Writing an algebraic expression when a phrase or a verbal expression is given is what this lesson will show you. When writing algebraic expressions, you may need to use variables, numbers, parentheses, minus sign, addition sign, multiplication sign, and exponents.

You will not need an equal sign as this is used for algebraic equations!

First, start by studying the simple examples in the table below.

Now you are ready to learn some more. With each example below, we show you the key word that is important to identify and understand in order to write the expression correctly.

**Example #1**

6 more than n

**Key word **: more than

More than indicates addition. Add the first number 6 to the second number n

The algebraic expression is n + 6

Notice that we added 6 to n and not n to 6. Technically, 6 + n is n more than 6 although n + 6 will yield the same answer as 6 + n.

**Example #2**

The difference of x and 9.

**Key word **: difference

The word difference indicates subtraction. Start with the first number x. Then, subtract the second number 9.

The algebraic expression is x - 9

Notice that we wrote x first. The number after ' of ' is written down first.

**Example #3**

The difference of 9 and x.

The expression is 9 - x

**Example #4**

Two less than m.

**Key word **: less than

Less than indicates subtraction. Subtract the first number or 2 from the second number m.

The algebraic expression is m - 2

Notice that the phrase " two subtracted from m " is the same as the phrase " two less than m "

Be careful!

Two less than m is not the same as m less than two.

Let m = 5 for instance. Two less than m is m - 2 = 5 - 2 = 3

However, m less than 2 is 2 - m = 2 - 5 = -3

**Example #5**

The product of x and 10

**Key word **: product

Product indicates multiplication. Multiply the first number x by the second number 10. We get x10, but we prefer to write 10x

The algebraic expression is 10x

**Example #6**

The quotient of n and 5

**Key word **: quotient

Quotient indicates division. Divide the first number n by the second number 5.

The algebraic expression is n / 5

**Example #7**

The sum of a number and the ratio of another number to 8.

Key words : sum and ratio

The sum indicates addition. The ratio indicates division.

Let x be the first number and y the other number.

The ratio of another number to 8 can be written as y/8

The sum of a number and the ratio of another number to 8 can be written as x + y/8.

**Example #8**

Six less than the product of 12 and y

**Key words **: six less and product

Product of 12 and y is 12y

Six less than the product of 12 and y is 12y - 6

**Example #9**

15 more than twice a number

**Key words **: more than and twice

Twice = two times

Let n be the number.

The algebraic expression is 2n + 15

**Example #10**

Five more than twice the difference of a number and thirteen.

**Key words **: more than, twice, and difference.

Twice = two times.

Difference of : Again, any number after 'of' comes first in the subtraction.

Less than : The number after 'than' comes first in the subtraction.

Let b be the number.

The difference of a number and thirteen can be written as b - 13.

Twice the difference of a number and thirteen can be written as 2(b - 13)

Five more than twice the difference of a number and thirteen can be written as 2(b - 13) + 5.

The algebraic expression is 2(b - 13) + 5.