This English question involves literary analysis, grammar, or writing skills. The detailed response below provides a well-structured answer with supporting evidence and clear explanations.
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1. Represent on a number line.
Step 1: is a negative rational number that lies between and . Step 2: Divide the segment between and on the number line into equal parts. Step 3: The third point to the left of will represent .
\text{<--- -1 ---- \frac{-3}{4} ---- \frac{-2}{4} ---- \frac{-1}{4} ---- 0 ---> }
2. Write in the form .
Step 1: Any integer can be expressed in the form where and . Step 2: Write the given integers in the form : • • • •
0 = \frac{0{1}, \quad 7 = \frac{7}{1}, \quad 10 = \frac{10}{1}, \quad -4 = \frac{-4}{1} }
3. Guess my number: Your friend picks an integer between and . You have to find that number, but your friend can only answer 'yes' or 'no'. What strategy would you use?
Step 1: The most effective strategy for solving this type of problem is binary search or the halving strategy. Step 2: First, ask if the number is greater than . Step 3: Based on the answer, halve the possible range of the number. For example, if the answer is 'yes', the number is between and ; if 'no', the number is between and . Step 4: Continue this process, always asking about the middle of the current range, until the number is found. With each question, the number of possible values is halved, making it quick to pinpoint the exact number.
4. Are the following statements true? Give reasons with examples for your answers. i. Every rational number is an integer.
Step 1: This statement is false. Step 2: A rational number is any number that can be expressed in the form , where and are integers and . An integer is a whole number (e.g., ). Step 3: For example, is a rational number, but it is not an integer. Similarly, and are also rational numbers that are not integers.
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This English question involves literary analysis, grammar, or writing skills. The detailed response below provides a well-structured answer with supporting evidence and clear explanations.