The Rule for 9: Subtract from 10

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The rule for multiplying by 6 is: Add the digit to half of its neighbor, plus 5 if the digit itself is odd.

This combines the concepts from the rule for 5 and the rule for 11.

Example: Multiply 254 by 6

Add a leading zero: 0254.

  1. Units Digit (from 4): Neighbor is 0. Half of 0 is 0. Digit 4 is even. 4+0=44 + 0 = 4. Result is 4.
  2. Tens Digit (from 5): Neighbor is 4. Half of 4 is 2. Digit 5 is odd, so add 5. 5+2+5=125 + 2 + 5 = 12. Write 2, carry 1.
  3. Hundreds Digit (from 2): Neighbor is 5. Half of 5 is 2. Digit 2 is even. 2+2+1(carry)=52 + 2 + 1 (\text{carry}) = 5. Result is 5.
  4. Thousands Digit (from 0): Neighbor is 2. Half of 2 is 1. Digit 0 is even. 0+1=10 + 1 = 1. Result is 1.

The final answer is 1,524.

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Frequently Asked Questions

What is the 'neighbor' in this rule?

The 'neighbor' is always the digit immediately to the right of the digit you are currently working on. For the rightmost digit of the number, its neighbor is considered to be 0.

Why do you add 5 only for odd digits?

This is a clever trick to handle decimals without actually using them. It mathematically compensates for the .5 that is dropped when taking 'half of the neighbor' if the neighbor is odd, along with other factors, to keep the calculation correct.

Is it really necessary to add the digit to itself?

Yes, this is the most common point of confusion. You always start with the digit you are working on, and then you add the other parts (half the neighbor, 5 for odd digits, and the carry) to it.

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Frequently Asked Questions

What is the 'neighbor' in this rule?

The 'neighbor' is always the digit immediately to the right of the digit you are currently working on. For the rightmost digit of the number, its neighbor is considered to be 0.

Why do you add 5 only for odd digits?

This is a clever trick to handle decimals without actually using them. It mathematically compensates for the .5 that is dropped when taking 'half of the neighbor' if the neighbor is odd, along with other factors, to keep the calculation correct.

Is it really necessary to add the digit to itself?

Yes, this is the most common point of confusion. You always start with the digit you are working on, and then you add the other parts (half the neighbor, 5 for odd digits, and the carry) to it.