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**Toast****Real Member**- Registered: 2006-10-08
- Posts: 1,321

List any shortcuts you've discovered:P:

Here's a simple one,

I just remembered back to when I had a discussion with a friend in 5th grade about the multiples of 11, and noticed that whenever a two digit number was multiplied by it, the answer was the sum of the two digits, whose result was placed in between them.

e.g

11*54=594 as 5+4 = 9

11*23=253 as 2+3 = 5

This mostly useless little novelty can work fast and efficiently as long as the digits don't add to 10 or more, in which case you're equally better off doing normal multiplication.

*Last edited by Toast (2006-11-04 00:06:40)*

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**luca-deltodesco****Member**- Registered: 2006-05-05
- Posts: 1,470

Toast wrote:

List any shortcuts you've discovered:P:

Here's a simple one,

I just remembered back to when I had a discussion with a friend in 5th grade about the multiples of 11, and noticed that whenever a two digit number was multiplied by it, the answer was the sum of the two digits, whose result was placed in between them.

e.g

im bored, so im giong to prove that.

the two digit number can be represented as

also, i wanted to add this this morning but i had to leave.

for integer multiplications of 9 up to 9x10 the sum of the two digits always adds up to 9, and the first digit is always the multiplication - 1

eg. 9*5 = 45, 4+5 = 9, 4=5-1

eg. 9*7 = 63, 6+3 = 9, 6=7-1

i find this one very helpful, although now its more a case of 'just knowing it' rather than applying this rule

*Last edited by luca-deltodesco (2006-11-04 06:37:26)*

The Beginning Of All Things To End.

The End Of All Things To Come.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,684

I have a few towards the bottom of this page: Multiplication - Times Tables

It might be interesting to compile a whole page of them.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**Toast****Real Member**- Registered: 2006-10-08
- Posts: 1,321

Hmmm, I've only looked briefly at everything else apart from the forum; i think i'll go look around now

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

Toast wrote:

List any shortcuts you've discovered:P:

Here's a simple one,

I just remembered back to when I had a discussion with a friend in 5th grade about the multiples of 11, and noticed that whenever a two digit number was multiplied by it, the answer was the sum of the two digits, whose result was placed in between them.

I'm not bored, but I'm going to disprove that.

77*11 = 847 ≠ 7147

Why did the vector cross the road?

It wanted to be normal.

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**Zach****Member**- Registered: 2005-03-23
- Posts: 2,075

Put the number in the middle and add anything more than a single digit to the beginning, I think was the rule.

55 * 11 = 605

66 * 11 = 726

77 * 11 = 847

88 * 11 = 968

99 * 11 = 1089

Boy let me tell you what:

I bet you didn't know it, but I'm a fiddle player too.

And if you'd care to take a dare, I'll make a bet with you.

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**Devantè****Real Member**- Registered: 2006-07-14
- Posts: 6,400

mathsyperson wrote:

Toast wrote:List any shortcuts you've discovered:P:

Here's a simple one,

I just remembered back to when I had a discussion with a friend in 5th grade about the multiples of 11, and noticed that whenever a two digit number was multiplied by it, the answer was the sum of the two digits, whose result was placed in between them.I'm not bored, but I'm going to disprove that.

77*11 = 847 ≠ 7147

You've used the rule in the wrong sense ; Using the rule Toast told us at the top of the forum;

77

7+7 = 14

Put a 0 in between the two 7s: 707

Multiply the sum of the two 7s by 10: 7+7 = 14, 14x10 = 140

707+140 = 847

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,684

Or just add neighboring digits as you go:

Units: 7

Tens: (7+7=14)7

Hundreds: (7+1)47

Answer: 847

But the topic "Shortcuts in math" is not just arithmetic, right?

I remember I had an assignment to find the maximum volume of a solid given various constraints which included surface area. I think I was supposed to create the formula, differentiate it and find a maxima. But instead I just said "the optimum solution is a sphere, and the closest this object can get to a sphere is (sizes)". Luckily I was right.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**pi man****Member**- Registered: 2006-07-06
- Posts: 251

It's not a shortcut but more of a verification. If a number is evenly divisible by 3, the sum of it's digits is divisble by 3.

123: 1 + 2 + 3 = 6, therefore divisible by 3 (41)

943: 9 + 4 + 3 = 16, therefore not divisble by 3 (314.333)

123456789: 1+2+3+4+5+6+7+8+9 = 45, therefore divisible by 3 (41152263)

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**Toast****Real Member**- Registered: 2006-10-08
- Posts: 1,321

Um, ok you can put all the shortcuts you've ever found in math (not just arithmetic), just so long as this doesn't become an infinitely broad topic

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 23,792

Toast,

I use the casting off of 9s, as a shortcut.

Here's an illustration.

23 x 4 = 92.

The ssum of 2 and 3 is 5. 5x4=20. Therefore, the result should also have a successive sum of digits equal to 2. You can see that 9+2=11, and 1+1=2

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Toast****Real Member**- Registered: 2006-10-08
- Posts: 1,321

When you're using the Pythagorean theorem and you have sides of equal length:

The base multiplied by the square root of the number of terms being sqrted gives the answer.

*Only works to the power of 2*

*Last edited by Toast (2006-11-08 19:22:53)*

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