Molly goes shopping with $20. She buys a new notebook for $4 and a soda for $2. How much money does she have left?
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Khan Academy Adding/Subtracting Negative Numbers
Guidance
To subtract one signed number from another, change the problem from a subtraction problem to an addition problem and change the sign of the number that was originally being subtracted. In other words, to subtract signed numbers simply add the opposite. Then, follow the rules for adding signed numbers.
The subtraction of integers can be represented with manipulatives such as color counters and algebra tiles. A number line can also be used to show the subtraction of integers.
Example A
\begin{align*}7-(-3)=?\end{align*}
Solution: This is the same as \begin{align*} 7+(+3)=?\end{align*}. The problem can be represented with color counters. In this case, the red counters represent positive numbers.
The answer is the sum of 7 and 3. \begin{align*}7+(+3)=10\end{align*}
Example B
\begin{align*}4-(+6)=\end{align*}
Solution: Change the problem to an addition problem and change the sign of the original number that was being subtracted.
\begin{align*}4-(+6)=4+(-6)=?\end{align*}
The remaining counters represent the answer. Therefore, \begin{align*}4-(+6)=-2\end{align*}. The answer is the difference between 6 and 4 and takes the sign of the larger number.
Example C
\begin{align*}5x-(+8x) = ?\end{align*}
Solution: You can rewrite the problem: \begin{align*}5x-(+8x)=5x+(-8x)= ?\end{align*}
The remaining algebra tiles represent the answer. There are three negative \begin{align*}x\end{align*} tiles remaining. Therefore, \begin{align*}(6x)-(+8x)=-3x\end{align*}.
Example D
\begin{align*}(-4)-(+3)=?\end{align*}
Solution: This is the same as \begin{align*}(-4)+(-3)=?\end{align*}. The solution to this problem can be determined by using the number line.
Indicate the starting point of -4 by using a dot. From this point, add a -3 by moving three places to the left. You will stop at -7.
The point where you stopped is the answer to the problem. Therefore, \begin{align*}(-4)-(+3)=-7\end{align*}
Concept Problem Revisited
Molly goes shopping with $20. She buys a new notebook for $4 and a soda for $2. You can figure out how much money she has left by subtracting.
\begin{align*}$20 - $4 - $2 = $14\end{align*}
Vocabulary
- Integer
- All natural numbers, their opposites, and zero are integers. A number in the list ..., -3, -2, -1, 0, 1, 2, 3...
- Number Line
- A number line is a line that matches a set of points and a set of numbers one to one.
Guided Practice
1. \begin{align*}(-2)-(-6)=?\end{align*}
2. \begin{align*}7-(+5)=?\end{align*}
3. \begin{align*}(-8)-(-5)=?\end{align*}
4. \begin{align*}(-4)-(+9)=?\end{align*}
Answers:
1. \begin{align*}(-2)-(-6)=-2+6=6-2=4\end{align*}.
2. \begin{align*}7-(+5)=7-5=2\end{align*}.
3. \begin{align*}(-8)-(-5)=-8+5=5-8=-3\end{align*}
4. \begin{align*}(-4)-(+9)=-4-9=-13\end{align*}
Practice
Subtract.
- \begin{align*}(-9)-(-2)\end{align*}
- \begin{align*}(5)-(+8)\end{align*}
- \begin{align*}(5)-(-4)\end{align*}
- \begin{align*}(-7)-(-9)\end{align*}
- \begin{align*}(6)-(+5)\end{align*}
- \begin{align*}(8)-(+4)\end{align*}
- \begin{align*}(-2)-(-7)\end{align*}
- \begin{align*}(3)-(+5)\end{align*}
- \begin{align*}(-6)-(-10)\end{align*}
- \begin{align*}(-4)-(-7)\end{align*}
- \begin{align*}(-13)-(-19)\end{align*}
- \begin{align*}(-6)-(+8)-(-12)\end{align*}
- \begin{align*}(14)-(+8)-(-6)\end{align*}
- \begin{align*}(18)-(+8)-(+3)\end{align*}
- \begin{align*}(10)-(-6)-(+4)-(+2)\end{align*}
For each of the following models, write a subtraction problem and answer the problem.
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