THE PRODUCT QUOTIENT CONNECTION

•  Did you know that multiplication and division are related to each other? Their relationship is that they are opposites, just like   addition and subtraction are opposites. We know that they are opposites, because multiplication is able to reverse, or “undo” division, and division is able to reverse or “undo” multiplication.  Mathematicians have a special word for operations that are the opposite of each other like this. They call them inverse operations.  Multiplication and division are inverse operations, and addition and subtraction are inverse operations.

• Because of their relationship as inverse operations, you can use division to “undo” an multiplication problem so you can check to see if your product (the answer to a multiplication problem) is correct. You can also use multiplication to “undo” a division problem so you can check to see if your quotient (the answer to a division problem) is correct.  Checking your answer to make sure it is correct is called justifying your answer, or proving your answer. If you do this with every problem, you can be confident that you are correct before you move on to another problem.

• Developing a good understanding of the ways in which the addition-subtraction and multiplication-division inverse operation relationships work is a skill that will allow you to be successful as you begin learning higher math, like algebra. You will be able to use your knowledge of inverse operations to balance equations that are much more complicated than anything you probably think that you can do now. Each new skill you learn in math now is a tool you are adding to the toolbox of your mind to help you be successful as your education continues.

 Name:__________________________________

Answer the following questions based on the  reading passage. Don’t forget to go back to the  passage whenever necessary to find or confirm   your answers.

1)  How are multiplication and division related  to each other?

2)  What is a benefit of checking your answer after you have solved a math problem?

3)  How are the things that you learn in math now going to help you later?

4)   What is a product?

5)   What is a quotient?