\( 1 \leftarrow \quad \) a. Find a number to add to -0.023 to obtain a sum greater than 4 but less than 5 . b. Find a number to subtract from -0.023 to obtain a difference greater than 4 but less than 5 c. Find a number to multiply times 0.023 to obtain a product greater than 4 but less than 5 . d. Find a number to divide into 0.023 to obtain a quotient greater than 4 but less than 5 . a. Choose the correct answer below. A. 4.002 B. 5.026 C. 4.375 D. 5.230

To solve part a, we want to add a number \( x \) to -0.023 such that \( 4 < -0.023 + x < 5 \). Rearranging gives us \( 4.023 < x < 5.023 \). Looking through the options, the only choice that fits is C. 4.375, since it falls between 4.023 and 5.023. For part b, we need to subtract a number \( y \) from -0.023 such that \( 4 < -0.023 - y < 5 \). Rearranging gives \( -5 < -y < -4.023 \), or \( 4.023 < y < 5 \). This means we again want to choose a number between these two bounds. The intervals we need will help lead to finding specific appropriate values. To solve parts c and d, you can explore how multiplication and division work in relation to scaling. For c, if you want a product greater than 4 but less than 5, you're looking for a multiplier of 0.023 that achieves that. Remember, consider the reciprocal for d, as dividing a number will change the bandwidth over which the solution exists.