## Algebraic expression With instance Problems and also Interactive Exercises

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

You are watching: Seven increased by the product of two numbers

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

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

In the trouble above, the change g represents the variety of groups in Ms. Jensen"s class. A **variable** is a symbol offered to stand for a number in an expression or one equation. The value of this number have the right to vary (change). Let"s look at an example in i m sorry we use a variable.

Example 1: Write each phrase as a mathematical expression.

Phrase | Expression |

the sum 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 called an arithmetic expression). The expression **9 + x** represents a worth that can change. If x is 2, then the expression **9 + x** has a worth of 11. If x is 6, then 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 exclusively with algebraic expressions.

Example 2: Write each phrase as one algebraic expression.

Phrase | Expression |

nine boosted 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 divided by a number y | 32 ÷ y or |

In instance 2, each algebraic expression contained one number, one operation and one variable. Let"s look at an instance in which the expression is composed of much more than one number and/or operation.

Example 3: Write each expression as one algebraic expression using the change n.

Phrase | Expression |

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

the product the a number and 6 | 6n |

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

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

Solution: Let e represent the variety of employees in the company. The quantity of money every employee will obtain is represented by the adhering to algebraic expression:

Example 5: An electrician charges $45 per hour and spends $20 a job on gasoline. Compose an algebraic expression to stand for his earnings for one day.Solution: Let x stand for the number of hours the electrician works in one day. The electrician"s earnings deserve to be represented by the complying with algebraic expression:

Solution: 45x - 20

Summary: A **variable** is a symbol offered to represent a number in an expression or one equation. The value of this number can change. An **algebraic expression** is a math expression that consists of variables, numbers and operations. The value of this expression deserve to change.

**Exercises**

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

1. | Fifteen less than twice a number |

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

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

3(a + 17)3a + 17(17 + 3)aNone of 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 separated by 7 times a number | |

30 + 7n | ||

30(7n) | ||

None that the above. See more: How Many Megabytes Is A Movie, How Many Mb'S It Takes To Stream 2 |

RESULTS BOX: |

5. | Jenny earns $30 a day working part time in ~ a supermarket. Create an algebraic expression to represent the quantity of money she will earn in d days. | |

30d | ||

30 + d | ||

None the the above |

RESULTS BOX: |