Here are the solutions to the questions: 1. $1 - \frac{1}{4}=$ Step 1: Convert the whole number to a fraction with the same denominator as the other fraction. $$1 = \frac{4}{4}$$ Step 2: Subtract the fractions. $$\frac{4}{4} - \frac{1}{4} = \frac{4-1}{4} = \frac{3}{4}$$ The answer is $\boxed{\frac{3}{4}}$. 2. Write "One hundred two thousand, five hundred and ninety two" in numerals. Step 1: Break down the number by place value. One hundred two thousand = $102,000$ Five hundred and ninety two = $592$ Step 2: Combine the parts. $$102,000 + 592 = 102,592$$ The answer is $\boxed{102,592}$. 3. Compare $\frac{1}{2}$ and $\frac{1}{10}$ using $<, > \text{ or } =$. Step 1: To compare fractions, find a common denominator. The least common multiple of $2$ and $10$ is $10$. Step 2: Convert $\frac{1}{2}$ to an equivalent fraction with a denominator of $10$. $$\frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}$$ Step 3: Compare $\frac{5}{10}$ and $\frac{1}{10}$. Since $5 > 1$, it follows that $\frac{5}{10} > \frac{1}{10}$. Therefore, $\frac{1}{2} > \frac{1}{10}$. The answer is $\boxed{>}$. 4. Write the operation used in a sequence of number below $123, 129, 135, 141, 147$. Step 1: Find the difference between consecutive terms. $129 - 123 = 6$ $135 - 129 = 6$ $141 - 135 = 6$ $147 - 141 = 6$ Step 2: Since the difference is constant, the operation is addition. The operation used is $\boxed{\text{addition of } 6}$. 5. Write "CMXXXIX" in words. Step 1: Break down the Roman numeral into its components. CM = $900$ (C before M means $1000 - 100$) XXX = $30$ ($10 + 10 + 10$) IX = $9$ (I before X means $10 - 1$) Step 2: Add the values. $$900 + 30 + 9 = 939$$ The number in words is $\boxed{\text{Nine hundred thirty-nine}}$. 6. Write $1005$ in Roman numerals. Step 1: Break down the number by place value. $1000 = M$ $5 = V$ Step 2: Combine the Roman numerals. $$1000 + 5 = MV$$ The Roman numeral is $\boxed{MV}$. 3 done, 2 left today. You're making progress.