Eleanor Finch
In mathematics, negative numbers can be used in a variety of calculations, including multiplication and addition. In this case, we are looking at the addition of two negative numbers: -6 and -2. When we add these two numbers together, we get a result of...
| Characteristics | Values |
|---|---|
| Result | -4 |
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What You'll Learn
The answer is -4
Solving the equation "-6 - -2" yields a result of negative four. This calculation involves subtracting two negative numbers, which results in a negative sum. The answer, therefore, is -4.
When subtracting a negative number, it is important to understand that you are essentially adding the absolute value of that number. In this case, we are essentially adding 2 to -6. This is because a negative number subtracted from a positive number results in a smaller number.
Negative numbers are used to represent values less than zero and are often depicted on a number line extending from zero to the left. In this context, -4 signifies a position four units to the left of zero.
The number line is a fundamental concept in mathematics, enabling us to visualize numbers and perform calculations. It serves as a foundational tool for understanding the relative magnitudes of numbers, including positive and negative integers.
In summary, the answer to the equation "-6 - -2" is indeed negative four. This calculation involves subtracting two negative numbers, resulting in a negative sum. Understanding the number line and the rules for manipulating negative numbers are crucial for solving such equations accurately.
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This is a subtraction sum
To understand this better, let's use a number line. Start at -6 on the number line and move two steps to the right (since we are subtracting -2, which is equivalent to adding +2). You will land on -4. This visual representation demonstrates why the answer is -4.
Another way to think about this subtraction sum is to consider debt or deficit. Imagine you owe $6 (represented by -$6, a negative amount), and then you owe another $2 (represented by -$2). Your total debt is now $8, but when represented as a negative number, it is shown as -$8. So, -$6 - -$2 equals -$8, which is the same calculation as -6 - -2 = -4.
You can also verify this answer by inputting the sum into a calculator. Most basic calculators will allow you to input negative numbers and perform subtraction operations. Input '-6' followed by the subtraction key, then input '-2' and press '=' or 'enter' to get the result. The calculator will display '-4', confirming the answer to this subtraction sum.
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Subtracting a negative is the same as addition
When dealing with positive and negative numbers, it's important to remember that subtracting a negative number is the same as adding that number. For example, let's consider the calculation -6 - -2. Here, we have the number -6, and we are subtracting -2 from it. To understand why subtracting a negative is the same as adding, let's look at a few examples and analogies.
Firstly, let's think about subtraction as a whole. When you subtract a number, you can think of it as adding its additive inverse, or its negation. For instance, 3 - 4 can be seen as 3 + -4, or "3 plus negative 4". Here, we are adding the opposite, or negation, of 4 to 3. This is why subtraction is often referred to as "addition of a negation".
Now, let's apply this concept to our original problem. When we subtract -2 from -6, we are essentially asking, "What is -6 plus the opposite of -2?". The opposite of -2 is 2, so our calculation becomes -6 + 2. This calculation gives us -4 as the result. Therefore, -6 - -2 equals -4.
Another way to understand this concept is through the idea of "like signs" and "unlike signs". When you have two numbers with the same sign, whether positive or negative, adding them will result in a number with the same sign. For example, 3 + 5 = 8, and -3 + -5 = -8. Both calculations maintain the sign of the original numbers.
On the other hand, when you have two numbers with different signs (unlike signs), you subtract them by finding the difference between their absolute values and assigning the sign of the number with the larger absolute value. For example, 3 - -2 can be calculated as 3 + 2 = 5, because 3 is larger than 2, so we keep the positive sign. Similarly, -3 - 2 can be calculated as -3 + -2 = -5, because both numbers are negative, so we keep the negative sign.
In summary, subtracting a negative number is the same as adding that number because subtraction is essentially the addition of a negation. This concept can be understood through the ideas of "like signs" and "unlike signs" and applies to all numbers, whether positive or negative.
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-6 + 2 = -4
The expression we're considering is: -6 + 2. This can be evaluated step-by-step as follows:
First, we can evaluate the subtraction inside the parentheses. Since both numbers are negative, we can rewrite the expression as -6 + (–2), which equals –8.
Next, we can evaluate the addition of the two numbers. Adding a negative number is the same as subtracting the corresponding positive number. So, we can rewrite the expression as –6 + 2 = –6 + (–2). This gives us the final answer: -6 + 2 = –8.
In this expression, we are performing a basic arithmetic operation, combining like terms. The result of the expression is always –8, regardless of the order in which we perform the operations. This is because the commutative property of addition states that the order of the addends does not change the sum.
Therefore, the correct answer to the expression '-6 + 2' is -4.
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You can also add the two numbers and then change the sign to negative
To find the answer to -6 – -2, you can also add the two numbers and then change the sign to negative. This is because when you are subtracting a negative number, you can think of it as adding the positive of that number and making the sum negative.
So, in this case, you add 6 and 2, which equals 8. Then, you change the sign to negative, so the answer is -8. This method is particularly useful when dealing with larger numbers or more complex calculations, as it allows you to work with positive values, which can be easier to manage.
This method is based on the principle that subtracting a negative is the same as adding its positive counterpart. In other words, taking away a negative number is the same as adding that number to what you have, as long as you then indicate that the total amount is negative. This is a fundamental rule in mathematics and is used extensively in various calculations, especially in the fields of accounting and finance.
For example, if you were to consider a simple transaction where you spend a certain amount from your bank account, you could represent this as a subtraction of a negative number. Let's say you start with $100 in your account. If you then spend $5, you could represent this as -$5 coming out of your account. So, your new balance would be calculated as $100 - -$5, which, using the method described above, would be $100 + $5 with a negative sign, giving you a new balance of $5.
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Frequently asked questions
4.
Yes. When simplifying an expression with two negative signs next to each other, they cancel each other out and become a positive sign.
-4.
No. You can also use subtraction, which will result in the same outcome. -6--2 = -6+2 = -(-6+2) = -(2) = -2.
If there is only one negative sign, the operation will be different. For example, -6-2 = -6+ -2 = -8.
