Writing some proportions

Got a question in today,
How can I solve the question, "write as many true proportions as you can with the numbers 3,6,9,12 and 18. Use a number only once".

This is a simple simple problem IF you know what the term "PROPORTION" means.

Proportion is simply an equation stating that one ratio is equal to another.

So to solve this, we play around and make ratios, and see if we can by happenstance come up with some equal ratios fitting the rule of using each number only once.

For example, 3:6 and 9:18 are two such ratios. So the PROPORTION then is (it needs an '=' sign)

3:6 = 9:18.

You can write the ratios using the fraction line, too.

Can you make others?

See also An idea of how to teach proportions.

Comments

Green Darner said…
When I read the question I wondered how we were to find the solution since there was an odd number of numerals. Then I realized that we weren't required to use ALL the numerals, just not to use them more than once in the solution.

So here are my solutions (for some reason I always think of proportions in fraction form - must be from working with sewing projects and all those 5/8's, 1/2's, and 1/4's lol):


9/18 = 6/12

3/9 = 6/18

6/9 = 12/18
6:05 PM, September 20, 2006
Post a Comment

Popular posts from this blog

Conversion chart for measuring units

Image
I was just sent a link to this site; all it is, is a handy one-page printable conversion chart for various US measures, metric measures, and US vs. metric measures. Includes even a comparative Fahrenheit vs. Celsius thermometer. http://metricconversioncharts.org/
Read more

Meaning of factors in multiplication: four groups of 2, or 4 taken two times?

Someone asked me about the interpretation or meaning of the two numbers in multiplication, such as 4 × 2. Do you view it as four groups of 2 , or as four, taken two times ? Here's their question: "...I noticed that your explanation about how to interpret a math phrase, such as 4 × 2, is different from how I have understood it and taught it to my older daughter who was using RightStart Math at this level. Let me explain:  I see that you are using the first factor to denote number of groups and the second factor tells how many are in each group (4 × 2 would be interpreted 4 groups of 2).  On the other hand, I have taught and thought of it reversed, with the first factor telling how many are in each group and the second factor telling you how many groups (4 × 2 would be 4 taken 2 times).  I know that the difference in explanations does not ultimately change the product, but I am wondering what you thoughts are.  When I conceptually picture what I'm doing I see i...
Read more

Geometric art project: seven-circle flower design

Image
I got inspired by the blogpost Art School | Geometric Design with Islamic Art where Deborah shows how to make a neat flower design with seven circles , using a compass, and then coloring it using 2, 3, or 4 colors (or however many of your own). I think it ties in neatly with mathematics, and lets students practice drawing circles with a compass.  My girls loved the art/math project. Here are pictures they made: Here are step-by-step instructions for the flower design: 1.  Draw a line and a circle so that the circle's center point is on the line. Then mark the points where this circle intersects the line. 2. Use those points as center points, and draw two more circles. The radius is the same all the time, so make sure you don't change it on your compass!We used 5 cm as the radius, and that made the whole design fit neatly on a regular letter size paper. 3. Now note the two points marked in the picture. They will be used as center points in the next...
Read more