What does it mean to write an expression in math

Algebraic expressions are combinations of variables , numbers, and at least one arithmetic operation.

For example, 2 x + 4 y − 9 is an algebraic expression.

Term: Each expression is made up of terms. A term can be a signed number, a variable, or a constant multiplied by a variable or variables.

Factor: Something which is multiplied by something else. A factor can be a number, variable, term, or a longer expression. For example, the expression 7 x ( y + 3 ) has three factors: 7 , x , and ( y + 3 ) .

Coefficient: The numerical factor of a multiplication expression that contains a variable. Consider the expression in the figure above, 2 x + 4 y − 9 . In the first term, 2 x , the coefficient is 2 : in the second term, 4 y , the coefficient is 4 .

Constant: A number that cannot change its value. In the expression 2 x + 4 y − 9 , the term 9 is a constant.

Like Terms: Terms that contain the same variables such as 2 m , 6 m or 3 x y and 7 x y . If an expression has more than one constant terms, those are also like terms.

Example:

Identify the terms, like terms, coefficients, and constants in the expression.

9 m − 5 n + 2 + m − 7

First, we can rewrite the subtractions as additions.

9 m − 5 n + 2 + m − 7 = 9 m + ( − 5 n ) + 2 + m + ( − 7 )

So, the terms are 9 m , ( − 5 n ) , m , 2 , and ( − 7 ) .

Like terms are terms that contain the same variables.

9 m and 9 m are a pair of like terms . The constant terms 2 and − 7 are also like terms.

Coefficients are the numerical parts of a term that contains a variable.

So, here the coefficients are 9 , ( − 5 ) , and 1 . ( 1 is the coefficient of the term m .)

The constant terms are the terms with no variables, in this case 2 and − 7 .

Algebraic expressions must be written and interpreted carefully. The algebraic expression 5 ( x + 9 ) is not equivalent to the algebraic expression, 5 x + 9 .

See the difference between the two expressions in the table below.

In writing expressions for unknown quantities, we often use standard formulas. For example, the algebraic expression for "the distance if the rate is 50 miles per hour and the time is T hours" is D = 50 T (using the formula D = R T ).

An expression like x n is called a power. Here x is the base, and n is the exponent. The exponent is the number of times the base is used as a factor. The word phrase for this expression is " x to the n th power."

Here are some of the examples of using exponents.

Lesson 6: Writing Algebraic Expressions

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Introduction

If you're learning algebra in school or are studying for a test, you've probably notice that many problems ask you to translate written words into algebraic expressions. In other words, there are plenty of word problems.

Some word problems have real-life details—almost like a short story. Others are simple, like descriptions of a math problem. We'll start with simple word problems, then move on to slightly more complex ones.

Writing simple expressions

Before you can tackle complex word problems, you need to know how to translate simple problems into algebra. Generally, you'll do this by replacing the words with operators that mean the same thing. So for instance, four divided by x could be 4 ÷ x. ÷and /are just two ways of writing divided.

Words commonly used in algebra problems

Here are some of the most common math words you'll see:

Many of these are probably familiar to you in everyday conversation. For instance:

• 3 more than 2 is equal to 3 + 2.
• Twice as much could be written as 2 ⋅x, or 2x.
• Have you ever split a check among three people? You could represent the amount of the check with the variable c, and write out that situation as c / 3.

Writing multi-part algebraic expressions

Some expressions are slightly more complicated than the ones we looked at on the last page. For instance, some expressions include more than one math operation. Take this one as an example:

Five times the sum of four and two

If you were to translate this word for word, you'd change the word times to a multiplication symbol (⋅) and put a plus sign (+) between the four and the two. Your expression would look like this:

5 ⋅ 4 + 2

However, this wouldn't get us the right answer. This is because the order of operations would call for you to multiply 5 times 4 first, then add 2. However, our written expression asks us to multiply 5 by the sum of 4 and 2. In other words, we need to add 4 and 2 first, then multiply that number by 5.

If you're familiar with algebraic notation, you know that parentheses are useful in cases like this—they let you group part of an expression and solve it separately from the rest. Here, we can use them to group 4 and 2—the numbers being added.

5 ⋅ (4 + 2)

This is the correct way to write the expression. Based on the order of operations, always solve operations in parentheses first. Here, you'd add 4 + 2, then multiply that sum by 5—in other words, exactly what was written in the original expression.

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