Subtraction of Four-Digit Numbers

Besides Ones, Tens, and Hundreds’ spots, four-digit numerals have an additional place value, which is the Thousands place.

When doing the subtraction of four-digit numbers, it’s the same as doing the subtraction of smaller numbers. OK, here’s how to do subtraction using four-digit numbers.

Related Topics

• Adding 2-Digit Numbers
• Addition of Hundreds
• Addition of 3-Digit Numbers
• Addition of Four-Digit Numbers

Way to do subtraction of four 4-digit numbers

Note: Subtraction equations have \(3\) parts:

– Minuend is the numeral you subtract from.

– Subtrahend is the numeral that gets subtracted.

– The difference is the number left over after you subtract.

Step one: First, you put the numerals in a column format, based on the place value. Therefore, put higher numbers over the others so the hundreds’ spot digits, as well as the tens’ spot digits and the ones’ spot digits, get lined up.

Step two: Do the subtraction, beginning with the ones spot. If there are not sufficient Ones in the minuend you can subtract from, you may proceed with regrouping. For this instance, remove \(1\) from the Tens to create \(10\) Ones. Put those \(10\) Ones over in the Ones position.

What’s regrouping?

If it’s not possible to do the subtraction of numerals without the result being negative numbers, it’s necessary to borrow one from over in the next column. Thus, the top numeral from the next column over gets lowered by one, as well as the numeral in the ‘ones’ column ends up a double-character number. Then it’s possible to subtract the bottom numeral from it.

Step three: Subtract the digits in the tens’ spot column, then put the result under the line as well as to the left of the ones’ spot amount.

Step three: Keep doing the subtraction, and then do the same thing for other numerals. Move one place to the left till you get to the Thousands spot.

Subtraction of Four-Digit Numbers – Example 1:

Subtract.

\(\begin{array}{r} &4,534\\ -\!\!\!\!\!&1,322\\ \hline \end{array} \)

Solution:

First line up the numbers: \(\begin{array}{r} &4,534\\ -\!\!\!\!\!&1,322\\ \hline \end{array}→ \) subtract the numerals in the ones’ spot column \((4 – 2 = 2)\) and put the resulting answer under the line. \(\begin{array}{r} &4,534\\ -\!\!\!\!\!\!&1,322 \\ \hline \end{array} \\ \ \ \ \ \ \ \ \ \ \ \ \ \ 2\), Continue with tens’ place. \(3 \ – \ 2=1\), \(\begin{array}{r} &4,534\\ -\!\!\!\!\!\!&1,322 \\ \hline \end{array} \\ \ \ \ \ \ \ \ \ \ \ \ 1\). subtract the numerals in the hundreds’ spot column then out this answer under the line, \(5 \ – \ 3=2\), \(\begin{array}{r} &4,534\\ -\!\!\!\!\!\!&1,322 \\ \hline \end{array} \\ \ \ \ \ \ \ \ \ \ \ 2\). subtract the numerals in the thousands’ spot column then out this answer under the line, \(4 \ – \ 1=3\) \(\begin{array}{r} &4,534\\ -\!\!\!\!\!\!&1,322 \\ \hline \end{array} \\ \ \ \ \ \ \ 3,212\)

Subtraction of Four-Digit Numbers – Example 2:

Subtract.

\(\begin{array}{r} &6,785\\ -\!\!\!\!\!&3,493\\ \hline \end{array} \)

Solution:

First line up the numbers: \(\begin{array}{r} &6,785\\ -\!\!\!\!\!&3,493\\ \hline \end{array}→ \) subtract the numerals in the ones’ spot column \((5 – 3 = 2)\) and put the resulting answer under the line. \(\begin{array}{r} &6,785\\ -\!\!\!\!\!\!&3,493 \\ \hline \end{array} \\ \ \ \ \ \ \ \ \ \ \ \ \ \ 2\), Continue with tens’ place. There are not sufficient tens’ in the minuend you can subtract from, you may proceed with regrouping. For this instance, remove \(1\) from the hundreds’ to create \(10\) Ones:\(7-1=6\). Put those \(10\) over in the ten’s position. \(18 – 9=9\), \(\begin{array}{r} &6,785\\ -\!\!\!\!\!\!&3,493 \\ \hline \end{array} \\ \ \ \ \ \ \ \ \ \ \ \ 9\). subtract the numerals in the hundreds’ spot column then out this answer under the line, \(6 \ – \ 4=2\), \(\begin{array}{r} &6,785\\ -\!\!\!\!\!\!&3,493 \\ \hline \end{array} \\ \ \ \ \ \ \ \ \ \ \ 2\). subtract the numerals in the thousands’ spot column then out this answer under the line, \(6 \ – \ 3=3\) \(\begin{array}{r} &6,785\\ -\!\!\!\!\!\!&3,493 \\ \hline \end{array} \\ \ \ \ \ \ \ 3,292\)

Exercises for Subtraction of Four-Digit Numbers

Find each difference.

1. \(\color{blue}{8,382-5,231}\)
2. \(\color{blue}{3,477-1,561}\)
3. \(\color{blue}{6,767-2,345}\)
4. \(\color{blue}{9,516-7,483}\)

1. \(\color{blue}{3,151}\)
2. \(\color{blue}{1,916}\)
3. \(\color{blue}{4,422}\)
4. \(\color{blue}{2,033}\)