Basic arithmetic

Complete the following as directed. It will help if you DO NOT convert to base 10.

Addition/subtraction

1. To help with addition and subtraction, create a number line in base 5 from \(1_\text{five}\) to \(20_\text{five}\):

\(1_\text{five}, 2_\text{five}, 3_\text{five}, \_\__\text{five}, \_\__\text{five}, \_\__\text{five}, \_\__\text{five}, \_\__\text{five}, \_\__\text{five}, \_\__\text{five} \)

2. Complete the addition chart for base-5:

+ \(1_\text{five}\) \(2_\text{five}\) \(3_\text{five}\) \(4_\text{five}\)
\(1_\text{five}\)        
\(2_\text{five}\)        
\(3_\text{five}\)        
\(4_\text{five}\)        

3. Solve the following problems visually (with base blocks) and using algorithms (partial sums or standard subtraction).

a. \(14_\text{five} + 4_\text{five}\) b. \(23_\text{five} + 14_\text{five}\)
c. \(123_\text{five} + 44_\text{five}\) d. \(123_\text{five} + 222_\text{five}\)
e. \(11_\text{five} - 4_\text{five}\) f. \(23_\text{five} - 14_\text{five}\)
g. \(123_\text{five} - 44_\text{five}\) h. \(321_\text{five} - 123_\text{five}\)

Multiplication/division

1. Complete the multiplication chart for base-5:

\(\times\) \(1_\text{five}\) \(2_\text{five}\) \(3_\text{five}\) \(4_\text{five}\)
\(1_\text{five}\)        
\(2_\text{five}\)        
\(3_\text{five}\)        
\(4_\text{five}\)        

2. Solve the following problems visually (with base blocks) and using algorithms (partial products or partial quotients).

a. \(14_\text{five} \times 3_\text{five}\) b. \(23_\text{five} \times 4_\text{five}\)
c. \(123_\text{five} \times 4_\text{five}\) d. \(123_\text{five} \times 14_\text{five}\)
e. \(22_\text{five} \div 3_\text{five}\) f. \(41_\text{five} \div 3_\text{five}\)
g. \(1111_\text{five} \div 3 _\text{five}\) h. \(1112_\text{five} \div 4 _\text{five}\)

3. Create and solve a multiplication problem in base 5 where both numbers have three digits. The multiplicand and multiplier must each have different digits (no zeros!).