steps. This helps me to identify the numbers. If you need a brush-up on this language, here’s a cheat sheet just in case:
In the number 123, the 3 is called the ones digit number, the 2 is referred to as the tens digit number, and the 1 is the hundreds digit number.
Let’s take 72 divided by 91. Here are the sequential steps to take:
• Step 1: Take the numerator, which in this case is 72, and add it to the tens digit of that number, which is the number 7. So 72 plus 7 equals 79. Put a decimal point in front. So now we have 0.79. (In case you didn’t notice, this first step means that every time you divide a number between 10 and 90 by 91, your answer will be a number less than 1. All answers will have a decimal point in front of them.)
• Step 2: Next, take the ones digit of the numerator, subtract 1, and tack that onto what we have so far. Hence, 2 minus 1 equals 1. Tack that number 1 onto what we have so far: 0.791.
• Step 3: Ask yourself: How far is the first digit of the answer (7) from the number 9? Seven is 2 away from 9. Tack on the 2 to get 0.7912.
• Step 4: Ask yourself: How far is the second digit of the answer (9) from 9? Nine is 0 away from 9. Tack on the 0 to get 0.79120.
• Step 5: Ask yourself: How far is the third digit of the answer (1) from 9? One is 8 away from 9. Tack on the 8 to get 0.791208.
• Step 6: Since the calculator repeats or carries out to show more numbers, you have to say it like the calculator, so to add one more number, just repeat the first digit after the decimal point. Tack on the 7 (or repeat the entire pattern, “791208”). And there you have your answer: 0.7912087 (or the longer version: 0.7912087912087).
Try three more on your own:
28 ÷ 91 = ___________
35 ÷ 91 = ___________
19 ÷ 91 = ___________
HOW MUCH?
I recommend that you attempt problems like these on a monthly basis at a minimum. Every last Sunday of the month, for instance, remind yourself of the secret formula and then work your brain through these problems. See if you can recall the shortcut without having to study it first!
If you’re feeling ambitious, you can attempt these on a biweekly or weekly basis. For a more advanced version of this shortcut, try doing this exercise without writing down the numbers and without giving or saying the answer until you have the entire six-digit answer. Here’s a hint: Once you have the first three digits of the answer using steps 1 and 2, start talking out the answer to find the last three digits using the final four steps. Don’t try to pack the entire answer in your head before speaking it. Let your brain flow through arriving at the remaining three digits as you think it through sequentially.
Remember, every number divided by 91 will go on forever, but after six digits it repeats itself. So, 72 divided by 91 equals 0.791208791208791208 … and so on.
JOTTO
This second exercise works your logic skills. It’s a two-person game, and you’ll need a pen and paper. It can be played as many times as you like. As with physical exercise, your bodycan’t ever get enough, so long as you rest between sessions! The more you play, the more your brain benefits from a serious workout. Try playing at least once a month to start and then more frequently once you have the basic rules down and find yourself going through the motions of this game relatively quickly and easily.
How to Play
Each player thinks of a five-letter word and writes it down, keeping their word to themselves. These words must contain five different letters. Each player then writes out the alphabet,
A
to
Z
, at the top of their page. It’s up to each player to guess the other’s word. They do this by saying other five-letter words to their opponent. It’s the opponent’s job to say how many letters this word has in common with the chosen word but not to say what those letters are.
Jotto can get busy: You’ll find yourselves volleying back and forth,
In the number 123, the 3 is called the ones digit number, the 2 is referred to as the tens digit number, and the 1 is the hundreds digit number.
Let’s take 72 divided by 91. Here are the sequential steps to take:
• Step 1: Take the numerator, which in this case is 72, and add it to the tens digit of that number, which is the number 7. So 72 plus 7 equals 79. Put a decimal point in front. So now we have 0.79. (In case you didn’t notice, this first step means that every time you divide a number between 10 and 90 by 91, your answer will be a number less than 1. All answers will have a decimal point in front of them.)
• Step 2: Next, take the ones digit of the numerator, subtract 1, and tack that onto what we have so far. Hence, 2 minus 1 equals 1. Tack that number 1 onto what we have so far: 0.791.
• Step 3: Ask yourself: How far is the first digit of the answer (7) from the number 9? Seven is 2 away from 9. Tack on the 2 to get 0.7912.
• Step 4: Ask yourself: How far is the second digit of the answer (9) from 9? Nine is 0 away from 9. Tack on the 0 to get 0.79120.
• Step 5: Ask yourself: How far is the third digit of the answer (1) from 9? One is 8 away from 9. Tack on the 8 to get 0.791208.
• Step 6: Since the calculator repeats or carries out to show more numbers, you have to say it like the calculator, so to add one more number, just repeat the first digit after the decimal point. Tack on the 7 (or repeat the entire pattern, “791208”). And there you have your answer: 0.7912087 (or the longer version: 0.7912087912087).
Try three more on your own:
28 ÷ 91 = ___________
35 ÷ 91 = ___________
19 ÷ 91 = ___________
HOW MUCH?
I recommend that you attempt problems like these on a monthly basis at a minimum. Every last Sunday of the month, for instance, remind yourself of the secret formula and then work your brain through these problems. See if you can recall the shortcut without having to study it first!
If you’re feeling ambitious, you can attempt these on a biweekly or weekly basis. For a more advanced version of this shortcut, try doing this exercise without writing down the numbers and without giving or saying the answer until you have the entire six-digit answer. Here’s a hint: Once you have the first three digits of the answer using steps 1 and 2, start talking out the answer to find the last three digits using the final four steps. Don’t try to pack the entire answer in your head before speaking it. Let your brain flow through arriving at the remaining three digits as you think it through sequentially.
Remember, every number divided by 91 will go on forever, but after six digits it repeats itself. So, 72 divided by 91 equals 0.791208791208791208 … and so on.
JOTTO
This second exercise works your logic skills. It’s a two-person game, and you’ll need a pen and paper. It can be played as many times as you like. As with physical exercise, your bodycan’t ever get enough, so long as you rest between sessions! The more you play, the more your brain benefits from a serious workout. Try playing at least once a month to start and then more frequently once you have the basic rules down and find yourself going through the motions of this game relatively quickly and easily.
How to Play
Each player thinks of a five-letter word and writes it down, keeping their word to themselves. These words must contain five different letters. Each player then writes out the alphabet,
A
to
Z
, at the top of their page. It’s up to each player to guess the other’s word. They do this by saying other five-letter words to their opponent. It’s the opponent’s job to say how many letters this word has in common with the chosen word but not to say what those letters are.
Jotto can get busy: You’ll find yourselves volleying back and forth,
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