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A tape diagram is a rectangular visual model resembling a piece of tape, that is used to assist with the calculation of ratios and addition, subtraction, and commonly multiplication. It is also known as a divided bar model, fraction strip, length model or strip diagram.
The bar notation also allows for fairly rapid composure of very large numbers. For instance, the number ¯ would contain more than a googolplex digits, while remaining fairly simple to write with and remember. However, the system reaches a problem when dealing with different exponents in a single expression.
On stronger computational models, specifically a pointer machine and consequently also a unit-cost random-access machine it is possible to multiply two n-bit numbers in time O(n). [ 6 ] Algebraic functions
The bar model can be drawn as a comparison model to compare two bars of unequal lengths, which can then be used to solve a subtraction problem. The whole-part model can also be used to solve problems involving multiplication or division. [26] A multiplication problem could be presented as follows:
They are also used as a safer alternative to a cheater bar as lever length and operator effort are both reduced. Finally, torque multipliers allow for more accurate torque. By reducing the amount of effort needed to tighten, a torque multiplier allows for slow and smooth application, ensuring more accurate torque levels, and preventing damage ...
In arbitrary-precision arithmetic, it is common to use long multiplication with the base set to 2 w, where w is the number of bits in a word, for multiplying relatively small numbers. To multiply two numbers with n digits using this method, one needs about n 2 operations.
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Multiplication by a positive number preserves the order: For a > 0, if b > c, then ab > ac. Multiplication by a negative number reverses the order: For a < 0, if b > c, then ab < ac. The complex numbers do not have an ordering that is compatible with both addition and multiplication. [30]