Todos numero negativo sempre será negativo

(Video) Integer Multiplication and Division

by Math Antics

Here’s a YouTube video by Math Antics that covers multiplying positives or zero, multiplying a negative by a negative, dividing positive integers, dividing negative integers, dividing a negative and a positive integer, multiplying a negative by a positive or zero, product of an even number of negatives, and product of an odd number of negatives.

$\large{\text{Summary}}$

The hardest part of any integer multiplication problem is deciding the sign of the final answer. Remember that negatives change the sign of a problem. For instance, a single negative in a problem will change the answer from a positive to a negative. In other words, we flip which side of the number line we are on. Positive numbers are on the right side of the number line, and negative numbers are on the left.

So a positive number times a negative number will be negative. If we multiply again by the same negative number, the answer becomes positive. And so on.

He uses an example with $3 \times -1$ multiple times.

$$\begin{align} 3 \times -1 &= -3\\ 3 \times -1 \times -1 &=3 \\ 3 \times -1 \times -1 \times -1 &=-3\\ 3 \times -1 \times -1 \times -1 \times -1 &= 3\\ 3 \times -1 \times -1 \times -1 \times -1 \times -1 &=-3 \end{align}$$

Notice that all of the lines with an even number of negatives have a positive answer. An even amount of negatives in a multiplication problem will always yield a positive number.

Try this problem for yourself:

The product will always be positive.

Every time you multiply something by a negative number, you "flip" the sign of that number. For example, if you multiply a positive number by a negative number, the answer will be a negative number. If you multiply a negative number by a negative number, the answer will be a positive number.

You can think of this like flipping a light switch. The light always starts out on, and every time you see a negative number as you read an expression, you flip the switch (even if it's the very first number). If the light ends up on when you've gotten to the end of the expression, the result should be positive. If it's off, it should be negative.

Whenever there's an even number of negatives, the switch will end up in the same position that it started from—on—so the answer will be positive.

Let's say you have $-1\times-1$ what's that equal? It equals 1. Now what if you have $-1\times-1\times-1$? Well that's essentially just a $1\times-1$ which equals $-1$.

So two $-1$'s gave us a positive one, $1$

And three $-1$'s gave us a negative one, $-1$

And four $-1$'s will give us a positive one, $1$

And five $-1$'s will give us a negative one, $-1$

Do you see the pattern? An even number of $-1$'s gives us a positive one, $1$. This can be applied to any set of products. The product of an even number of negatives give us a positive number.

An odd number of $-1$'s gives us a negative one, $-1$. This can be applied to any set of products. The product of an odd number of negatives give us a negative number.

Example$\\ -2\times-3\times-1\times-4\times-1\times-5\\$

So since $6$ is even that means the answer will be positive! Just multiply the numbers out now.