Co-prime numbers are those that do not share a greatest common denominator larger than 1. The list of single digit co-primes is below (note that each co-prime also has a conjunctive, where the terms are reversed) (1, 1)(1, 2)(1, 3)(1, 4)(1, 5)(1, 6)(1, 7)(1, 8)(1, 9)(2, 1)(2, 3)(2, 5)(2, 7)(2, 9)(3, 1)(3, 2)(3, 4)(3, 5)(3, 7)(3, 8)(4, 1)(4, 3)(4, 5)(4, 7)(4, 9)(5, 1)(5, 2)(5, 3)(5, 4)(5, 6)(5, 7)(5, 8)(5, 9)(6, 1)(6, 5)(6, 7)(7, 1)(7, 2)(7, 3)(7, 4)(7, 5)(7, 6)(7, 8)(7, 9)(8, 1)(8, 3)(8, 5)(8, 7)(8, 9)(9, 1)(9, 2)(9, 4)(9, 5)(9, 7)(9, 8)
3. 1 4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9 5 0 2 8 8 4 1 9 7 1 6 9 3 9 9 3 7 5 1 0
3+1+4+1+5+9+2+6+5+3+5+8+9+7+9+3+2+3+8+4+6+2+6+4+3+3+8+3+2+7+9+5+0+2+8+8+4+1+9+7+1+6+9+3+9+9+3+7+5+1 = 247
9/8 = 1/2 + 5/8 as multiply 1/2 by 4 to make lower number the same, i.e. 1/2 = 4/8 then 4/8 + 5/8 = 9/8 which is 1 and 1/8
40 possible combinations listed below 1+2+3+4+5+6 1+2+3+4+11 1+2+3+5+10 1+2+3+6+9 1+2+3+7+8 1+2+4+10 1+2+5+9 1+2+6+8 1+3+4+5+8 1+3+4+6+7 1+3+6+11 1+3+7+10 1+3+8+9 1+4+5+11 1+4+6+10 1+4+7+9 1+5+6+9 1+5+7+8 1+9+11 2+3+4+5+7 2+3+5+11 2+3+6+10 2+3+7+9 2+4+5+10 2+4+6+9 2+4+7+8 2+5+6+8 2+8+11 2+9+10 3+4+5+9 3+4+6+8 3+5+6+7 3+8+10 4+6+11 4+7+10 4+8+9 5+6+10 5+7+9 6+7+8 10+11
3. 1 4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9 5 0 2 8 8 4 1 9 7 1 6 9 3 9 9 3 7 5 1 0 5 8 2 0 9 7 4 9 4 4 5 9 2 3 0 7 8 1 6 4 0 6 2 8 6 2 0 8 9 9 8 6 2 8 0 3 4 8 2 5 3 4 2 1 1 7 0 6 7 9 8 2 1 4 8 0 8 6 5 1 3 2 8 2 3 0 6 6 4 7 0 9 3 8 4 4 6 0 9 5 5 0 5 8 2 2 3 1 7 2 5 3 5 9 4 0 8 1 2 8 4 8 1 1 1 7 4 5 0 2 8 4 1 0 2 7 0 1 9 3 8 5 2 1 1 0 5 5 5 9 6 4 4 6 2 2 9 4 8 9 5 4 9 3 0 3 8 1 9 6 4 4 2 8 8 1 0 9 7 5 6 6 5 9 3 3 4 4 6 1 2 8 4 7 5 6 4 8 2 3 3 7 8 6 7 8 3 1 6 5 2 7 1 2 0 1 9 0 9 1 4 5 6 4 8 5 6 6 9 2 3 4 6 0 3 4 8 6 1 0 4 5 4 3 2 6 6 4 8 2 1 3 3 9 3 6 0 7 2 6 0 2 4 9 1 4 1 2 7 3 7 2 4 5 8 7 0 0 6 6 0 6 3 1 5 5 8 8 1 7 4 8 8 1 5 2 0 9 2 0 9 6 2 8 2 9 2 5 4 0 9 1 7 1 5 3 6 4 3 6 7 8 9 2 5 9 0 3 6 0 0 1 1 3 3 0 5 3 0 5 