*Last Updated on April 9, 2024.*

To be successful on any Mathematics test, it is important to understand the language of Math.

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In this post, we’ll talk about words, terms, and expressions you may encounter when it comes to Division.

The expressions used in Division are similar to those used in Multiplication. To pass any Math exam, it is key to be sure you understand and use the correct vocabulary.

We’ll also explain the most frequently used words and expressions used in Math Division.

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## Key Math Words

You’ll have to understand what words like factor, product, dividend, divisor, quotient, remainder, leftover, etc., stand for and how to use them. Let’s start with a few examples:

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Let’s say we have 4 x 6 = 24. The 4 and the 6 are called “factors,” while 24 is referred to as the “product.” So the numbers that we multiply together are factors, whereas the answer to the multiplication is the product. So we say that “factor times factor equals product.”

Now, let’s look at one more example. Let’s look at 56 / 7 = 8. We refer to the number 56 as the “dividend.” The number 7 is called the “divisor,” and the number 8 is called the “quotient.”

So the number that’s being broken down, or divided, is our dividend. The divisor is the number that we divide by, while our answer to the division problem is called the quotient. So we say that “dividend divided by divisor equals quotient.” Sound complicated? Well, not really. You’ll get used to it quickly enough!

Another word you’ll have to know in division problems is “remainder. This is the “leftover” number that cannot be divided any further by the divisor.

So we can say that if there is no remainder in a division problem (if the remainder is zero), the divisor divides the dividend evenly.

If there is a remainder, however, the common notation we use is to write first our quotient, then an “*R,”* and then the remaining value. So 8/5 (8 divided by 5) results in 1*R*3. Simply put, the number 5 goes into our number 8 one time, with a leftover of 3.

## Division and Multiplication

Well, as you probably know, in Math, Division is related to Multiplication. We can say that 63 / 7 = 9 since 9 x 7 = 63. This is telling us that division is the opposite of (or undoes) multiplication.

When we use this rule, however, we need to be aware that there is one restriction. Division is actually the only basic arithmetic operation with a restriction!

Let’s explain this. Look at eight divided by zero, or 8 / 0. If we say that 8 / 0 = a, our definition says it is equivalent to say that a x 0 = 8. However, 0 times any number will always give us 0, so saying a x 0 = 8 is not possible! So, division by 0 (zero) is undefined. It simply doesn’t exist! That’s our restriction.

Keep in mind, though, that zero can very well be divided by non-zero numbers. Just look at 0 / 8 = 0. This is true since 8 x 0 = 0. So the number zero can very well be a quotient or a dividend. It can, however, not be a divisor.

So now, let’s look at some of the most frequently occurring terms, words, and expressions when dealing with Math Division Vocabulary. Included are also expressions related to multiplication since division and multiplication are related. Here we go:

## Math Division Vocabulary

**Fraction:** Fractions are quotients of two (2) rational numbers. Fractions are division problems

**Base:** The number that’s being multiplied

**Exponent:** Exponents tell us how many times the base is multiplied

**Factor:** Factors are numbers that are multiplied together to result in a product. So factors are all numbers that result in a product when we multiply them together. As said above, 6 x 4 = 24. The numbers 6 and 4 are factors of 24

**Denominator:** The bottom number of fractions, the fraction’s divisor

**Numerator:** The top number of fractions, the fraction’s dividend

**Dividend:** Dividends are the numbers that are being divided

**Divisor:** Divisors are the numbers we are dividing by

**Product:** Products are answers to multiplication problems. So products are quantities we obtain when we multiply

**Distributive Property** (of multiplication): Just the factors’ order changes

**Associative Property** (of multiplication): Just the groups of factors change

**Identity Property** (of multiplication): Multiplication by one (1) doesn’t change factors

**Zero Property** (of multiplication): Multiplication by zero (0) will always give us zero (0)

**Inverse Operations:** Doing the opposite (for example, division by 4 and multiplication by 4)

**Multiple:** For example, 24 is a multiple of 4 because 4 goes evenly into 24). So multiples are products of a number (4 in our example) and another whole number (6 in our example, as 4 x 6 = 24)

**Per:** For each. For example, $12 per hour

**Quotient:** Quotients are answers to division problems. S0 quotients are the numbers we obtain by division

**Remainder:** Remainders are the numbers that are left over after we have found quotients

**Plus:** This is the arithmetic operation of adding (or summing)

**Difference:** The difference is the number remaining after subtracting

**Combine:** Adding or putting together

**Separate:** Take, pull, or force apart (cutting up)

**Together:** Assembled, or added, in one place

**Change:** In Math or Finance, change is the balance of money received, so it has to do with subtraction

**Times:** Times is multiplication. An arithmetic operation that’s the inverse of division

**Remaining:** In subtraction, not used up

**Increased:** Made greater, added, or enlarged, in amount, degree, or size

**Decreased:** Made less in amount or size

**Total:** In addition, the whole number or amount

**Half:** A half is 1 (one) of 2 (two) equal portions (parts) of a whole when divided by 2

**Quarter:** A Quarter is 1 (one) of 4 (four) equal parts of a whole when divided by 4

**Cube:** A cube is, in multiplication, the product of 3 (three) equal terms

**Shared:** This means held, experienced, or have in common. Equally shared is division

**Split:** In division, split means to separate into portions or parts

**Sum:** The sum is a quantity we obtain by adding a group of numbers

**Leftover:** In subtraction, a leftover is what is not used up

**More:** Greater or larger in amount, degree, size, or extent

**Less:** In Math, less means fewer. For example, 12 less 5 means 12 – 5 = 7. Be aware, though, that 12 less than 5 is totally different: 5 – 12 = -7!

**Fewer:** In Math, fewer is a subtraction quantifier that means a “smaller number of” or “less”. For example, John has 3 fewer books than Janet who has 8 books. How many books does John have?

**Square:** In Math, the word “square” can have two meanings. First, in Geometry, squares are polygons with 4 (four) right angles and 4 (four) equal sides. Secondly, a square can also refer to a number multiplied by itself

**Addend:** Addends are numbers that are combined with other numbers. For example. in 8 + 4 = 12, 8 and 4 are the addends

**Average:** This is about addition and division. You get the average on an evaluation scale by adding all the values up and then dividing that number by the total number of values

**Equation:** Equations are mathematical statements that two (2) expressions are the same. Equations must have equal signs

**Expression:** Expressions are groups of symbols that make mathematical statements. Expressions do NOT have equal signs

**Estimate:** Estimates are approximate calculations of quantities, degrees, values, or worth

**Integer:** Integers are naturals number or their negatives, or zero. So integers are positive or negative whole numbers

**Mean:** The mean is the average value of a series of values. Add the values together and divide by the number of values. So the mean is the average

**Median:** The median relates, in an ordered series of values, to the middle value. It is the middle position number in ordered number lists

**Mode:** The mode is the value that appears the most frequently in a series of values

**Prime:** Prime numbers are numbers that have no factors but themselves and 1 (one). Examples are 2, 3, 5, 7, 11, 13…

Some of the words and expressions listed here do not refer to division and multiplication only. It is important, however, to know what these words mean or refer to.