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Single Variable Expressions

Use symbols and operations to understand and define variables.

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Practice Single Variable Expressions
Progress
Estimated12 minsto complete
%
Single Variable Expressions

Shelly is making bracelets to sell at her town's market this summer. She spent $150 on supplies and will make$4 for every bracelet she sells. Her profit for selling  bracelets is given by the expression . How can Shelly calculate her profit if she sells 50 bracelets this summer?

In this concept, you will learn how to evaluate single variable expressions.

Expressions

An expression is a mathematical phrase that contains numbers and operations.

Here are some examples of expressions:

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A variable is a symbol or letter (such as , or ) that is used to represent a quantity that might change in value. A variable expression is an expression that includes variables. Another name for a variable expression is an algebraic expression.

Here are some examples of variable expressions:

A single variable expression is a variable expression with just one variable in it.

You can use a variable expression to describe a real world situation where one or more quantities has an unknown value or can change in value.

To evaluate a variable expression means to find the value of the expression for a given value of the variable. To evaluate, substitute the given value for the variable in the expression and simplify using the order of operations. To follow the order of operations, you always need to do any multiplication/division first before any addition/subtraction.

Here is an example.

Evaluate the expression  for .

First, remember that when you see a number next to a letter, like “”, it means to multiply.

Next, substitute 12 in for the letter  in the expression.

Notice that you can put parentheses around the 12 to keep it separate from the number 10.

Now, simplify the expression using the order of operations. You will need to multiply first and then subtract.

Here is another example that involves division.

Evaluate the expression  for .

First, remember that a fraction bar is like a division sign.  is the same as .

Next, substitute 24 in for the letter  in the expression.

Now, simplify the expression using the order of operations. You will need to divide first and then add.

Examples

Example 1

Earlier, you were given a problem about Shelly and her bracelet business. Shelly is selling bracelets this summer and her profit for selling  bracelets is given by the expression . Shelly wants to calculate what her profit will be if she sells 50 bracelets.

To calculate her profit from selling 50 bracelets, Shelly needs to evaluate the expression   for .

First, substitute 50 in for the letter  in the expression.

Now, simplify the expression using the order of operations. You will need to multiply first and then subtract.

Shelly's profit from selling 50 bracelets would be \$50.

Example 2

Evaluate  if  is 49.

First, substitute 49 in for the letter  in the expression.

Now, simplify the expression using the order of operations. You will need to divide first and then subtract.

Example 3

Evaluate  if  is 20.

First, substitute 20 in for the letter  in the expression.

Now, simplify the expression using the order of operations. You will need to multiply first and then subtract.

Example 4

Evaluate  if  is 9.

First, substitute 9 in for the letter  in the expression.

Now, simplify the expression using the order of operations. You will need to multiply first and then add.

Example 5

Evaluate  if  is 36.

First, substitute 36 in for the letter  in the expression.

Now, simplify the expression using the order of operations. You will need to divide first and then subtract.

Review

Evaluate each expression if the given value of  is 9.

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Evaluate each expression for .

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To see the Review answers, open this PDF file and look for section 1.4.

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Color Highlighted Text Notes

Vocabulary Language: English

Algebraic Expression

An expression that has numbers, operations and variables, but no equals sign.

Evaluate

To evaluate an expression or equation means to perform the included operations, commonly in order to find a specific value.

Expression

An expression is a mathematical phrase containing variables, operations and/or numbers. Expressions do not include comparative operators such as equal signs or inequality symbols.

Variable Expression

A variable expression is a mathematical phrase that contains at least one variable or unknown quantity.