Divisibility Rules - 7 04:21 minutes

Video Transcript

Transcript Divisibility Rules - 7

Mirror, mirror, on the wall, who's the cleverest of them all? The evil witch, Snow White, or her 7 friends Stay tuned to see how this story ends The witch has a notion she thinks is terrific to make a potion that's also a soporific. With Snow White in dreamland, the evil witch can unveil her plan. There's just one glitch, a hitch for the witch To avoid a one-way ticket to heaven, Snow White leans on the Divisibility Rules for the number 7.

In an attempt to trick Snow White, the witch offers her a basket filled with 15, delicious-looking apples. Snow White doesn’t know the apples are laced with a sleeping potion, but she rejects them regardless. Why? Because she can’t divide the 15 apples among the 7 dwarfs evenly, and she doesn't play favorites. The witch is not discouraged. So the very next day, she returns. This time, she has a cart full of apples. The witch doubts that Snow White can calculate such a large quotient quickly and will simply decide to accept the cart and its poisonous contents. The witch proudly declares that she has 543 apples, more than the dwarves and Snow White can ever eat. Again, Snow White refuses because she can’t divide the number of apples evenly into groups of 7. How did she determine this so quickly?

Divisibility by 7

Snow White is a master of the divisibility rule for the number 7, so she doesn’t have to always rely on long division. To check if a number is evenly divisible by 7: Take the last digit of the number, double it Then subtract the result from the rest of the number If the resulting number is evenly divisible by 7, so is the original number. Let’s try the trick on the number of apples in the cart, 543. The last digit is 3, double that to make 6, subtract from 6 from the remaining digits. 54 minus 6 is equal to 48. 48’s not evenly divisible by 7, so 543 isn't evenly divisible by 7 either.

Let's check, just to make sure. 7 goes into 54 seven times. Subtract 49 from 54, bring down the 3, 7 goes into 53 seven times, subtract 49 from 53, which leaves us with a remainder of 4. So we were right! 543 isn't evenly divisible by 7!

Foiled again. What's an evil witch to do? Has Snow White simply outsmarted her?

The evil witch doesn't give up. She gathers all the apples in the kingdom, 2478 to be exact, and delivers them to Snow White. Let’s see.Ok. The last digit is 8. Double it, and we get 16. Subtract 16 from 247. The difference is 231. That’s still a big number, so we just do the same steps again. Double the last digit, that's equal to 2 and 23 minus 2 is equal to 21. 21 is evenly divisible by 7, so the ginormous pile of apples must also be evenly divisible by 7! 7 goes into 24 three times, subtract 21 from 24, bring down the 7, 7 goes into 37 five times.

Subtracting from 37 gives us 2 and 7 goes into 28 exactly 4 times. Whaddya know? Snow White was correct! 2478 IS evenly divisible by 7!

While we were busy calculating, 77 pies are now ready and waiting. Prepared by Snow White with love and care, her pies are famous far, wide and everywhere. And because she's so super sweet, she offers the witch a pie that can't be beat.