Solving Equations Using the Multiplication Principle

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  • 0:02 The Multiplication Principle
  • 0:48 How to Use It
  • 1:31 Multiplication Example
  • 2:35 Division Example
  • 3:22 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

When it comes to solving equations in algebra, one of the essential skills you need is the ability to multiply. Watch this video lesson to learn how you can use the multiplication principle to isolate your variable.

The Multiplication Principle

In algebra, whenever you change an equation to get closer to solving it, you want to keep the equation the same on both sides. Picture a pair of scales where one side has one side of the equation on it, and the other side has the other side of the equation. The middle part of the scales is the equals sign. If we change one side of the scale and it starts tipping, what do you think we have to do to the other side to keep it balanced? That's right, we have to change it the same way we changed the first side. That is what the multiplication principle tells us. It tells us that if we multiply or divide one side of an equation, then we must multiply or divide the other side with the same number so the equation stays the same.

How to Use It

How do we use this principle to help us solve equations? How do we know when to multiply and when to divide? The key lies in our equation. We have to look to see what our equation looks like.

We multiply if we see that our equation has our variable being divided by a number. To solve this equation, we multiply by that number. When we do this, we cancel that number on one side so that our variable is alone.

We divide if we see our variable is being multiplied by a number. Division cancels the multiplication on the one side so that once again our variable is alone.

Let's see how these work with a couple examples.

Multiplication Example

If we see an equation like x/2 = 4, then we know that we will be multiplying. Why is this? We know we are going to multiply because we see our variable being divided by a number. What number are we going to use to multiply? We are going to use the number 2 because that is the number that our variable is being divided by. The multiplication principle tells us that if we multiply one side by a number, then we have to multiply the other side by the same number. Remember we want to keep both sides of the equation equal to each other. If we make changes to one side, we have to make the same change to the other side. So, let's go ahead and do that.

(x/2)*2 = 4*2

Since we have division by 2 on the one side, when we multiply that side by 2, the 2s cancel each other out, and we are left with just our variable.

x = 8

So our answer is 8.

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