# 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 . 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, .

Now, say we have . 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, .

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, , because 5 goes into 8 one time, which gives us 3 left over.

We can also relate division to multiplication. We say because . 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 . Let’s say . This is equivalent to saying that , but 0 times any number results in 0, so 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, , because Zero can be a dividend or a quotient—just not a divisor.

## Activity: Find the Quotient

(a) What is the quotient of ?

### Discussion

Use multiplication. For example, .

a.

A. 27

b.

B. 10

c.

C. 6

d.

D. 9

(a) Because , the correct answer is 10, which is letter B.

(b) What is the quotient of ?

a.

A. 8

b.

B. 10

c.

C. 3

d.

D. 2