Negative Numbers
Table of Contents
Negative Numbers
Negative numbers are numbers that are less than zero. When first learning to count, we start counting positive numbers beginning with 1, then proceeding to 2, 3, 4, 5, etc. Soon we also learn about 0, which has no value. Creating a number line is a helpful tool for understanding positive and negative numbers.
Positive Number Line
The following positive number line has no negative numbers, only positive numbers, and the numbers increase in value to the right.
Negative Number Line
The following negative number line has no positive numbers, only negative numbers, and the numbers increase in value to the left.
Positive and Negative Number Line
A number line may expand to the right or left and include both positive and negative numbers. This expanded number line is a great way to illustrate how positive and negative numbers relate to each other.
Adding Negative Numbers
When adding negative numbers, the addition converts into a subtraction.
Subtracting Negative Numbers
When subtracting negative numbers, the negative and subtraction cancel each other, and the subtraction turns into adding two positive numbers.
Multiplying Negative Numbers
When multiplying negative numbers, an odd number of negatives results in a negative answer, while multiplying an even number of negatives results in a positive answer because the negatives cancel.
Dividing Negative Numbers
When dividing negative numbers, an odd number of negatives results in a negative answer, while dividing an even number of negatives results in a positive answer because the negatives cancel.
Multiplying or dividing two negatives results in a positive. Breaking down multiplication into addition illustrates how this is possible.
Negative Number Squared
A negative number squared will follow the same method as multiplying negative numbers, because a square indicates multiplying a number by itself. Since both numbers are negative, the resulting answer will be positive.
Frequently Asked Questions
Are negative numbers whole numbers?
No, whole numbers cannot be negative. Whole numbers are real numbers that cannot be fractions, decimals, or negative values.
Are negative numbers real numbers?
Yes, negative numbers are real numbers. Real numbers are any number on a positive and negative number line.
Are negative numbers integers?
Yes and no. Negative numbers are not integers if they have decimals. Integers are positive and negative whole numbers. However, we know whole numbers cannot be negative, which is why the term integer is used.
Are negative numbers rational?
Yes, negative numbers are rational. Rational numbers are numbers that can be represented in the form of a fraction or ratio.
Can you take the square root of a negative number?
Yes, you can take the square root of any number. However, when you take the square root of a negative number, the result is an imaginary number. When you square a negative number, the negatives cancel and the result is positive. Since a squared number is always positive, the square root of a negative number is imaginary and is represented with an ‘i’ next to it.
More Information
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