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:

$3(x+3)$

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,

$a\times a\times a=a^3$

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.

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Get help learning about word problems involving equivalent expressions

Tutoring is an excellent way for your student to get a handle on word problems involving equivalent expressions. A tutor can walk your student through the statements step by step, helping them to understand what mathematical symbols each phrase refers to. Your student's tutor can help discover any knowledge gaps your student may have that prevent them from being able to perform the operations, and bridge those gaps so your student can move forward with these and other math problems. To learn more about how tutoring can help your student and to get help finding the right tutor for your student, contact Varsity Tutors and speak to one of our Educational Directors. They will be happy to find your student a qualified tutor.