3.3.3 Multiplication and Division Math Terminology

Let’s review the pieces of a multiplication or division problem to be sure we are using the correct vocabulary. All the words in bold are important math vocabulary, so add them to your math notebook with your definitions as you come across them.

Suppose we have six times normal x times four equals 24. The 6 and 4 are referred to as factors, and 24 is called the product. The numbers being multiplied together are the factors, and the answer to a multiplication problem is the product. So, factor multiplication factor equals product.

Now, say we have 56 division seven equals eight. The name for the 56 in this example is dividend, 7 is the divisor, and 8 is the quotient. The number being divided, or broken down, is the dividend. The number we divide by is the divisor, and the answer to a division problem is the quotient. So, dividend division divisor equals quotient.

The remainder in a division problem is the number “left over” that the divisor can no longer divide into. We say a divisor evenly divides a dividend if the remainder is zero. However, if there is a remainder, then the common notation is to write the quotient, then R, followed by the value. For example, equation left hand side eight division five equals right hand side one times cap r times three, because 5 goes into 8 one time, which gives us 3 left over.

We can also relate division to multiplication. We say 56 division seven equals eight because eight multiplication seven equals 56. This shows that division undoes or is the opposite of multiplication.  We can use this rule to show that division is the only basic arithmetic operation that has a restriction. Consider six division zero. Let’s say six division zero equals a. This is equivalent to saying that a multiplication zero equals six, but 0 times any number results in 0, so a multiplication zero equals six is impossible. Thus, division by zero is not defined; it does not exist.

However, zero can be divided by any non-zero number. For example, zero division eight equals zero, because eight multiplication zero equals zero full stop Zero can be a dividend or a quotient—just not a divisor.

Activity symbol Activity: Find the Quotient

(a) What is the quotient of 30 division three?

Hint symbol

Discussion

Use multiplication. For example, three postfix multiplication question mark equals 30.

Solution symbol

a. 

A. 27


b. 

B. 10


c. 

C. 6


d. 

D. 9


The correct answer is b.

Answer

(a) Because three multiplication 10 equals 30, the correct answer is 10, which is letter B.

(b) What is the quotient of 12 division four?

Solution symbol

a. 

A. 8


b. 

B. 10


c. 

C. 3


d. 

D. 2


The correct answer is c.

Answer

(b) Because four multiplication three equals 12, the correct answer is letter C.

3.3.2 Checking Your Math

3.3.4 Relationships Among Operations