Divisibility by 7 and Its Proof

This is the 6th post in the Divisibility Rules Series.  In this post, we discuss divisibility by 7.

Simple steps are needed to check if a number is divisible by 7. First, multiply the rightmost (unit) digit by 2, and then subtract the product from the remaining digits. If the difference is divisible by 7, then the number is divisible by 7.

Example 1: Is 623 divisible by 7?

3 x 2 = 6
626 = 56
56 is divisible by 7, so 623 is divisible by 7.

If after the process above, the number is still large, and it is difficult if to know if it is divisible by 7, the steps can be repeated. We take the difference as the new number, we multiply the rightmost digit by 2, and then subtract from the remaining digits.

Example 2:  Is 3423 divisible by 7?

3 x 2 =
3426 = 336

We repeat the process for 336. We multiply 6 by 2 and then subtract it from 33

6 x 2 = 12
3312 = 21
21 is divisible by 7, so 3423 is divisible by 7.

Note that if the number is still large, this process can be repeated over and over again, until it is possible to determine if the remaining digits is divisible by 7. Continue reading

New Archive Page, Language Translation, and more

Hi everyone. Here are some few updates and announcements:

  • Due to the growing number of posts, I have created an archive page where the complete list of posts are arranged by month. If you want to view the posts by category, you can go to the Mathematics, Multimedia, and GeoGebra pages. You can also visit the Freebies page. 
  • You can now translate Math and Multimedia to 50 languages with just two clicks, courtesy of Google Translate. Just click the drop down list box at the TRANSLATE BLOG section on the right part of your screen. 
  • To all math and math teaching enthusiasts, the Math Teachers at Play 47 is now live at Math Hombre. You may also want to visit this month’s edition of the Math and Multimedia Carnival.
  • The next edition of the Math and Multimedia Carnival will be hosted by Math Concepts Explained. To submit your blog posts, click here or email mathconcepts@gmail.com.
  • You may want to check out my new blog, the Mathematical Palette – a blog about mathematical beauty and appreciation.

That’s all for today. If you want to subscribe to Math and Multimedia, please use the following links: Facebook, Twitter, RSS

For comments and suggestions, please use the comment box or email me at mathandmultimedia@gmail.com.

GeoGebra Tutorial 33 – Lunes and Layers

This is the 33rd tutorial of the GeoGebra Intermediate Tutorial Series. If this is your first time to use GeoGebra, I strongly suggest that you read the GeoGebra Essentials Series.

In this tutorial, we are going to draw the figure below, the Lunes of Hippocrates. Although it looks like a simple drawing,  it requires the knowledge of layers  in GeoGebra especially when colors are applied.

 

In doing this tutorial, we learn how to use the semi-circle tool and how to set up layers. Continue reading

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