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Proportion

by

Bernadette Dvorscak


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This lesson is for students in grades 5 through 7

 The objectives are:

A ratioSneaker Tigers PP Walking 041A HB Detroit Shoes Fan Baseball gZqxwzOzT a comparison of two quantities. The ratio of dogs to cats is 3 to 2.  The ratio of gerbils to guinea pigs is 9 to 6.  A proportion is a comparison of two quantities.  The ratio of 3 to 2 is the same as the ratio of 9 to 6.  


          

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 For every three animals of one species there are two of the other species. These two ratios are equal to each other:  This is a proportion.

3/2 = 9/6

Hey! That look's like a pair of equivalent fractions.  Right, fractions are rational numbers.  When two fractions represent the same amount, they are equivalent fractions.  Two ratios that are equivalent to each other are a proportion.

How do you know if two ratios are a proportion?

5 x 12 = 60         8 x 12 = 96     therefore 5/8 = 60/96

60 / 12 = 5          96 / 12 = 8     therefore 5/8 = 60/96

7:3 = 28:12

Multiply 7 by 12.   7 x 12 = 84

Multiply 3 x 28.     3 x 28 = 84

Both products are 84, therefore 7:3 = 28:12

What if one term in a proportion is missing?  How can you find the missing term?

4/9 = 96/?

4 x 24 = 96  therefore 9 x 24 = 216.  

4/9 = 96/216

27/5 = 8/?

27 x = 5 . 8

27 x = 40

x = 40/27

x = 1.48

There are many real-life applications for proportions. Some of these are:

In Activity 1, you will find the reduced scale for buildings, bridges, and tunnels.  For a printable worksheet, click here.

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Activity 1

Benassi Nike Flip Swarovski with Slides Crystals JDI Flops customized In this activity, you will convert the actual height of skyscrapers or the actual length of bridges and tunnels into a reduced scale of inches. The scale you will use is 50 feet  = 1inch; this is the ratio of 50/1.  Round all answers to the nearest hundredth.  To find the actual height or length, click on the name of the structure. Remember to keep the order of the terms the same in both proportions.  

Name of structure

Actual height or length

Scale 

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Bonus:  Using the data for either skyscrapers, bridges, or tunnels, create a graph comparing all the structures in the category.  

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In Activity 2, you will either increase or decrease the amounts of a selected set of ingredients for a recipe.  For a printable worksheet, click here.

 Activity 2

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Number of Servings

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3

7

15

29

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Other Resources

Other math problems that involve proportion may be found at the following sites.  

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  Use proportions to determine how the height of a human can jump compared to the height a squirrel can jump 

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  Compare cat steps to dog steps

  Use proportion to compare the volume of two objects.

  Use proportion to find data about continental drift

The following unit deals with scale, ratio, and proportion through model building.

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© Bernadette Dvorscak