Fun with Math (inspired by yesterday's post) - Part 3: How to tell if a number is divisible by 7 (and bonus, by 11).

After posting yesterday about the importance of being able to master basic mathematical skills, and the best way of going about it (spoiler alert - it takes practice, practice, practice, similar to Simone Biles with her gymnastics routines), a number of reasonable people commented that children need to improve their numerical skills. As a result, I thought I would add a 3rd part in the series of math tricks after the guess the calendar date and squaring numbers. Here are those links:

What day of the week were you born?

https://thrivingwithinterest.blogspot.com/2021/05/fun-with-math-doomsday-rule-coolest.html

How to square 2 digit numbers in your head quickly and easily:

https://thrivingwithinterest.blogspot.com/2021/05/fun-with-math-part-deux-squaring-2.html

Onto today's math trick... I feel comfortable saying that most of us would know if a number is divisible by:

• 2: if it's even
• 3: if the sum of the digits in the number is divisible by 3
• 4: if the last 2 digits of the number is divisible by 4
• 5: if the last digit is a 0 or a 5
• 6: if the number is even and divisible by 3
• 8: if the last 3 digits are divisible by 8
• 9: if the sum of the digits in the number is divisible by 9
• 10: if the last digit is 0

Now onto 7, because most students I poll would not know how to figure this out. Here it how you can do it in 3 easy steps:

1. Double the last digit of the number in question
2. Subtract the answer obtained in part 1 from the remaining digits of the original number
3. If the answer from part 2 is divisible by 7 then the original is divisible by 3. If this is not evident, you can repeat steps 1-3 with the new number and see if that is divisible by 7

Example: is 693 divisibly 7?  

1. Take 3 and double it: 6
2. Subtract 6 from 69: 63
3. Is 63 divisible by 7? It sure is. So 693 is as well! (answer 693/7 = 99)

Another example: Is 16,940/7 divisible by 7?

1. Take 0 and double it: 0
2. Subtract 0 from 1694: 1694
3. Still too big? Start again. Take 4 and double 4: 8.
4. Subtract 8 from 169: 161. Yes it is, answer 23. So 16,940 is divisible by 7 (answer 16,940/7 = 2,420)

BONUS: How to tell if a number is divisible by 11 in 2 easy steps:

1. Take the alternating sum of the original number (read from left to right)
2. If that sum is divisible by 11 then the original number is divisible by 11 too!

Example: Is 399,619 divisible by 11?

1. Alternating sum: 3 - 9 + 9 - 6 + 1 - 9 = -11
2. Since -11 is divisible by 11, so is 399,619

Enjoy your next party impressing your friends :)

P.S. If you know any other fun math tricks, please let me know!