tell me how to do the sums in easy way and explain
1. divide 120 into two parts such that 2/3 of one part is equal to 2/5 of the other part
2.. a number is 42 more than the average of its half , one - third and one - fifteenth . find the number
3. a number consists of two digits whose sum is 6 . if 18 is added to the number , its digits are reversed find the number .
4. the difference between the squares of two consecutive numbers is 15. find the numbers
5. the numerator of a fraction is 4 less than its denominator . if 2 is added to the numerator , then the fraction becomes 5/7 . find the fraction
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The duodecimal system (also known as base 12 or dozenal) is a positional notation numeral system using twelve as its
base. In this system, the number ten may be written by a rotated "2" ( ) and the number eleven by a rotated "3" ( ). This notation was introduced by Sir Isaac Pitman .[1] These digit forms are available as Unicode characters on computerized systems since June 2015[2] as ↊ (Code point 218A) and ↋ (Code point 218B), respectively. [3] Other notations use "A", "T", or "X" for ten and "B" or "E" for eleven. The number twelve (that is, the number written as "12" in the
base ten numerical system) is instead written as "10" in duodecimal (meaning "1 dozen and 0 units", instead of "1 ten and 0 units"), whereas the digit string "12" means "1 dozen and 2 units" (i.e. the same number that in decimal is written as "14"). Similarly, in duodecimal "100" means "1 gross ", "1000" means "1 great gross", and "0.1" means "1 twelfth" (instead of their decimal meanings "1 hundred", "1 thousand", and "1 tenth").
The number twelve, a superior highly composite number, is the smallest number with four non-trivial factors (2, 3, 4, 6), and the smallest to include as factors all four numbers (1 to 4) within the subitizing range. As a result of this increased factorability of the radix and its divisibility by a wide range of the most elemental numbers (whereas ten has only two non-trivial factors: 2 and 5, and not 3, 4, or 6), duodecimal representations fit more easily than decimal ones into many common patterns, as evidenced by the higher regularity observable in the duodecimal multiplication table. As a result, duodecimal has been described as the optimal number system. [4] Of its factors, 2 and 3 are prime , which means the
reciprocals of all 3-smooth numbers (such as 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, ...) have a terminating representation in duodecimal. In particular, the five most elementary fractions ( 1 ⁄2 , 1 ⁄ 3 , 2 ⁄ 3, 1⁄ 4 and 3 ⁄4 ) all have a short terminating representation in duodecimal (0.6, 0.4, 0.8, 0.3 and 0.9, respectively), and twelve is the smallest radix with this feature (because it is the least common multiple of 3 and 4). This all makes it a more convenient number system for computing fractions than most other number systems in common use, such as the decimal,
vigesimal, binary, octal and hexadecimal systems. Although the trigesimal and sexagesimal systems (where the reciprocals of all 5-smooth numbers terminate) do even better in this respect, this is at the cost of unwieldy multiplication tables and a much larger number of symbols to memorize.
base. In this system, the number ten may be written by a rotated "2" ( ) and the number eleven by a rotated "3" ( ). This notation was introduced by Sir Isaac Pitman .[1] These digit forms are available as Unicode characters on computerized systems since June 2015[2] as ↊ (Code point 218A) and ↋ (Code point 218B), respectively. [3] Other notations use "A", "T", or "X" for ten and "B" or "E" for eleven. The number twelve (that is, the number written as "12" in the
base ten numerical system) is instead written as "10" in duodecimal (meaning "1 dozen and 0 units", instead of "1 ten and 0 units"), whereas the digit string "12" means "1 dozen and 2 units" (i.e. the same number that in decimal is written as "14"). Similarly, in duodecimal "100" means "1 gross ", "1000" means "1 great gross", and "0.1" means "1 twelfth" (instead of their decimal meanings "1 hundred", "1 thousand", and "1 tenth").
The number twelve, a superior highly composite number, is the smallest number with four non-trivial factors (2, 3, 4, 6), and the smallest to include as factors all four numbers (1 to 4) within the subitizing range. As a result of this increased factorability of the radix and its divisibility by a wide range of the most elemental numbers (whereas ten has only two non-trivial factors: 2 and 5, and not 3, 4, or 6), duodecimal representations fit more easily than decimal ones into many common patterns, as evidenced by the higher regularity observable in the duodecimal multiplication table. As a result, duodecimal has been described as the optimal number system. [4] Of its factors, 2 and 3 are prime , which means the
reciprocals of all 3-smooth numbers (such as 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, ...) have a terminating representation in duodecimal. In particular, the five most elementary fractions ( 1 ⁄2 , 1 ⁄ 3 , 2 ⁄ 3, 1⁄ 4 and 3 ⁄4 ) all have a short terminating representation in duodecimal (0.6, 0.4, 0.8, 0.3 and 0.9, respectively), and twelve is the smallest radix with this feature (because it is the least common multiple of 3 and 4). This all makes it a more convenient number system for computing fractions than most other number systems in common use, such as the decimal,
vigesimal, binary, octal and hexadecimal systems. Although the trigesimal and sexagesimal systems (where the reciprocals of all 5-smooth numbers terminate) do even better in this respect, this is at the cost of unwieldy multiplication tables and a much larger number of symbols to memorize.
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