Subtracting Integers 02:29 minutes
Transcript Subtracting Integers
Have you ever tried to balance a seesaw? I will explain to you what this has to do with subtracting integers. How can we bring this seesaw into balance?
We need to put a value here, on the right side, to get it in balance. In this case, a positive 3 balances the seesaw. We can write this as an addition: + 3. Let us go back to the first situation. Can you imagine another way to bring this seesaw in balance? Right!
Subtracting a Negative Number – Example 1
Another way is to take something away on the left side. In this case, negative 3 can be taken away from the left side. We can express this mathematically as minus a negative 3. As you can see the seesaw is in balance again, which is the same as in the situation before. Taking negative 3 away equals adding positive 3. Remember: Subtracting a number equals the same as adding the opposite. So, subtracting a negative 3 is the same as adding a positive 3.
Subtracting a Negative Number – Example 2
Now let's look at a different example. Find the value of negative 2 minus negative 4 minus 3. Instead of minus 3 you can also write minus positive 3. You have learned that subtracting a number equals the same as adding the opposite number. In our example minus negative four becomes plus positive four and instead of minus positive three you can write plus negative three. Ok, let's calculate from left to right: −2 + 4 = 2 and 2 + −3 = −1.
You have learned that subtracting a negative number is the same as adding the opposite number. But might this knowledge help our little friend in his situation? Maybe...
Subtracting Integers Übung
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Find the integer that brings the seesaw back into balance.
Tipps
Which of the numbers on the left side of the seesaw do not have an opposite pair on the right side?
The absolute value of the left side is $16$. Remember, absolute value is the value of a number without the sign.
Lösung
If we look at the left side of the equation, we see the integers $7$ and $9$. On the righthand side, we have a $+7$.
The opposite of $7$ is $+7$, since the absolute value of these numbers is equal.
Since there's also a $9$ on the lefthand side, we can balance the seesaw by putting a number that is equal to the opposite of $9$ on the righthand side.
In this case, a $+9$ would balance the equation (seesaw).

Identify the correct statements regarding subtracting integers.
Tipps
Try comparing different combinations of adding and subtracting positive and negative numbers.
Lösung
The statements are provided below:
 'Subtracting a positive number is the same as adding the negative of the number.' This definition is true. $4(4)$ is the same as $4+4$. Try it out!
 'Adding two numbers always results in a larger number.' This statement is false. If just one of the numbers is negative, this answer is not true. When we add $4+(3)$, the answer, $1$, is smaller than $4$.
 'Subtracting two numbers always results in a larger number.' This statement is also false. While this is true if just one of the numbers is negative, this answer is not true. When we add $62$, the answer, $4$, is smaller than $6$.
 'Subtracting a negative number is the same as subtracting a positive number.' This answer is false. In the equation $8(1)$, subtracting a positive number will result in $7$, which is incorrect. When we add $8(1)$, $9$ is the correct answer.

Describe how to solve the equation $2  (4) 3$.
Tipps
Subtracting a negative number is the same as adding a positive number.
Subtracting a positive number is the same as adding a negative number.
Remember to use the proper Order of Operations. (PEMDAS)
Lösung
Let's start with the given equation:
 $(2)(4)3$
 $(2)+(+4)3$
 $(2)+43$
 $(2)+4+(3)$
 $(2)+4=2$
 $2+(3)=1$

Identify the equivalent expressions.
Tipps
Adding two positive integers always yields a positive sum while adding two negative integers always yields a negative sum.
However, subtracting a negative number is like adding the same number.
Lösung
Let's simplify the signs to find an equivalent equation.
 If we have an equation $7  (1) + 3$, and we know that subtracting a negative number is the same as adding a positive number, we can simplify this equation to $7 + 1 + 3$.
 For the equation $7 + (1) + (3)$, we know that adding a negative number is the same as subtracting a positive number. So now we can simplify this equation to $7  1  3$.
 Given the equation $7  1  (3)$, if we remember that subtracting a negative number is the same as adding a positive number, we can simplify this equation to $7  1 + 3$.
 Lastly, for the equation $7  (1) + 3$, we know that subtracting a negative number is the same as adding a positive number, so we can simplify this equation to $7 + 1 + 3$.

Calculate the temperature change by subtracting integers.
Tipps
Subtracting a negative number is the same as adding a positive number.
To calculate the difference of two numbers they have to be subtracted.
The result is always a positive value.
Lösung
The temperature on day one is $4$ degrees. The temperature on day two is $3$ degrees. In order to find the difference in the temperatures, you should subtract $3$ from $4$. We can write this equation as follows:
$4(3)$
Since we know that subtracting a negative number is the same as adding a positive number, we can rewrite the equation and solve:
$4+3=7$
So the temperature changed by $7$ degrees.
$\begin{array}{rcl} 4  (3) & = & 4 + 3\\ & = & 7 \end{array}$

Evaluate John's final score by adding and subtracting integers.
Tipps
Adding a negative number is the same as subtracting a positive number.
Subtracting a negative number is the same as adding a positive number.
To solve mathematical expressions, follow the rules of PEMDAS.
Lösung
Let's look at John's throws:
John's first throw results in a positive $2$. On John's second throw, he hits $(+/)$ and a $3$ on his third throw. The fourth throw is a $(/)$, and he hits a $6$ on his final throw.
That will leave us with $2+(3)(6)$. Using the Order of Operations (PEMDAS), we can now solve from left to right.
$\begin{array}{rcl} 2 + (3) (6) & = & ~~~2 + (3) + 6\\ & = & 1 + 6 \\ & = & ~~~5 \end{array}$
John's final score is $5$.