1. Mathematical operation such as adding, subtracting, multiplying and dividing can be used regardless of the base number system used. It is important to remember that none of the digits in the solution are greater than or equal to the base. For example with a base three/ ternary number system, the only digits used are 0,1,2. AdditionDivisionMultiplicationSubtraction

2. Add 16 and 19 in base 10 (decimal). 16 +19 To add, start with adding the 10 0 column. 16 +19 1 16 +19 5 6+9=15 Which is equal to 1 X 10 1 + 5 X 10 0 Put five ones in ones or 10 0 column. Put one ten in tens or 10 1 column. Add the tens or 10 1 column. 1 16 +19 5 1+1+1=3 Since this is in the tens column, this means there are 3 tens. Put 3 in ten in tens or 10 1 column. The answer is 35. 16 +19 35 Next

3. Add 16 and 19 in base 5 (quinary) 31 +34 To add, start with adding the 5 0 column. 31 +34 1 31 +33 0 1+4=5. Which is equal to 1 X 5 1 Put a zero in 5 0 column. Put one in the 5 1 column. Add the tens or 10 1 column. 1 31 +33 0 1+3+3=7 Which is equal to 1 X 5 2 and 2 X 5 1 because it is in the 5 1 column. Put a two in 5 1 column. Put one in the 5 2 column. The answer is 120 in quinary. 31 +33 120

4. Subtract 25 from 54 in base 10 (decimal). 54 -25 54 -25 4 14 54 -25 To subtract, start with subtracting 10 0 column. Since 5 is greater than 4, borrow a 10 from the 10 1 column. There is 14 in the 10 0 column There is 4 in the 10 1 column Subtract each column. 14-5=9 in 10 0 column 4-2=2 in 10 1 column 4 14 54 -25 29 Answer is 29 in decimal. Next

5. Subtract 25 from 54 in base 6 (heximal). 130 - 41 130 - 41 To subtract, start with subtracting 6 0 column. Since 1 is greater than 0, borrow a 6 from the 6 1 column. There is 6 in the 6 0 column There is 2 in the 6 1 column Subtract 6 0 column. 6-1=5 in 6 0 column Subtract 6 1 column 8-4=4 Answer is 45 in heximal. 26 130 - 41 26 130 - 41 5 Then, subtract 6 1 column. Since 4 is greater than 2, borrow a 6 from the 6 2 column. There is 8 in 6 1 column. There is 0 in 6 2 column 086 130 - 41 5 086 130 - 41 45

6. Next Multiply 19 by 9 in base 10 (decimal). 19 x 9 Start with multiplying 9 x 9 19 x 9 8 19 x 9 1 9 x 9=81 Which is equal to 8 X 10 1 + 1 X 10 0 Put 1 in the 10 0 column Put 8 in the 10 1 column Next multiply 9 x 1 8 19 x 9 171 9 x 1=9 then add 8 to get 17 The answer is 171 in decimal. 8 19 x 9 1

7. Multiply 19 by 9 in base 5 (quinary) 34 x 14 34 x 14 4 x 4=16 Which is equal to 3 X 5 1 + 1 X 5 0 Put 1 in the 5 0 column Put 3 in the 5 1 column Start with multiplying 4 x 4 3 34 x 14 1 Next multiply 3 x 4 3 34 x 14 1 3 x 4=12 then add 3 to get 15, which is equal to 3 X 5 1 Put 0 in the 5 1 column and 3 in the 5 2 column 3 34 x 14 301 Next

8. 34 x 14 301 Next multiply 1 x 4 34 x 14 301 40 Since the 1 is in the 5 1 column put a 0 in 5 0 column 1 x 4 =4, put in 5 1 column 34 x 14 301 340 Next multiply 1 x 3 1 x 3=3 put in 5 2 column 34 x 14 301 340 1141 Add the two solutions, since it is in base 5 remember that any addition greater or equal to five carries over. The answer is 1141 in quinary.

9. 174 6 Next Divide 174 by 6 in base 10 (decimal). 174 6 Start by seeing how many times 6 goes into 1. Zero times. Next see how many times 6 goes into 17 Two times 6 x 2= 12 Subtract 12 from 17 which equal 5. 174 6 2 -12 5 6 2 174 -12 54 6 2929 Drop the four down. See how many times 6 goes into 54. Nine times. 6 x 9= 54 Subtract 54 from 54, get zero. The answer is 29. 174 -12 54 0 6 2929

10. Divide 174 by 6 in base 7 (septenary). 336 6 6 Start by seeing how many times 6 goes into 3. Zero times. Next see how many times 6 goes into 33 as base 7 Four times 6 x 4= 33 in base 7 Subtract 33 from 33 which equal 0. 336 6 4 -33 0 6 4 336 -33 06 6 4141 Drop the six down. See how many times 6 goes into 6. 0ne times. 6 x 1= 6 Subtract 6 from 6, get zero. The answer is 41 in septenary. 174 -12 06 6 0 6 4141