Complete the following as directed. It will help if you DO NOT convert to base 10.
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. \(321_\text{five} - 123_\text{five}\) |
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!).