An algebraic expression comprises both numbers and variables together with at least one arithmetic operation. A variable, as we learned in pre-algebra, is a letter that represents unspecified numbers. One may use a variable in the same manner as all other numerals:. To evaluate an algebraic expression you have to substitute each variable with a number and perform the operations included.

Where 5 is called the base and 3 is called the exponent. The exponent corresponds to the number of times the base is used as a factor. More classes on this subject Algebra 1 Discovering expressions, equations and functions: Composing expressions Algebra 1 Discovering expressions, equations and functions: Composing equations and inequalities Algebra 1 Discovering expressions, equations and functions: Representing functions as rules and graphs.

Share on Facebook. Search Pre-Algebra All courses. All courses. Algebra 1 Discovering expressions, equations and functions Overview Expressions and variables Operations in the right order Composing expressions Composing equations and inequalities Representing functions as rules and graphs About Mathplanet. Algebra 1 Exploring real numbers Overview Integers and rational numbers Calculating with real numbers The Distributive property Square roots. Algebra 1 How to solve linear equations Overview Properties of equalities Fundamentals in solving equations in one or more steps Ratios and proportions and how to solve them Similar figures Calculating with percents.

Algebra 1 Visualizing linear functions Overview The coordinate plane Linear equations in the coordinate plane The slope of a linear function The slope-intercept form of a linear equation.

Algebra 1 Formulating linear equations Overview Writing linear equations using the slope-intercept form Writing linear equations using the point-slope form and the standard form Parallel and perpendicular lines Scatter plots and linear models.

Algebra 1 Linear inequalitites Overview Solving linear inequalities Solving compound inequalities Solving absolute value equations and inequalities Linear inequalities in two variables. Algebra 1 Systems of linear equations and inequalities Overview Graphing linear systems The substitution method for solving linear systems The elimination method for solving linear systems Systems of linear inequalities. Algebra 1 Exponents and exponential functions Overview Properties of exponents Scientific notation Exponential growth functions.

Algebra 1 Radical expressions Overview The graph of a radical function Simplify radical expressions Radical equations The Pythagorean Theorem The distance and midpoint formulas. Algebra 1 Rational expressions Overview Simplify rational expression Multiply rational expressions Division of polynomials Add and subtract rational expressions Solving rational expressions.There are two things that you must be able to do when simplifying algebraic expressions.

The first is to be able to use the distributive property. The second math concept that you must understand is how to combine like terms. Before we dive into analyzing "like terms", let's first discuss what a term is and the vocabulary associated with terms.

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The 7 does not have a variable. It is called a constant. Since it doesn't have a variable, its' value will always remain the same, 7. That's why it is called a constant. The 2 in the term 2x is called a coefficient. A coefficient is a number by which a variable is multiplied.

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The 5 in the term 5y is also a coefficient. So, now you know what these important vocabulary words mean: A constant is a term that is just a number, it does not contain a variable.

A coefficient is the number that you multiply by a variable. The coefficients do not have to be the same, just the variables! For example, for the 6 terms above, 2x and 3x are like terms because they both just contain an x. Yes, 7 and 9 are like terms.

Neither of them have a variable and that is what makes them like terms. Ok, enough vocabulary We are going to simplify each expression by combining like terms. When you combine like terms, you MUST take the sign in front of the term with it or your answer may be incorrect! I like to rewrite my like terms together.

I feel that it makes it easier to compute and will help you to not lose your sign when you a lot of terms to combine. Ok, are you confident enough to use the distributive property when simplifying algebraic expressions? Sure you are, let's go! If you see an addition or subtraction problem inside a set of parenthesis, you must use the distributive property BEFORE simplifying the expression.

As you review the next example, notice how the distributive property was used first, then the algebraic expression was simplified. We have a new platform with updated videos and worksheets. Click here to login to our Learn Worlds platform. Algebra Class. Tip for Combining Like Terms Each term is separated by a plus sign or a minus sign. Comments We would love to hear what you have to say about this page!

Need Help? Try This Online Calculator! Let Us Know How we are doing!You've learned how to work with variables and how to evaluate algebra expressions, now we are going to translate words into algebraic expressions.

Simplify any Algebraic Expression

This skill will come in handy when working with word problems or real life situations. Pay close attention to the "key words" that represent mathematical operations. The good news is that these very same words that we use to write numerical expressions are going to be used to write algebra expressions. The difference between a numerical expression and an algebra expression is that we will be using variables when writing an algebraic expression.

Instead of "8 plus 9" with two given numbersyou would see, "a number plus 9". We don't know exactly "what number", so we would use a variable to indicate that it can be any number. Key words for each operation are indicated in bold.

This will help you to easily translate the expression. As, you can see from the red, bold words, the key words for addition are: sum, more than, plus, increase, add, older than. Please also remember that addition is commutative; therefore, you can reverse the digits and you will end up with the same answer. Our key words for subtraction are: minus, less, subtract, decrease, younger than, and lowered. Remember that subtraction is not commutative, so the order in which write the digits does matter!

The key words for multiplication are: times, product, twice, doubled, multiplied, and of. Of is the tricky word. This is mostly used when you are multiplying a fraction times a number. The last operation that we will study is division.

Algebraic Expressions Worked Examples

Division is not commutative, so you must pay close attention to the order in which you write the expression. Division is much more simple. The key words are: divided by and divided into. Play close attention to the order in which it is written. As you begin to work with algebraic expressions more, you will see word problems that require you to use more than one operation.

