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# Word Problems: Equivalent Expressions

An algebraic expression is an expression that consists of variables, coefficients, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Generally, if two things are the same, then they are called equivalent. Similarly, in mathematics, equivalent expressions are the same, even though they look different. If the values are plugged into the expression, both expressions give the same result.

For example, if we have an expression $3x+9$ , we can make an equivalent expression by factoring a 3 on the outside of parentheses, like this:

$3\left(x+3\right)$

## Word problems with equivalent expressions

Sometimes we need to change equivalent expressions from words to symbols and back again. As an example, you could state that "cubing a number and dividing the result by 8 is the same thing as dividing the number by 2 and finding its cube."

We can translate this sentence into math symbols quite easily.

First, cubing a number means multiplying it by itself three times. So,

$a×a×a={a}^{3}$

Now we divide this cubed number by 8:

$\frac{{a}^{3}}{8}$

To match the other part of the statement, we start by dividing a by 2 and then cubing the result. This is done with parentheses.

${\left(\frac{a}{2}\right)}^{3}$

The full translation of the word problem statement above is:

$\frac{{a}^{3}}{8}={\left(\frac{a}{2}\right)}^{3}$

Therefore, the two equations are equivalent equations.

## Flashcards covering the Word Problems: Equivalent Expressions

Algebra 1 Flashcards