How to solve basic algebraic equations with the properties of equality: Multiplication and Division

When you see the equation you’d probably know what the answer is. But the real question is, do you know how to show how you got your answer?

Remember: Our goal is to get y on one side and numbers and operations on the others.

Let’s look at the equation. We need to get rid of ÷3 and one way to get rid of it is by doing the inverse operation, multiplication!

y÷3=4

×m

So since we multiplied 3, we have moved y to one side and removed ÷3. But, we still have to do one more thing. Do you remember the math rule with equations and expressions? We have to also multiply the 3 to 4!

y÷3=4

×m ×m

We have now gotten y on one side, removed ÷3 by multiplying 3 itself, and did the same to 4. In summary, our equation has now simplified into y=12. Let’s plugin our answer into the equation!

12÷3=4

Yup! Our answer is correct. We can check by multiplying 3 and 4, which does equal 12. Make sure to always plugin your answer and check!

Now that you solved a division equation, let’s do multiplication. You may be thinking that you would divide the number out but this is not truly correct.

When dealing with equations, expressions, and variables, we try not to use division as often. Let’s make an equation, 5y=30. Remember, when variables and numbers are side to side, this means we multiply.

We can also write this equation as 5×y=30 so we can picture it finer. When you first look equation, your desire is probably to divide 5. But this actually not the case. Instead, we’re going to multiply 5 by the reciprocal, 1/5.

5×y=30

×1/5

You may be wondering what a reciprocal is. It’s basically 1 divided by the number, in this case, 5. 1 divided by 5 can also be written as 1/5. 1/5 also is another way of saying 1 over 5, which means 1 divided by 5.

So we have now multiplied 5 by 1/5 and got y on one side. Now, we have to multiply 1/5 to 30 because of our math rule. REMEMBER: The math rule is ,”Whatever you do on one side, you have to do on the opposite.”

5×y=30

×1/5 ×1/5

Now, our equation has simplified to y=6. Let’s plugin our answer!

5×6=30

Yup! Our answer’s correct. Good job learning about addition, subtraction, multiplication, and division in equations!