加负数

Adding Negative Integers

Adding negative integers moves you further down (to the left) on the number line.

Let’s take a look at an example. Solve $4+(-5)$.

First, draw a number line and start at $4$.

Next, add $-5$ to $4$. This is essentially the same as subtracting $5$ from $4$.

In conclusion, $4+(-5)=4-5=-1$

When you add two negative integers together, the sum is a more negative number since you are moving further down (to the left) of the number line.

Take a look at the expression $(-7)+(-3)$.

First, let’s draw a number line and start at $-7$.

Next, add $-3$ to $-7$. This is essentially the same as subtracting $3$ from $-7$.

In conclusion, $(-7)+(-3)= -7-3= -10$.

When you add zero to an integer, the integer does not change.

Take a look at $6+0$.

First, let’s draw a number line and start at $6$.

Next, add $0$ to $6$. The integer does not change, so the answer is $6$.

Now, try a couple of examples without drawing a number line.

$$\begin{align} (-5) + (-3) &= -5 - 3 \\ &= -8 \end{align}$$

$$\begin{align} 23+(-5)+(-43)&= 23-5+ (-43) \\ &= 18+(-43) \\ &= 18-43 \\ &= -25 \\ \end{align}$$

$$\begin{align} 17+(-2)+(-3)+0&= 17-2+(-3)+0 \\ &=15+(-3)+0 \\ &= 15-3+0 \\ &= 12+0\\ &=12 \end{align}$$

Positive numbers live on the right side of $0$ on the number line, while negative numbers live on the left side. Positive numbers have a positive sign in front ($+$) but we usually don't write it. However we always write the negative sign in front of a negative number. The sign of the number determines which side of the number line we fall on. See below.

When you add a negative number to a positive number, first find the positive number on the number line. Then, find the negative number on the number line. Next, find the distance between the negative number and $0$ and transpose that difference over to the positive number. Let's try it with $3 + (-6)$.

This means that $3 + (-6)) = -3$. You can use this method to add pretty much any two numbers together, whether they're negative or positive. Just make sure to use the first number as your anchor point, then find the second relative to it instead of to $0$.

(Video) Adding and Subtracting Integers

by Math Antics

This video by Math Antics goes over all the different ways to add and subtract integers. It covers adding and subtracting whole numbers, adding negatives, and subtracting negatives.

$\large{\text{Summary}}$

Adding a negative makes a number smaller. This is because adding a negative number is the same as subtracting a positive number. $$-3+-7$$ We are starting at $-3$ and moving $7$ units to the left on the number line. This will take us to $-10$.

Subtracting a positive is the same thing. $$-7-3$$ We are going to start at $-7$ and move to the left $3$ units. This will take us to $-10$.

We have a special case when this process leads us back to $0$. That means the two numbers we added together are additive inverses.