4 8 8 2 0 4 6 6 5 2 1 3 8 4 1 4 6 9 5 1 9 4 1 5 1 1 6 0 9 4 3 3 0 5 7 2 7 0 3 6 5 7 5 9 5 9 1 9 5 3 0 9 2 1 8 6 1 1 7 3 8 1 9 3 2 6 1 1 7 9 3 1 0 5 1 1 8 5 4 8 0 7 4 4 6 2 3 7 9 9 6 2 7 4 9 5 6 7 3 5 1 8 8 5 7 5 2 7 2 4 8 9 1 2 2 7 9 3 8 1 8 3 0 1 1 9 4 9 1 2 9 8 3 3 6 7 3 3 6 2 4 4 0 6 5 6 6 4 3 0 8 6 0 2 1 3 9 4 9 4 6 3 9 5 2 2 4 7 3 7 1 9 0 7 0 2 1 7 9 8 6 0 9 4 3 7 0 2 7 7 0 5 3 9 2 1 7 1 7 6 2 9 3 1 7 6 7 5 2 3 8 4 6 7 4 8 1 8 4 6 7 6 6 9 4 0 5 1 3 2 0 0 0 5 6 8 1 2 7 1 4 5 2 6 3 5 6 0 8 2 7 7 8 5 7 7 1 3 4 2 7 5 7 7 8 9 6 0 9 1 7 3 6 3 7 1 7 8 7 2 1 4 6 8 4 4 0 9 0 1 2 2 4 9 5 3 4 3 0 1 4 6 5 4 9 5 8 5 3 7 1 0 5 0 7 9 2 2 7 9 6 8 9 2 5 8 9 2 3 5 4 2 0 1 9 9 5 6 1 1 2 1 2 9 0 2 1 9 6 0 8 6 4 0 3 4 4 1 8 1 5 9 8 1 3 6 2 9 7 7 4 7 7 1 3 0 9 9 6 0 5 1 8 7 0 7 2 1 1 3 4 9 9 9 9 9 9 8 3 7 2 9 7 8 0 4 9 9 5 1 0 5 9 7 3 1 7 3 2 8 1 6 0 9 6 3 1 8 5 9 5 0 2 4 4 5 9 4 5 5 3 4 6 9 0 8 3 0 2 6 4 2 5 2 2 3 0 8 2 5 3 3 4 4 6 8 5 0 3 5 2 6 1 9 3 1 1 8 8 1 7 1 0 1 0 0 0 3 1 3 7 8 3 8 7 5 2 8 8 6 5 8 7 5 3 3 2 0 8 3 8 1 4 2 0 6 1 7 1 7 7 6 6 9 1 4 7 3 0 3 5 9 8 2 5 3 4 9 0 4 2 8 7 5 5 4 6 8 7 3 1 1 5 9 5 6 2 8 6 3 8 8 2 3 5 3 7 8 7 5 9 3 7 5 1 9 5 7 7 8 1 8 5 7 7 8 0 5 3 2 1 7 1 2 2 6 8 0 6 6 1 3 0 0 1 9 2 7 8 7 6 6 1 1 1 9 5 9 0 9 2 1 6 4 2 0 1 9 8 9
There are 10!/(4!(10-4)!) = 210 such combinations assuming no repeats are allowed: {0, 1, 2, 3}, {0, 1, 2, 4}, {0, 1, 2, 5}, {0, 1, 2, 6}, {0, 1, 2, 7}, {0, 1, 2, 8}, {0, 1, 2, 9}, {0, 1, 3, 4}, {0, 1, 3, 5}, {0, 1, 3, 6}, {0, 1, 3, 7}, {0, 1, 3, 8}, {0, 1, 3, 9}, {0, 1, 4, 5}, {0, 1, 4, 6}, {0, 1, 4, 7}, {0, 1, 4, 8}, {0, 1, 4, 9}, {0, 1, 5, 6}, {0, 1, 5, 7}, {0, 1, 5, 8}, {0, 1, 5, 9}, {0, 1, 6, 7}, {0, 1, 6, 8}, {0, 1, 6, 9}, {0, 1, 7, 8}, {0, 1, 7, 9}, {0, 1, 8, 9}, {0, 2, 3, 4}, {0, 2, 3, 5}, {0, 2, 3, 6}, {0, 2, 3, 7}, {0, 2, 3, 8}, {0, 2, 3, 9}, {0, 2, 4, 5}, {0, 2, 4, 6}, {0, 2, 4, 7}, {0, 2, 4, 8}, {0, 2, 4, 9}, {0, 2, 5, 6}, {0, 2, 5, 7}, {0, 2, 5, 8}, {0, 2, 5, 9}, {0, 2, 6, 7}, {0, 2, 6, 8}, {0, 2, 6, 