Formulas and Equations from Words

Constructing Formulas and Equations

Understanding the Language of Algebra

Algebraic expressions often involve variables, numbers and operators. A variable stands for an unknown quantity that can change or vary.
Terms in algebraic expressions are separated by + and - signs, where each term can be a single variable (e.g x), a number (e.g 5) or a combination (e.g 5x or xyz).

Translating Words into Symbols

Translating words into algebraic symbols involves identifying the variables and constants from the word problem, and understanding mathematical operatons as terms of everyday language phrases.
For example, “a number added to ten” translates to x + 10 where x is the unknown number.
“10 more than a number” also translates to x + 10 even though words are in a different order, underlining the need to understand the concept rather than the exact wording.

Forming Equations

When given a mathematical relationship in words, it can be translated to an algebraic equation. The equals sign (=) signifies that the two expressions on either side are equal.
For example, “Three times a number, decreased by seven, is equal to twenty” can be translated to an equation as 3x - 7 = 20.

Building Formulas

Formulas are special types of equations, used to describe a relationship between different quantities.
For example, in physics, speed = distance / time is a formula that explains the relationship between speed, distance and time. In algebra, it would be written as s = d/t.

Using and Rearranging Formulas

Evaluating Expressions and Formulas

Once the unknowns are defined by the context or problem, substitute known values into the expression or formula to calculate the result.
For instance, using the previous formula (s = d/t), if we know that a car travels 120km in 2 hours, we can insert these values into the formula to find speed: s = 120/2 = 60km/h.

Rearranging Formulas

Sometimes, the need comes to isolate a particular variable in the formula.
This process is called rearranging the formula. For example, if we need to find the time travelled in the previous example knowing the speed and distance, we rearrange the formula to t = d/s.

Practice

To improve your skills, practice with a variety of word problems that involve translating words into algebraic expressions or equations.
As you become more proficient, the process becomes faster and the possibility of making a mistake decreases. Exercise frequently and work on problems from real-world contexts to fully understand and appreciate the use of algebra.

Remember, algebra provides a method to represent and solve problems involving unknown numbers or relationships between different variables. Proficiency in algebra is essential for advancing in math, science, and many other fields.