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

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Problem: Ms. Jensen likes to division her course into groups of 2. Usage mathematical signs to represent all the student in her class.

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.

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

PhraseExpression
nine raised by a number x9 + x
fourteen diminished 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 separated by a number y32 ÷ y or
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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.

PhraseExpression
five more than double a number2n + 5
the product of a number and also 66n
seven separated by twice a number÷ 2n or
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three times a number decreased by 113n - 11

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Example 4: A small company has $1000 to distribute to that employees as a bonus. Exactly how much money will each employee get?

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:

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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
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30(7n)
None the the above.

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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
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30 + d
None of the above
 
RESULTS BOX: