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(i) Both numbers have the same value.
(ii) Both numbers end in a 5.
This is one of those techniques designed specifically for dividing for when the divisor and dividend share a special relationship. The relation is based on parts of the dividend where one part is evenly divisible by the divisor. A compensation step is required but it is relatively easy to perform.
The technique consists of simple math addition and multiplication procedures versus the standard approach, which involves multiplying an identical two-digit number together and then completing the arithmetic. Squaring a two-digit number such as 32 means to multiply 32 by 32.
So how would you square numbers with only 1s? Multiplication is not even necessary using this technique.
For example, to find the square root of 1.4641 is to determine a decimal number when multiplied to itself gives 1.4641 (rounded). So this means the decimal number that was multiplied to itself is the square root of 1.4641 because it requires multiplying the decimal number to itself in producing 1.4641.
Generally, when adding two fractions to each other the lowest common denominator (LCD) is required before other arithmetic processes can be used in finding the answer. Using the technique here does not require the LCD.
This technique is very efficient and easy to learn but most of all it is manageable even when performed mentally. General mental math techniques for adding two fractions together are also available in the Mental Math Unleash The Power eBook. This is a unique technique designed for the specific purpose mentioned.
The eBook also has several techniques for dividing between different
types of fractions (proper/improper/mixed).