EEI - Interpreting Algebraic Expressions Lesson

Interpreting Algebraic Expressions

An expression is a mathematical phrase that contains operations, numbers, and/or variables. It does not contain an equal sign! A numerical expression contains only numbers and operations while an algebraic expression contains at least one variable. We will focus on algebraic expressions!

A term is a part of an expression that is added. The coefficient of a term is the numerical factor of the term. The constant is the numerical term with no variable.

LaTeX: 3x^2+x-7 $3x^2+x-7$

Explanation of an algebraic expression

Recall, the order of operations helps us know how to simplify numerical expressions.

explanation of pemdas

Let's use order of operations to simplify an expression.

Explanation	Mathematical Operation
Simplify inside parenthesis	1 + 3(9 - 2) -3³ = 1 + 3(7) - 3³
Simplify exponents	= 1 + 3(7) - 27
Multiplication and Division (from left to right)	= 1 + 21 - 27
Addition and Subtraction (from left to right)	= 22 - 27
	= -5

Evaluate Expressions

When asked to evaluate an algebraic expression, you would substitute the value(s) of the variable(s) into the expression and simplify.

Watch this video on evaluating algebraic expressions.

Evaluate Expressions Practice

Try these practice problems to be sure you have it down. Evaluate the following expressions if a = 2, b = 3, x = 4, and y = 5.

$LaTeX: b^2+3\left(2x-y\right)$ $b^2+3\left(2x-y\right)$
$4ab+ya^3$
$LaTeX: \frac{y+ab}{6b+x}$ $\frac{y+ab}{6b+x}$
$LaTeX: \frac{x^2-ab}{y}$ $\frac{x^2-ab}{y}$

TO VIEW THE SOLUTIONS ONCE YOU HAVE PRACTICED, CLICK HERE. Links to an external site.

Operation	Words	Examples
Addition	sum, add to, more, plus, increased by, altogether	a number increased by 7 7 more than a number the sum of a number and 7 x + 7
Subtraction	minus, less than, decreased by, difference, how many less, how many more	a number decreased by 4 4 less than a number x - 4
Multiplication	of, product, twice, double, triple, percent, multiply	the product of 0.25 and a number 25% of a number 0.25x
Division	divide into, quotient, half of, two - thirds, the ratio of	half of a number the quotient of a number and 2 x/2

Translate Expressions

Translate the following from words to expressions:

Gwen types 74 words per minute. Write an expression for the number of words she types in m minutes. Solution: 74m
Jake is 2 years younger than Jill, who is y years old. Write an expression for Jake’s age. Solution: y - 2
Jamil runs a mile in 10 minutes. Write an expression for the number of miles that Jamil runs in m minutes. Soution: $LaTeX: \frac{m}{10}$ $\frac{m}{10}$

Remember that you will need to look for clues when translating words to Algebra and the value of an algebraic expression will always be numeric.

Example

Approximately seventy-five 20-ounce plastic bottles must be recycled to produce the filling for one sleeping bag. Write an expression for number of bottles to make b sleeping bags.

Now, use your expression to find the number of bottles needed to make 25, 50, and 300 sleeping bags.

75(25) = 1875
75(50) = 3750
75(300) = 22,500

Expressions containing percentages can be tricky! Watch this video to help with that:

Translate Expressions Practice

30% of a number
twice a number increased by 7
a quotient of a number and 4
2 less than triple a number
the sum of twenty percent of a number and 7

TO VIEW THE SOLUTIONS ONCE YOU HAVE PRACTICED, CLICK HERE. Links to an external site.

Expressions Practice

If you would like to practice more problems and check your work, click Here. Links to an external site. Make sure you check your answers and look at the course resources or ask your teacher if there are any problems you do not understand. Links to an external site.

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