In these lessons, we will learn how to write algebraic expressions for word problems. We will start with some common phrases found in word problems.

Related Topics:

More Algebra Word Problems

More Algebra Topics

The following table gives some common words or phrases that are usually imply one of the four operations: add, subtract, multiply, divide. However, depending on the word problem, there are exceptions. Scroll down the page for more examples and explanations.

### Phrase to Algebraic Expression

Some examples of common phrases and corresponding expressions that involve**subtraction** are:

Some examples of common phrases and corresponding expressions that involve**multiplication **are:

Some examples of common phrases and corresponding expressions that involve**division** are:

Some examples of common phrases and corresponding expressions that involve**two operations** are:

**How Do You Write Mathematical Expressions from Word Problems?**

There are so many words that you come across when you're working on algebra problems, and these words are really code for very specific mathematical symbols.**How to write algebraic expressions for word phrases, by analyzing the language used?**

An algebraic expression is a mathematical phrase that contains a combination of numbers, variables and operational symbols.

A variable is a letter that can represent one or more numbers.

**How to write expressions with variables?**

Examples:

Write the algebraic expressions to represent the statements.

a) The sum of -7 and the quantity 8 times x

b) Take the quantity -3 times x and then add 1.

c) -6 plus the product of -1 and x.

**How to write algebraic expressions with parentheses?**

Examples:

1: First consider the expression for

-5 plus the quantity of 4 times x

Now take the product of -8 and that expression and then add 6.

2: First consider the expression for

the sum of 7 and the product of -2 and x

What expression would be:

4 plus the quantity of 2 times that expression**How to Write Equations from Word Problems?**

This video teaches how to dissect a word problem in order to define a variable and write an equation.

Example:

1: Half of a number is 16. Write an equation to represent the situation. Define your variable and solve.

2: Mrs. Gaddie has two dogs. Her friend Anna-Marie has three less than twice as many as Mtr. Gaddie. How many dogs does Anna-Marie have?

3: A recycling plant recycles 2 tons of cans yesterday. This is a third of their usual amount. How much does the plant usually recycle?**How to Write Algebraic Expressions for Situations?**

Example:

Translate the following phrases into algebraic or numeric expressions.

a) 173 less than a number 'b'

b) Quotient of 173 and 'b'

c) 'b' times 173

d) 173 more than 'b'

Related Topics:

More Algebra Word Problems

More Algebra Topics

The following table gives some common words or phrases that are usually imply one of the four operations: add, subtract, multiply, divide. However, depending on the word problem, there are exceptions. Scroll down the page for more examples and explanations.

To write an expression, we often have to interpret a written phrase.

For example, the phrase “ 6 added to some number” can be written as the expression *x* + 6, where the variable *x* represents the unknown number.

Some examples of common phrases and corresponding expressions that involve **addition** are:

Phrase | Expression |

4 more than some number | x + 4 |

a number increased by 10 | y + 10 |

8 plus some number | t + 8 |

the sum of a number and 12 | w + 12 |

Some examples of common phrases and corresponding expressions that involve

Phrase | Expression |

4 less than some number | x – 4 |

a number decreased by 10 | y – 10 |

8 minus some number | 8 – t |

the difference between a number and 12 | w – 12 |

Some examples of common phrases and corresponding expressions that involve

Phrase | Expression |

4 times some number | 4x |

twice a number | 2y |

one-third of some number | |

the product of a number and 12 | 12w |

Some examples of common phrases and corresponding expressions that involve

Phrase | Expression |

the quotient of 4 and some number | |

a number divided by 2 | |

the ratio of 8 and some number | |

the quotient of a number and 12 |

Some examples of common phrases and corresponding expressions that involve

Phrase | Expression |

6 more than 5 times a number | 5x + 6 |

4 times the sum of a number and 7 | 4(y + 7) |

5 less than the product of 3 and a number | 3w – 5 |

twice the difference between a number and 9 | 2(z – 9) |

There are so many words that you come across when you're working on algebra problems, and these words are really code for very specific mathematical symbols.

An algebraic expression is a mathematical phrase that contains a combination of numbers, variables and operational symbols.

A variable is a letter that can represent one or more numbers.

Examples:

Write the algebraic expressions to represent the statements.

a) The sum of -7 and the quantity 8 times x

b) Take the quantity -3 times x and then add 1.

c) -6 plus the product of -1 and x.

Examples:

1: First consider the expression for

-5 plus the quantity of 4 times x

Now take the product of -8 and that expression and then add 6.

2: First consider the expression for

the sum of 7 and the product of -2 and x

What expression would be:

4 plus the quantity of 2 times that expression

This video teaches how to dissect a word problem in order to define a variable and write an equation.

Example:

1: Half of a number is 16. Write an equation to represent the situation. Define your variable and solve.

2: Mrs. Gaddie has two dogs. Her friend Anna-Marie has three less than twice as many as Mtr. Gaddie. How many dogs does Anna-Marie have?

3: A recycling plant recycles 2 tons of cans yesterday. This is a third of their usual amount. How much does the plant usually recycle?

Example:

Translate the following phrases into algebraic or numeric expressions.

a) 173 less than a number 'b'

b) Quotient of 173 and 'b'

c) 'b' times 173

d) 173 more than 'b'

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