\( 1 \leftarrow \) Mentally compute the number to fill in the blank in each of the following equations. Complete parts (a) through (d) below. a. \( 9.8 \cdot 6.0=4.9 \cdot \square \) (Type an integer or a decimal.) b. \( 10.2 \div 0.4=20.4 \div \square \) (Type an integer or a decimal.) c. \( \mathrm{ab}=\left(\frac{\mathrm{a}}{9}\right) \cdot \square \) (Simplify your answer.) d. \( \mathrm{a} \div \mathrm{b}=(9 \mathrm{a}) \div \square \) (Simplify your answer.)

To solve the equations: a. \( 9.8 \cdot 6.0 = 4.9 \cdot \square \) First, compute \( 9.8 \cdot 6.0 = 58.8 \). Now, we have \( 58.8 = 4.9 \cdot \square \). Dividing \( 58.8 \) by \( 4.9 \), we get \( \square = 12 \). b. \( 10.2 \div 0.4 = 20.4 \div \square \) Calculate \( 10.2 \div 0.4 = 25.5 \). Thus, we have \( 25.5 = 20.4 \div \square \). Rearranging gives \( \square = 20.4 \div 25.5 \). Performing this division results in \( \square \approx 0.8 \). c. \( \mathrm{ab} = \left(\frac{\mathrm{a}}{9}\right) \cdot \square \) To find \( \square \), we can rearrange the equation as follows: \( \square = \mathrm{ab} \cdot 9 / a \). Simplifying gives \( \square = 9b \). d. \( \mathrm{a} \div \mathrm{b} = (9 \mathrm{a}) \div \square \) Rearranging results in \( \square = 9 \mathrm{b} \), since \( \mathrm{a} \div \mathrm{b} = 9 \mathrm{a} \div (9 \mathrm{b}) \) simplifies to \( 1 \). In summary: a. \( 12 \) b. \( 0.8 \) c. \( 9b \) d. \( 9b \)