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

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Problem: Ms. Jensen likes to divide her class into teams of 2. Use mathematical icons to stand for all the student in she class.

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.

PhraseExpression
the amount of nine and eight9 + 8
the amount of nine and also a number x9 + 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.

PhraseExpression
nine raised by a number x9 + x
fourteen reduced by a number p14 - p
seven much less than a number tt - 7
the product that 9 and also a number n· n or 9n
thirty-two split by a number y32 ÷ y or
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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.

PhraseExpression
five more than twice a number2n + 5
the product of a number and also 66n
seven divided by twice a number÷ 2n or
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three time a number diminished by 113n - 11

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Example 4: A little company has $1000 to distribution to that is employees as a bonus. Just how much money will certainly each employee get?

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:

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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
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30(7n)
None of the above.

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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
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30 + d
None the the above
 
RESULTS BOX: