## Algebraic expressions With instance Problems and also Interactive Exercises

Use the complying with examples and also interactive practice to learn about Writing Algebraic Expressions.

You are watching: Seven less than a number divided by 3 is five

Solution: Let g stand for the variety of groups in Ms. Jensen"s class.

Then 2 **·** g, or 2g can represent "g teams of 2 students".

In the problem above, the change g to represent the variety of groups in Ms. Jensen"s class. A **variable** is a symbol supplied to stand for a number in one expression or one equation. The worth of this number can vary (change). Let"s watch at an example in i beg your pardon we use a variable.

Example 1: Write each expression as a mathematics expression.

Phrase | Expression |

the amount of nine and eight | 9 + 8 |

the amount of nine and also a number x | 9 + x |

The expression **9 + 8** represents a single number (17). This expression is a numerical expression, (also referred to as an arithmetic expression). The expression **9 + x** represents a worth that have the right to change. If x is 2, then the expression **9 + x** has a value of 11. If x is 6, climate the expression has a value of 15. So **9 + x** is an algebraic expression. In the next couple of examples, we will certainly be working solely with algebraic expressions.

Example 2: Write each expression as one algebraic expression.

Phrase | Expression |

nine raised by a number x | 9 + x |

fourteen reduced by a number p | 14 - p |

seven much less than a number t | t - 7 |

the product that 9 and also a number n | 9 · n or 9n |

thirty-two split by a number y | 32 ÷ y or |

In instance 2, every algebraic expression included one number, one operation and one variable. Let"s look at at an instance in i beg your pardon the expression consists of more than one number and/or operation.

Example 3: Write each expression as one algebraic expression making use of the change n.

Phrase | Expression |

five more than twice a number | 2n + 5 |

the product of a number and also 6 | 6n |

seven divided by twice a number | 7 ÷ 2n or |

three time a number diminished by 11 | 3n - 11 |

Solution: Let e represent the number of employees in the company. The quantity of money each employee will obtain is represented by the following algebraic expression:

Example 5: An electrician dues $45 every hour and also spends $20 a job on gasoline. Compose an algebraic expression to stand for his income for one day.Solution: Let x represent the number of hours the electrician functions in one day. The electrician"s earnings can be stood for by the adhering to algebraic expression:

Solution: 45x - 20

Summary: A **variable** is a symbol provided to represent a number in one expression or an equation. The worth of this number can change. An **algebraic expression** is a mathematical expression that is composed of variables, numbers and also operations. The value of this expression have the right to change.

**Exercises**

Directions: choose the algebraic expression that correctly represents the expression provided. Select your prize by clicking its button. Feedback to your answer is detailed in the outcomes BOX. If you make a mistake, choose a different button.

1. | Fifteen much less than twice a number |

15 - 2x2x + 152x - 15None that the above. RESULTS BOX: |

2. | Three time a number, raised by seventeen |

3(a + 17)3a + 17(17 + 3)aNone that the above. RESULTS BOX: |

3. | The product the nine and also a number, lessened by six |

9(m - 6)6(9 - m)9m - 6None the the above. RESULTS BOX: |

4. | Thirty split by 7 times a number | |

30 + 7n | ||

30(7n) | ||

None of the above. See more: What Does ' I Didnt Mean To Hurt You ' Really Mean? “I Didn'T Mean To Hurt You” |

RESULTS BOX: |

5. | Jenny earns $30 a work working component time in ~ a supermarket. Compose an algebraic expression to represent the lot of money she will earn in d days. | |

30d | ||

30 + d | ||

None the the above |

RESULTS BOX: |