## Algebraic expressions With instance Problems and Interactive Exercises

Use the following examples and interactive exercises to learn around Writing Algebraic Expressions.

You are watching: The product of six and a number

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

Then 2 **·** g, or 2g have the right to represent "g teams of 2 students".

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

Example 1: Write each expression as a math 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 solitary number (17). This expression is a numerical expression, (also referred to as an arithmetic expression). The expression **9 + x** represents a value that deserve 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 be working solely with algebraic expressions.

Example 2: Write each phrase as an algebraic expression.

Phrase | Expression |

nine raised by a number x | 9 + x |

fourteen diminished 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 separated by a number y | 32 ÷ y or |

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

Example 3: Write each phrase as an algebraic expression making use of the variable n.

Phrase | Expression |

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

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

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

three times a number decreased by 11 | 3n - 11 |

Solution: Let e represent the number of employees in the company. The lot of money every employee will obtain is stood for by the adhering to algebraic expression:

Example 5: An electrician fees $45 per hour and spends $20 a day on gasoline. Create an algebraic expression to represent his revenue 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 supplied to stand for a number in one expression or one equation. The worth of this number have the right to change. An **algebraic expression** is a mathematical expression that consists of variables, numbers and also operations. The value of this expression can change.

**Exercises**

Directions: select the algebraic expression that correctly represents the phrase provided. Pick your answer by clicking its button. Feedback to her answer is noted in the outcomes BOX. If you make a mistake, pick a different button.

1. | Fifteen much less than twice a number |

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

2. | Three times a number, enhanced by seventeen |

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

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

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

4. | Thirty divided by seven times a number | |

30 + 7n | ||

30(7n) | ||

None the the above. See more: 2000 Vw Jetta Camshaft Position Sensor Location, Camshaft Position Sensor Location |

RESULTS BOX: |

5. | Jenny earns $30 a work working component time at a supermarket. Compose an algebraic expression to stand for the amount of money she will certainly earn in d days. | |

30d | ||

30 + d | ||

None of the above |

RESULTS BOX: |