Basic arithmetic

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. $$321_\text{five} - 123_\text{five}$$

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!).