### Learning Outcomes

- Translate word phrases representing subtraction to mathematical expressions
- Use subtraction to solve word applications

## Translate Word Phrases to Math Notation

As with addition, word phrases can tell us to operate on two numbers using subtraction. To translate from a word phrase to math notation, we look for key words that indicate subtraction. Some of the words that indicate subtraction are listed in the table below.

Operation | Word Phrase | Example | Expression |
---|---|---|---|

Subtraction | minus | [latex]5[/latex] minus [latex]1[/latex] | [latex]5 - 1[/latex] |

difference | the difference of [latex]9[/latex] and [latex]4[/latex] | [latex]9 - 4[/latex] | |

decreased by | [latex]7[/latex] decreased by [latex]3[/latex] | [latex]7 - 3[/latex] | |

less than | [latex]5[/latex] less than [latex]8[/latex] | [latex]8 - 5[/latex] | |

subtracted from | [latex]1[/latex] subtracted from [latex]6[/latex] | [latex]6 - 1[/latex] |

### example

Translate and then simplify:

- The difference of [latex]13[/latex] and [latex]8[/latex]
- Subtract [latex]24[/latex] from [latex]43[/latex]

Solution

1. The word *difference* tells us to subtract the two numbers. The numbers stay in the same order as in the phrase.

The difference of [latex]13[/latex] and [latex]8[/latex] | |

Translate. | [latex]13 - 8[/latex] |

Simplify. | [latex]5[/latex] |

2. The words *subtract* *from* tells us to take the second number away from the first. We must be careful to get the order correct.

Subtract [latex]24[/latex] from [latex]43[/latex] | |

Translate. | [latex]43 - 24[/latex] |

Simplify. | [latex]19[/latex] |

### try it

For more examples of how to translate a phrase that represents subtraction, watch the video below.

## Subtract Whole Numbers in Applications

To solve applications with subtraction, we will use the same plan that we used with addition. First, we need to determine what we are asked to find. Then we write a phrase that gives the information to find it. We translate the phrase into math notation and then simplify to get the answer. Finally, we write a sentence to answer the question, using the appropriate units.

### example

The temperature in Chicago one morning was [latex]73[/latex] degrees Fahrenheit. A cold front arrived and by noon the temperature was [latex]27[/latex] degrees Fahrenheit. What was the difference between the temperature in the morning and the temperature at noon?

### try it

The high temperature on [latex]\text{June}{1}^{\text{st}}[/latex] in Boston was [latex]77[/latex] degrees Fahrenheit, and the low temperature was [latex]58[/latex] degrees Fahrenheit. What was the difference between the high and low temperatures?

The weather forecast for June [latex]2[/latex] in St Louis predicts a high temperature of [latex]90[/latex] degrees Fahrenheit and a low of [latex]73[/latex] degrees Fahrenheit. What is the difference between the predicted high and low temperatures?

### example

A washing machine is on sale for [latex]\text{\$399}[/latex]. Its regular price is [latex]\text{\$588}[/latex]. What is the difference between the regular price and the sale price?

### try it

Watch the following video for more examples of how to write a mathematical statement to solve a problem involving the difference of two numbers.