Expression Versus Equation

An expression is a mathematical phrase that represents a quantity and does not have an equals sign, while an equation uses an equals sign to show that two expressions are equal and can be used to find unknown values.

For example, a graduate student named Michael is planning a research study. He wants to pay each participant 20 dollars, but he has not decided how many participants to recruit.

Michael uses the variable p to represent the number of participants. The expression 20p represents the total incentive cost. He also needs 100 dollars for survey software and data storage.

The expression 20p plus 100 helps Michael estimate the study’s cost for different numbers of participants.

Later, he receives a research grant of 1000 dollars and wants to know how many participants the grant can support.

So, he writes the equation 20p plus 100 equals 1000. Solving it gives p equals 45. This means he can recruit 45 participants.

The expression represents the study's cost, while the equation helps Michael to find how many participants he can recruit.