Subtraction is taking an amount away from another amount. The steps outlined will help keep you organized as we start subtracting numbers too big to do in your head.

Steps for Subtraction:

• Place the biggest number on top.
• Stack in columns according to place value.
• Regroup when needed.
• Subtract in columns by place value starting on the right and going left.
• The strongest wins. (If the bigger number was negative then the answer is negative. If the bigger number was positive then the answer is positive.)

The following videos introduce the concept of subtraction, then explain what it means to subtract with negative numbers:

Video Source (02:17 mins) | Transcript

Video Source (03:22 mins) | Transcript

Video Source (03:03 mins) | Transcript

Subtraction is the same as adding, but going in the opposite direction. On a number line, we add going to the right. When we subtract, we go to the left.

\(5 - 4 = 1\) looks like this on the number line. We start at \(5\) and move to the left \(4\) spaces ending at \(1\).

This is the same as \(5 + (-4) = 1\)

Video Source (04:39 mins) | Transcript

Examples: \(5 - 4\) does not equal \(4 - 5\)
\(5 + (-4) = (-4) + 5\)

Video Source (05:58 mins) | Transcript

When we talk about the strongest number, we mean the number that is furthest from \(0\) in either the positive or negative direction. It is the biggest number regardless of its sign.

Additional Resources

• Khan Academy: Basic Subtraction (08:31 mins, Transcript)
• Khan Academy: Subtracting Different Ways (12:31 mins, Transcript)
• Khan Academy: Subtracting with Regrouping (05:26 mins, Transcript)

Practice Problems

1. \(9 - 7\) = ? (
   Solution

   x

   Solution: \(2\)
   Details:
   To represent this problem graphically, we will use \(9\) circles.
   
   
   Next, we shade \(7\) circles.
   
   
   The difference between the unshaded and shaded circles is \(2\). The answer to \(9 - 7 = 2\)
   
   )
2. \(8 - 4\) = ? (
   Solution

   x

   Solution:
   4
   )
3. \(11 - 8\) = ? (
   Video Solution

   x

   Solution: 3
   Details:
   

   
   (Video Source | Transcript)
   )
4. \(10 - 2\) = ? (
   Video Solution

   x

   Solution: 8
   Details:
   

   
   (Video Source | Transcript)
   )
5. \(17 - 8\) = ? (
   Solution

   x

   Solution: \(9\)
   Details:
   To show the solution to this problem a number line from \(0\) to \(20\) is created. There is an arrow pointing to the number \(17\). This is our starting point.
   
   
   We are subtracting \(8\) from \(17\) so we will move \(8\) spaces to the left:
   
   
   When we move \(8\) spaces to the left, we end up at \(9\), so \(17 - 8 = 9\).
   )
6. \(11 - 9\) = ? (
   Solution

   x

   Solution:
   2
   )

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