**Writing algebraic expressions :**

An algebraic expression is an expression that contains one or more variables and may also contain operation symbols, such as + or -

A variable is a letter or symbol used to represent an unknown or unspecified number. The value of a variable may change.

A constant is a specific number whose value does not change.

In algebraic expressions, multiplication and division are usually written without the symbols × and ÷

Write 3 × n as 3n, 3 · n, or n · 3

Write 3 ÷ n as n/3

Some different ways to describe expressions with words are shown below.

**Example 1 : **

Write the given phrase as an algebraic expression.

"The sum of 7 and x"

**Answer : **

The operation is addition.

Expression : 7 + x

**Example 2 : **

Write the given phrase as an algebraic expression.

"The quotient of z and 3"

**Answer : **

The operation is division.

Expression : z/3

**Example 3 : **

Write the given algebraic expression as a phrase.

"11x"

**Answer : **

The operation is multiplication.

Phrase : The product of 11 and x

**Example 4 : **

Write the given algebraic expression as a phrase.

"8 - y"

**Answer : **

The operation is subtraction.

Phrase : "y" less than 8

**Example 5 : **

Write the given phrase as an algebraic expression.

"The sum of 5 times a number and 8"

**Answer : **

Let "x" be the number

The operations are multiplication and addition.

Expression : 5x + 8

**Example 6 : **

Write the given phrase as an algebraic expression.

"7 less than 4 times a number"

**Answer : **

Let "x" be the number

The operations are multiplication and subtraction.

Expression : 4x - 7

**Example 7 : **

Write the given phrase as an algebraic expression.

"One fifth of sum of 3 times a number and 9"

**Answer : **

Let "x" be the number

The operations are multiplication, addition and division.

Expression : (3x + 9) / 5

**Example 8 : **

Write the given algebraic expression as a phrase.

"5x - 8"

**Answer : **

The operations are multiplication and subtraction.

Phrase : 5 times of a number is decreased by 8

**Example 9 : **

Write the given algebraic expression as a phrase.

"(4x - 3) / 7"

**Answer : **

The operations are multiplication, subtraction and division.

Phrase : One seventh of 3 less than 4 times a number

**Example 10 : **

Write the given algebraic expression as a phrase.

"3(x - 6) / 4"

**Answer : **

The operations are subtraction, multiplication and division.

Phrase : One fourth of 3 times the difference between a number and 6

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