9}, {0, 2, 7, 8}, {0, 2, 7, 9}, {0, 2, 8, 9}, {0, 3, 4, 5}, {0, 3, 4, 6}, {0, 3, 4, 7}, {0, 3, 4, 8}, {0, 3, 4, 9}, {0, 3, 5, 6}, {0, 3, 5, 7}, {0, 3, 5, 8}, {0, 3, 5, 9}, {0, 3, 6, 7}, {0, 3, 6, 8}, {0, 3, 6, 9}, {0, 3, 7, 8}, {0, 3, 7, 9}, {0, 3, 8, 9}, {0, 4, 5, 6}, {0, 4, 5, 7}, {0, 4, 5, 8}, {0, 4, 5, 9}, {0, 4, 6, 7}, {0, 4, 6, 8}, {0, 4, 6, 9}, {0, 4, 7, 8}, {0, 4, 7, 9}, {0, 4, 8, 9}, {0, 5, 6, 7}, {0, 5, 6, 8}, {0, 5, 6, 9}, {0, 5, 7, 8}, {0, 5, 7, 9}, {0, 5, 8, 9}, {0, 6, 7, 8}, {0, 6, 7, 9}, {0, 6, 8, 9}, {0, 7, 8, 9}, {1, 2, 3, 4}, {1, 2, 3, 5}, {1, 2, 3, 6}, {1, 2, 3, 7}, {1, 2, 3, 8}, {1, 2, 3, 9}, {1, 2, 4, 5}, {1, 2, 4, 6}, {1, 2, 4, 7}, {1, 2, 4, 8}, {1, 2, 4, 9}, {1, 2, 5, 6}, {1, 2, 5, 7}, {1, 2, 5, 8}, {1, 2, 5, 9}, {1,2, 6, 7}, {1, 2, 6, 8}, {1, 2, 6, 9}, {1, 2, 7, 8}, {1, 2, 7, 9}, {1, 2, 8, 9}, {1, 3, 4, 5}, {1, 3, 4, 6}, {1, 3, 4, 7}, {1, 3, 4, 8}, {1, 3, 4, 9}, {1, 3, 5, 6}, {1, 3, 5, 7}, {1, 3, 5, 8}, {1, 3, 5, 9}, {1, 3, 6, 7}, {1, 3, 6, 8}, {1, 3, 6, 9}, {1, 3, 7, 8}, {1, 3, 7, 9}, {1, 3, 8, 9}, {1, 4, 5, 6}, {1, 4, 5, 7}, {1, 4, 5, 8}, {1, 4, 5, 9}, {1, 4, 6, 7}, {1, 4, 6, 8}, {1, 4, 6, 9}, {1, 4, 7, 8}, {1, 4, 7, 9}, {1, 4, 8, 9}, {1, 5, 6, 7}, {1, 5, 6, 8}, {1, 5, 6, 9}, {1, 5, 7, 8}, {1, 5, 7, 9}, {1, 5, 8, 9}, {1, 6, 7, 8}, {1, 6, 7, 9}, {1, 6, 8, 9}, {1, 7, 8, 9}, {2, 3, 4, 5}, {2, 3, 4, 6}, {2, 3, 4, 7}, {2, 3, 4, 8}, {2, 3, 4, 9}, {2, 3, 5, 6}, {2, 3, 5, 7}, {2, 3, 5, 8}, {2, 3, 5, 9}, {2, 3, 6, 7}, {2, 3, 6, 8}, {2, 3, 6, 9}, {2, 3, 7, 8}, {2, 3, 7, 9}, {2, 3, 8, 9}, {2, 4, 5, 6}, {2, 4, 5, 7}, {2, 4, 5, 8}, {2, 4, 5, 9}, {2, 4, 6, 7}, {2, 4, 6, 8}, {2, 4, 6, 9}, {2, 4, 7, 8}, {2, 4, 7, 9}, {2, 4, 8, 9}, {2, 5, 6, 7}, {2, 5, 6, 8}, {2, 5, 6, 9}, {2, 5, 7, 8}, {2, 5, 7, 9}, {2, 5, 8, 9}, {2, 6, 7, 8}, {2, 6, 7, 9}, {2, 6, 8, 9}, {2, 7, 8, 9}, {3, 4, 5, 6}, {3, 4, 5, 7}, {3, 4, 5, 8}, {3, 4, 5, 9}, {3, 4, 6, 7}, {3, 4, 6, 8}, {3, 4, 6, 9}, {3, 4, 7, 8}, {3, 4, 7, 9}, {3, 4, 8, 9}, {3, 5, 6, 7}, {3, 5, 6, 8}, {3, 5, 6, 