Operations on Integers – Addition

Introduction

The set of integers is composed of the negative integers, zero, and the positive integers.  The integers can be visualized using the number line (see first figure), a horizontal line, where, by convention (agreed upon by mathematicians), the negative numbers are located at the left of zero, and the positive integers at the right of 0. In the number line, the number a is greater than the number b if a is at the right of b. Therefore, -2 is greater than -3, -1 is less than 1, 0 is greater than -4.

As shown in the figure above, each integer has a specific location (coordinate) on the number line. Aside from being a coordinate on the number line, each integer can also be considered as movement from 0. For example, +2 means moving 2 units to the right of 0, while -3 is moving 3 units to the left of 0.

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Eratosthenes and the Earth’s Circumference

Eratosthenes was one of the most famous mathematicians in the early times. He was famous for his sieve – a strategy for finding prime numbers – but one of his greatest achievements was estimating the circumference of the earth. In this post, we learn how Eratosthenes used mathematics to solve the size of the earth. We  leave out some of the technical details (such that the assumption that the sun is so far away that its rays are almost parallel), since this post is for elementary school mathematics students.

How did he do it?

Eratosthenes knew that at noon in Syene, the sun casts no shadows. This can be tested using a sundial – a device used to tell the time using its shadow during the ancient time.

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Making Sense of Exponential Growth

Money on Chess Squares

A chessboard has 64 squares. If we are going to place 1 cent in the first square, 2 cents in the second square, 4 cents in the third square, and so on, how much money do we need to fill all the 64 squares?

From the pattern above, it is clear that the amount of money placed in each square is twice than that of the amount placed in the preceding square.  If we are going to number the squares from 1 through 64, then the amount of money needed to be placed in each square is shown in the table below.

As we can see from the table, the amount of money in the 64th square is 184,464,625,987,328,000.00. If we have indeed placed the money, the total money on our chess board is » Read more

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