Multiplication is a foundational piece in the puzzle we call mathematics. From very early in our education, we are exposed to basic mathematical concepts, and multiplication is one of them. In elementary school, multiplication can be quite easy. In fact, there are a host of tips and tricks that make multiplication more straightforward, but some of the more advanced topics that cover multiplication require more than simple shortcuts and memory aids. Critical thinking, comprehension, and practice play key roles in the more complex side of multiplication.

Now what happens if you need to multiply by zero, or even by a negative number? Multiplying a number by zero has one simple rule to follow, but multiplication involving negative numbers involves more knowledge. While not necessarily difficult, these instances in multiplication are important to learn.

## By or With a Zero

Multiplication of any number by zero has a very simple answer: **zero**.

2 x 0 = 0

567 x 0 = 0

0 x 93 = 0

This is because you are multiplying it by nothing, essentially there is nothing to multiply so the answer is zero. It does not matter where in the equation the 0 is, just as long as it is a standalone zero.

This is certainly different from multiplying by a number that *includes* a zero. This rule would not apply there. Multiplying by a number that includes a zero simply means that there will be a zero at the end of the answer.

20 x 2 = 40

450 x 1 = 450

## Negative and Positive

A negative number would be an integer that includes the negative sign, “-” in the front. A positive number would be an integer that includes the positive sign, “+” ahead of it. Oftentimes you will find that a positive number actually does not include the positive sign at all. To avoid any confusion, it is helpful to include parentheses around the number like so: (-3 or (+7)).

Multiplying by negatives and positive numbers have three easy rules to follow. When multiplying two positive numbers, you keep the answer positive. When multiplying two negative numbers, they essentially cancel each other out and create a positive number. Yet when you multiply a negative number by a positive number, the answer will always be negative. An even easier way to remember these would be that two *alike *make a positive, while two *unlike *make a negative.

Why would two negative numbers make a positive? In a non-mathematical situation, let’s say we are watching a video of someone running backwards. Instead of playing the video as normal, if we play it in reverse, it would then look like they are running *forwards.* Backwards (-) being played in reverse (-) comes out to it being forwards (+). Here we have two negatives making a positive.

An example involving mathematics could be trying to find out how much was in a gas tank two days ago. If we know that the tank currently contains 50,000 gallons and 8,000 gallons get used every day, we can find the answer. (-2 days) x (-8000 gallons) = (+16,000 gallons). Two days ago there were 16,000 more gallons than today. 16,000 + 50,000 = 66,000.

If we multiply two positive numbers, the answer will remain positive as there is no negative factor involved at all. “Yes run” combined with “Do run” would come out to “Yes do run”, or in mathematical terms: (+3) x (+3) = (+9). Do not forget that oftentimes positive numbers do not have the positive sign at all so an equation may simply look like so: 3 x 3 = 9.

Multiplication with more than two numbers may not sound as easy but it follows the same rules. If we were to solve for (-3) x (-2) x (-4), we would solve for the first part of the equation (-3) x (-2) giving us (+6). If you plug that back into the equation: (+6) x (-4) we would see the answer is (-24). Remembering the rules and solving it in order will keep the problem quite simple to solve.

## At Online Math Center

Multiplication is a core concept of mathematics. Understanding the basics of it along with more complex problems are important for every student. These topics within mathematics help with real life situations, from anything to cooking, budgeting, traveling and more.

At Online Math Center, we ensure that all students leave our school with a deep understanding of relevant multiplication concepts such as multiplying by zero, positive, or negative numbers. Whether struggling with mathematics or a natural, students can strengthen their skills in foundational topics at OMC through our classes and tutoring. OMC works to get every student to their full potential or more in math class and beyond.

Reach out to OMC today to ensure your child gains a solid, complete understanding of the most important mathematical concepts like these by signing them up for classes that are made to fit their specific educational needs.