9}, {3, 5, 7, 8}, {3, 5, 7, 9}, {3, 5, 8, 9}, {3, 6, 7, 8}, {3, 6, 7, 9}, {3, 6, 8, 9}, {3, 7, 8, 9}, {4, 5, 6, 7}, {4, 5, 6, 8}, {4, 5, 6, 9}, {4, 5, 7, 8}, {4, 5, 7, 9}, {4, 5, 8, 9}, {4, 6, 7, 8}, {4, 6, 7, 9}, {4, 6, 8, 9}, {4, 7, 8, 9}, {5, 6, 7, 8}, {5, 6, 7, 9}, {5, 6, 8, 9}, {5, 7, 8, 9}, {6, 7, 8, 9} If repeats are allowed, the number increases to 715 combinations - I'll leave it as an exercise for the reader to list the extra 505 combinations.
1, 2, 3, 4, 5, 6, 7, 8, 9, 10 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
1/2 + 5/8 = 4/8 + 5/8 = 9/8 = 1 1/8
1+4+1+5+9+2+6+5+3+5+8+9+7+9+3+2+3+8+4+6+2+6+4+3+3+8+3+2+7+9+5+0+2+8+8+4+1+9+7+1+6+9+3+9+9+3+7+5+1+0+5+8+2+0+9+7+4+9+4+4+5+9+2+3+0+7+8+1+6+4+0+6+2+8+6
Co-prime numbers are those that do not share a greatest common denominator larger than 1. The list of single digit co-primes is below (note that each co-prime also has a conjunctive, where the terms are reversed) (1, 1)(1, 2)(1, 3)(1, 4)(1, 5)(1, 6)(1, 7)(1, 8)(1, 9)(2, 1)(2, 3)(2, 5)(2, 7)(2, 9)(3, 1)(3, 2)(3, 4)(3, 5)(3, 7)(3, 8)(4, 1)(4, 3)(4, 5)(4, 7)(4, 9)(5, 1)(5, 2)(5, 3)(5, 4)(5, 6)(5, 7)(5, 8)(5, 9)(6, 1)(6, 5)(6, 7)(7, 1)(7, 2)(7, 3)(7, 4)(7, 5)(7, 6)(7, 8)(7, 9)(8, 1)(8, 3)(8, 5)(8, 7)(8, 9)(9, 1)(9, 2)(9, 4)(9, 5)(9, 7)(9, 8)
3. 1 4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9 5 0 2 8 8 4 1 9 7 1 6 9 3 9 9 3 7 5 1 0
3+1+4+1+5+9+2+6+5+3+5+8+9+7+9+3+2+3+8+4+6+2+6+4+3+3+8+3+2+7+9+5+0+2+8+8+4+1+9+7+1+6+9+3+9+9+3+7+5+1 = 247
9/8 = 1/2 + 5/8 as multiply 1/2 by 4 to make lower number the same, i.e. 1/2 = 4/8 then 4/8 + 5/8 = 9/8 which is 1 and 1/8
(8 + 1)*5 + 2 = 9*5 + 2 = 45 + 2 = 47
40 possible combinations listed below 1+2+3+4+5+6 1+2+3+4+11 1+2+3+5+10 1+2+3+6+9 1+2+3+7+8 1+2+4+10 1+2+5+9 1+2+6+8 1+3+4+5+8 1+3+4+6+7 1+3+6+11 1+3+7+10 1+3+8+9 1+4+5+11 1+4+6+10 1+4+7+9 1+5+6+9 1+5+7+8 1+9+11 2+3+4+5+7 2+3+5+11 2+3+6+10 2+3+7+9 2+4+5+10 2+4+6+9 2+4+7+8 2+5+6+8 2+8+11 2+9+10 3+4+5+9 3+4+6+8 3+5+6+7 3+8+10 4+6+11 4+7+10 4+8+9 5+6+10 5+7+9 6+7+8 10+11
