Addition of negative numbers

Adding numbers using the coordinate line

It is convenient to perform the addition of numbers of small modulus on a coordinate line, mentally imagining how a point denoting a number moves along a number axis.

Take some number, for example, 3. We denote it on the number axis by point A.

Let us add the positive number 2 to the number. This will mean that the point A should be moved to two unit segments in the positive direction, that is, to the right. As a result, we get point B with coordinate 5.

In order to add a negative number (- 5) to a positive number, for example, to 3, point A should be moved 5 units of length in the negative direction, that is, to the left.

In this case, the coordinate of point B is equal to - 2.

So, the order of addition of rational numbers using the number axis will be as follows:

• mark on the coordinate line a point A with a coordinate equal to the first term;
• move it to a distance equal to the modulus of the second term in the direction that corresponds to the sign in front of the second number (plus - move it to the right, minus - to the left);
• the point B obtained on the axis will have a coordinate that will be equal to the sum of the given numbers.

Example.

Moving from the point - 2 to the left (since there is a minus sign in front of 6), we get - 8.

Addition of numbers with the same characters

It is easier to add rational numbers if you use the concept of a module.

Let us need to add the numbers that have the same signs.

For this, we discard the signs of numbers and take the modules of these numbers. We add the modules and put a sign before the sum, which was common to the given numbers.

Example.

An example of the addition of negative numbers.

Addition of numbers with different signs

If the numbers have different signs, then we act somewhat differently than when adding numbers with the same signs.

• We discard signs in front of numbers, that is, we take their modules.
• From the larger module, subtract the smaller one.
• Before the difference, we put the sign that the number had with a higher module.

An example of the addition of negative and positive numbers .

An example of the addition of mixed numbers.

To add the numbers of a different sign :

• from the larger module subtract the smaller module;
• put the sign of a number with a larger module before the difference obtained.