Tuesday

October 21, 2014

October 21, 2014

Posted by **Mike** on Monday, April 4, 2011 at 8:11am.

- algebra -
**MathMate**, Monday, April 4, 2011 at 8:35amYou can find the sum of the first 102 counting numbers using Gauss's method, namely:

"the sum of the first n counting numbers is n*(n+1)/2" whether n is odd or even.

For n = 102, the sum is 102*103/2=10506.

So divide 10506 by 5220 to get a quotient of 2, with a remainder of 66.

Mental calculation tip:

To multiply two numbers close to a hundred can be done in the head as follows, no paper, no calculators:

Let the numbers be (100+x) and (100+y), where x and y are small numbers. Take the example of 102 and 103, then x=2, y=3.

Start with the left most digit, which is a 1.

The next two digits are the sum of x and y, that gives 105.

The next two digits are the product of x and y, that gives 10506, et voilą!

Try with 107*109, that should give 11663.

- algebra - oops -
**MathMate**, Monday, April 4, 2011 at 8:39amForgot to divide 10506 by 2 according to Gauss's rule:

10506/2=5253, divided by 5220 gives a quotient of 1 with 33 as a remainder, and divided by 5250 gives a quotient of 1 and 3 as a remainder.

- algebra -
**Anonymous**, Monday, February 11, 2013 at 5:51pmi have no clue i am tring ti find the answer

**Answer this Question**

**Related Questions**

Algebra - What is the remainder when the sum of the first 102 counting numbers ...

Algebra - Sorry Iposted that previous question wrong. Here is the right question...

algebra - The sum of the swuares of the first n counting numbers: 1² + 2² + 3...

Math - How many integers between 200 and 500 inclusive leave a remainder 1 when ...

Math - How many integers bewteen 200 and 500 inclusive leave a remainder 1 when ...

math - what is the least common positive integer that meets the following ...

algebra - The sum of the first n counting numbers 1 + 2 + 3 + 4 + 5 ... + n is ...

Algebra 2 - Find a positive integer smaller than 500 that has a remainder of 3 ...

Algebra - If p(x) is a polynomial and is divided by (x-k) and a remainder is ...

Math - Find the least positive integer that leaves the remainder 3 when divided...