1 123+45-67+8-9 2 123+4-5+67-89 3 123+4*5-6*7+8-9 4 123-45-67+89 5 123-4-5-6-7+8-9 6 12+34+5*6+7+8+9 7 12+34-5+6*7+8+9 8 12+34-5-6+7*8+9 9 12+34-5-6-7+8*9 10 12+3+4+5-6-7+89 11 12+3+4-56/7+89 12 12+3-4+5+67+8+9 13 12+3*45+6*7-89 14 12+3*4+5+6+7*8+9 15 12+3*4+5+6-7+8*9 16 12+3*4-5-6+78+9 17 12-3+4*5+6+7*8+9 18 12-3+4*5+6-7+8*9 19 12-3-4+5-6+7+89 20 12-3-4+5*6+7*8+9 21 12-3-4+5*6-7+8*9 22 12*3-4+5-6+78-9 23 12*3-4-5-6+7+8*9 24 12*3-4*5+67+8+9 25 12/3+4*5-6-7+89 26 12/3+4*5*6-7-8-9 27 12/3+4*5*6*7/8-9 28 12/3/4+5*6+78-9 29 1+234-56-7-8*9 30 1+234*5*6/78+9 31 1+234*5/6-7-89 32 1+23-4+56+7+8+9 33 1+23-4+56/7+8*9 34 1+23-4+5+6+78-9 35 1+23-4-5+6+7+8*9 36 1+23*4+56/7+8-9 37 1+23*4+5-6+7-8+9 38 1+23*4-5+6+7+8-9 39 1+2+34-5+67-8+9 40 1+2+34*5+6-7-8*9 41 1+2+3+4+5+6+7+8*9 42 1+2+3-45+67+8*9 43 1+2+3-4+5+6+78+9 44 1+2+3-4*5+6*7+8*9 45 1+2+3*4-5-6+7+89 46 1+2+3*4*56/7-8+9 47 1+2+3*4*5/6+78+9 48 1+2-3*4+5*6+7+8*9 49 1+2-3*4-5+6*7+8*9 50 1+2*34-56+78+9 51 1+2*3+4+5+67+8+9 52 1+2*3+4*5-6+7+8*9 53 1+2*3-4+56/7+89 54 1+2*3-4-5+6+7+89 55 1+2*3*4*5/6+7+8*9 56 1-23+4*5+6+7+89 57 1-23-4+5*6+7+89 58 1-23-4-5+6*7+89 59 1-2+3+45+6+7*8-9 60 1-2+3*4+5+67+8+9 61 1-2+3*4*5+6*7+8-9 62 1-2+3*4*5-6+7*8-9 63 1-2-34+56+7+8*9 64 1-2-3+45+6*7+8+9 65 1-2-3+45-6+7*8+9 66 1-2-3+45-6-7+8*9 67 1-2-3+4*56/7+8*9 68 1-2-3+4*5+67+8+9 69 1-2*3+4*5+6+7+8*9 70 1-2*3-4+5*6+7+8*9 71 1-2*3-4-5+6*7+8*9 72 1*234+5-67-8*9 73 1*23+4+56/7*8+9 74 1*23+4+5+67-8+9 75 1*23-4+5-6-7+89 76 1*23-4-56/7+89 77 1*23*4-56/7/8+9 78 1*2+34+56+7-8+9 79 1*2+34+5+6*7+8+9 80 1*2+34+5-6+7*8+9 81 1*2+34+5-6-7+8*9 82 1*2+34-56/7+8*9 83 1*2+3+45+67-8-9 84 1*2+3+4*5+6+78-9 85 1*2+3-4+5*6+78-9 86 1*2+3*4+5-6+78+9 87 1*2-3+4+56/7+89 88 1*2-3+4-5+6+7+89 89 1*2-3+4*5-6+78+9 90 1*2*34+56-7-8-9 91 1*2*3+4+5+6+7+8*9 92 1*2*3-45+67+8*9 93 1*2*3-4+5+6+78+9 94 1*2*3-4*5+6*7+8*9 95 1*2*3*4+5+6+7*8+9 96 1*2*3*4+5+6-7+8*9 97 1*2*3*4-5-6+78+9 98 1*2/3+4*5/6+7+89 99 1/2*34-5+6-7+89 100 1/2*3/4*56+7+8*9 101 1/2/3*456+7+8+9