6. Determine the base of the numbers in each case for the following operations to be correct: (a) 14/2 = 5 [0.5 mark] (b) 54/4 = 13 [0.5 mark] (c) 24 + 17 = 40

(a) For the operation 14/2 = 5 to be correct, the base of the numbers must be 7. Here's why:

In base 7, the number 14 is equivalent to 11 in base 10 (17^1 + 47^0 = 7 + 4 = 11). The number 2 is the same in all bases, so we don't need to convert it. So, the operation becomes 11/2 = 5.5 in base 10, which rounds down to 5.

(b) For the operation 54/4 = 13 to be correct, the base of the numbers must be 8. Here's why:

In base 8, the number 54 is equivalent to 44 in base 10 (58^1 + 48^0 = 40 + 4 = 44). The number 4 is the same in all bases, so we don't need to convert it. So, the operation becomes 44/4 = 11 in base 10, which is 13 in base 8.

(c) For the operation 24 + 17 = 40 to be correct, the base of the numbers must be 6. Here's why:

In base 6, the number 24 is equivalent to 20 in base 10 (26^1 + 46^0 = 12 + 4 = 16). The number 17 is equivalent to 13 in base 10 (16^1 + 76^0 = 6 + 7 = 13). So, the operation becomes 16 + 13 = 29 in base 10, which is 40 in base 6.