Subtract 42,403 - 1,675

(1) 40728

Explanation

We will write the subtraction in vertical form. To subtract in the ones column, we will borrow from the hundreds column of the minuend 42,403.  Since the digit in the tens column of 42,403 is 0, it is not possible to borrow from that column. 

We write the subtraction in vertical form so that the corresponding digits are lined up. Each step of this subtraction is explained separately.  Your solution should look like the last step.

\( \begin{array}{r} \phantom{-}42,403 \\ - \underline{\phantom{9}1,675} \\[4pt] \phantom{-} \end{array} \)

Since 5 in the ones column of 1,675 is greater than 3 in the ones column of 42,403, we cannot immediately subtract. It is not possible to borrow from the digit 0 in the tens column of 42,403. We can, however, borrow from the hundreds column to regroup in the tens column, as shown below. In this process, we use the fact that 1 hundred = 10 tens.

\( \require{cancel} \begin{array}{r} \phantom{-}42,\overset{\color{red}{3}}{\not{4}}\overset{\color{red}{10}}{\not{0}}3 \\ - \underline{\phantom{9}1,675} \\[4pt] \phantom{-} \end{array} \)

Borrow 1 hundred from 4 in the hundreds column and change the 4 to 3. Add the borrowed 10 to the digit 0 in the tens column of the minuend to get 10.

Now we can borrow from the 10 in the tens column to subtract in the ones column.

\( \require{cancel} \begin{array}{r} \phantom{-}42,\overset{\color{red}{3}}{\not{4}}\overset{\color{red}{\overset{9}{\not{10}}}}{\not{0}}\overset{\color{red}{13}}{\not{3}} \\ - \underline{\phantom{9}1,675} \\[4pt] \phantom{-} \color{red}{8}\end{array} \)

Borrow 1 ten from 10 in the tens column and change the 10 to 9. Add the borrowed 10 to the digit 3 in the ones column of the minuend to get 13. Then subtract in the ones column: 13 - 5 = 8.

Next, we perform the subtraction in the tens column: 9 - 7 = 2.

\( \require{cancel} \begin{array}{r} \phantom{-}42,\overset{\color{red}{3}}{\not{4}}\overset{\color{red}{\overset{9}{\not{10}}}}{\not{0}}\overset{\color{red}{13}}{\not{3}} \\ - \underline{\phantom{9}1,675} \\[4pt] \phantom{-} {\color{red}{2}}8\end{array} \)

To subtract in the hundreds column, we borrow from the 2 in the thousands column. In this process, we use the fact that 1 thousand = 10 hundreds.

\( \require{cancel} \begin{array}{r} \phantom{-}4\overset{\color{red}{1}}{\not{2}},\overset{\color{red}{\overset{13}{\not{3}}}}{\not{4}}\overset{\color{red}{\overset{9}{\not{10}}}}{\not{0}}\overset{\color{red}{13}}{\not{3}} \\ - \underline{\phantom{9}1,675} \\[4pt] \phantom{-} {\color{red}{7}}28\end{array} \)

Borrow 1 thousand from 2 in the thousands column and change the 2 to 1. Add the borrowed 10 to the digit 3 in the hundreds column of the minuend to get 13. Then subtract in the hundreds column: 13 - 6 = 7.

Complete the solution by subtracting in the thousands column (1 - 1 = 0) and bringing down the 4 in the ten thousands column.

\( \require{cancel} \begin{array}{r} \phantom{-}4\overset{1}{\not{2}},\overset{\overset{13}{\not{3}}}{\not{4}}\overset{\overset{9}{\not{10}}}{\not{0}}\overset{13}{\not{3}} \\[-2pt] -\underline{\phantom{9}1,6\text{ }7\text{ }5} \\[4pt] \phantom{-}40,\text{ }7\text{ }2\text{ }8 \end{array} \)

The difference is 40,728