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The first mechanical calculating machine was invented in 1887 in America.
These were made to do the calculations by rotating the mechanism with a handle. This action was replaced by electrical motors but they were still essentially mechanical.

Numbers are entered by sliding the leavers down to the correct number, then rotating the handle clockwise. The number appears on the right hand section of the carriage.
The arrow on the bar at the top indicates the position of a decimal point.
To add, change the leavers to the number required and rotate the handle clockwise. The answer will appear below.
To subtract, turn the handle anti-clockwise.
To multiply, rotate the handle as many times as required (e.g. to multiply 6 x 3 enter the number 6 and rotate the handle 3 times; to multiply 6 by 33, enter the number six, rotate the handle 3 times then move the carriage to the right by one step (equivalent to multiplying the number by 10) and rotate the handle once.
Division is more complex and involves subtracting one number from another until the answer is less than one, then moving the carriage back one place and repeating the process until the right-hand section of the carriage is zero. The answer appears in the left-hand side.