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Many people struggle with translating word problems into algebraic expressions. This is a very brief lesson on simple algebraic expressions. One of the most important things to remember is to look for key words and to make sure that your expression matches the context of the word problem. This is most important for operations that are not commutative, such as subtraction and division.If we can't tunnel through the Earth, how do we know what's at its center? All Rights Reserved. The material on this site can not be reproduced, distributed, transmitted, cached or otherwise used, except with prior written permission of Multiply.

Hottest Questions. Previously Viewed. Unanswered Questions. School Subjects. Math and Arithmetic. Wiki User Related Questions Asked in Algebra What is an example of an algebraic expression?

Algebraic expressions are mathematical phrases that contain numbers, operations and at least one variable. Asked in Math and Arithmetic How do you make algebraic expression? Asked in Math and Arithmetic, Algebra What is the difference between a variable and a algebraic expression? A variable is a single letter that represents a number. For example x is a variable.

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An algebraic expression can contain variables, numbers, mathematical symbols, etcetera. Numerical expressions solely include numbers, while algebraic expressions may contain a variable like x. Asked in Computer Programming, Algebra What is a algerbraic expression? An algebraic expression is a mathematical sentence that includes a variable but does not have an equal sign.

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Asked in Algebra What is the antonym of algebraic expression? There is no official antonym for algebraic expression.Join Newsletter News.

Basic Algebra

Welcome to the Algebra worksheets page at Math-Drills. On this page, you will find Algebra worksheets mostly for middle school students on algebra topics such as algebraic expressions, equations and graphing functions. This page starts off with some missing numbers worksheets for younger students. We then get right into algebra by helping students recognize and understand the basic language related to algebra.

The rest of the page covers some of the main topics you'll encounter in algebra units. Remember that by teaching students algebra, you are helping to create the future financial whizzes, engineers, and scientists that will solve all of our world's problems. Algebra is much more interesting when things are more real. Solving linear equations is much more fun with a two pan balance, some mystery bags and a bunch of jelly beans. Algebra tiles are used by many teachers to help students understand a variety of algebra topics.

And there is nothing like a set of co-ordinate axes to solve systems of linear equations. Most Popular Algebra Worksheets this Week. The commutative law or commutative property states that you can change the order of the numbers in an arithmetic problem and still get the same results. In the context of arithmetic, it only works with addition or multiplication operationsbut not mixed addition and multiplication. A fun activity that you can use in the classroom is to brainstorm non-numerical things from everyday life that are commutative and noncommutative.

Putting on socks, for example, is commutative because you can put on the right sock then the left sock or you can put on the left sock then the right sock and you will end up with the same result. Putting on underwear and pants, however, is noncommutative. The associative law or associative property allows you to change the grouping of the operations in an arithmetic problem with two or more steps without changing the result. The order of the numbers stays the same in the associative law.

As with the commutative law, it applies to addition-only or multiplication-only problems. It is best thought of in the context of order of operations as it requires that parentheses must be dealt with first. Students might think of some examples from their experience such as putting items on a tray at lunch. They could put the milk and vegetables on their tray first then the sandwich or they could start with the vegetables and sandwich then put on the milk.Writing an algebraic expression when a phrase or a verbal expression is given is what this lesson will show you.

First, start by Studying the simple examples in the table below. Now you are ready to learn some more. With each example below, we show you the key word that is important to identify and understand in order to write the expression correctly.

Notice that we added 6 to n and not n to 6. Difference indicates subtraction. Start with the first number x.

Then, subtract the second number 9. Notice that the phrase " two subtracted from m " is the same as the phrase " two less than m ". Product indicates multiplication. Multiply the first number x by the second number We get x10, but we prefer to write 10x. Difference of : Again, any number after 'of' comes first in the subtraction.

Writing an algebraic expression. Lesson about orthographic drawing and see some examples on how to make them. An orthographic drawing is Formula for percentage. Finding the average. Basic math formulas Algebra word problems. Types of angles. Area of irregular shapes Math problem solver. Math skills assessment. Compatible numbers. Surface area of a cube.

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Tough Algebra Word Problems. If you can solve these problems with no help, you must be a genius! Real Life Math Skills Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.There is no single strategy for translating math phrases into algebraic expressions. As long as you can remember the basics, you should be able to tackle the more challenging ones. Just make sure that you can justify how you come up with your own algebraic expression, and more importantly that it makes sense to you.

Always ask for help from your teachers, as needed or collaborate with your classmates so that you can verify your answers. To build your skills in writing algebraic expressions, we will go over different ways of how each operation may show up as a word or phrase in the problem.

The four arithmetic operations involved are addition, subtraction, multiplication, and division. Key Words for Addition. Key Words for Subtraction. Key Words for Multiplication. Key Words for Division. It is time now time to go over some examples to practice writing algebraic expressions. I separate the examples into two:. Notice that we want to add two quantities: one unknown number and the number 4. You may use any letters of the alphabet. This means that an unknown number has been added to Either of the two above is a correct answer. In addition, when you encounter this math word difference make sure to pay attention to the order.

The number 1 comes first then an unknown number comes in second. That means the number 1 is the minuend and the unknown number is the subtrahend. The final answer is 1 - x. While the quantity that comes after it becomes the minuend. In other words, we are going to subtract the unknown number from the number 8.

The final answer is 8 - a. Solution : To find the product of two quantities or values, it means that we will multiply them together. The final answer is 5m. In this case, we want to double an unknown value or quantity. Let the letter d be the unknown number, when we double it we get the algebraic expression 2d. The final answer is 2d. We will divide an unknown number by 7. Choosing the letter w as our variable, the math phrase above can be expressed as the algebraic expression below.

The order here is very important. The first quantity is the number 10 and the second quantity is the unknown number.