Compute. \[ \begin{array}{r}4.32-12.751=\square \\ 9.37+(-4.63)=\square\end{array} \]
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First, let's compute \( 4.32 - 12.751 \): To perform the subtraction, we can align the numbers by their decimal points: \[ \begin{array}{r} 4.320 \\ -12.751 \\ \hline \end{array} \] Now subtracting from right to left: - In the thousandths place: \( 0 - 1 \) cannot be done, so we borrow from the next column. This makes it \( 10 - 1 = 9 \), and it reduces the next column (the hundredths) from \( 2 \) to \( 1 \). - In the hundredths place now: \( 1 - 5 \) cannot be done again, so we borrow from the next column, turning \( 4 \) into \( 3 \) and adding \( 10 \) to the \( 1 \), making it \( 11 - 5 = 6 \). - In the tenths place now: \( 3 - 7 \) cannot be done; we borrow from the \( 4 \), making it \( 13 - 7 = 6 \). - In the ones place: \( 3 - 2 = 1 \). Combining all the results, we have: \[ -8.431 \] Now, let’s calculate \( 9.37 + (-4.63) \): This operation is the same as subtracting: \[ 9.37 - 4.63 \] Align the decimal points: \[ \begin{array}{r} 9.370 \\ - 4.630 \\ \hline \end{array} \] Now, perform the subtraction: - In the thousandths place: \( 0 - 0 = 0 \). - In the hundredths place: \( 7 - 3 = 4 \). - In the tenths place: \( 3 - 6 \) requires borrowing, making it \( 13 - 6 = 7 \). - In the ones place: \( 8 - 4 = 4 \). So, the result is: \[ 4.74 \] Putting it all together, we have the final results: \[ \begin{array}{r} 4.32 - 12.751 = -8.431 \\ 9.37 + (-4.63) = 4.74 \\ \end{array} \]
