  When figuring its dimensions, proportions can come in very useful.

 

Example 2:  A builder is constructing a new building and has made model with a scale factor of 1 inch = 8 feet.  If the scale model is 33 inches tall, then what will be the height of the actual building?

Solution:

W__S_Proportions_vis_8 

Proportions can often be used in word problems such as example 2.  The same kind of thinking can be used to find an unknown value in a stand-alone proportion. 

 

Example 3:  Find the missing value in the proportion.

W__S_Proportions_vis_9

Solution:

W__S_Proportions_vis_10 

Try It

Determine whether each pair of fractions is a proportion

1)  W__S_Proportions_vis_11a

 2)  W__S_Proportions_vis_12a

 3)  W__S_Proportions_vis_13a 

Find the missing number in the proportion

4)  W__S_Proportions_vis_14a

 5)  W__S_Proportions_vis_15a

 6)  W__S_Proportions_vis_16a 

 

 

Scroll down for answers:

 

 

 

 

 

 

 

 

Answers:

1)  W__S_Proportions_vis_11b 

 

2)  W__S_Proportions_vis_12b 

 

3)  W__S_Proportions_vis_13b 

 

4)  W__S_Proportions_vis_14b 

 

5)  W__S_Proportions_vis_15b 

 

6)  W__S_Proportions_vis_16b 


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