Translating Words to Equations
Translating words to equations for percent problems requires mapping three key phrases to mathematical symbols: what percent or what number becomes the variable, of becomes multiplication, and is becomes an equals sign. The sentence what percent of 50 is 10 translates directly to W_p times 50 = 10. In Grade 7 Saxon Math Course 2, Chapter 8, this translation technique converts any percent word problem into a one-variable equation that can be solved with basic algebra, providing a systematic method that works for finding the percent, the part, or the whole.
Key Concepts
Property Use this key to translate percent problems: 'What percent/number' becomes the variable ($W p$ or $W N$), 'of' becomes multiplication ($\times$), 'is' becomes equals ($=$).
Examples "What percent of 50 is 10?" translates to $W p \times 50 = 10$. "Fifty is what percent of 200?" translates to $50 = W p \times 200$. "Twenty percent of what number is 40?" translates to $0.20 \times W N = 40$.
Explanation Every percent problem is a sentence waiting to be translated into the language of math. The key is to swap specific words for math symbols. 'Of' is your cue to multiply, 'is' signals the equals sign, and 'what number' or 'what percent' is your unknown variable. Once translated, you just have a simple equation to solve for your answer.
Common Questions
How do you translate a percent word problem into an equation?
Replace of with multiplication, is with an equals sign, and what percent or what number with a variable. For example, 15 is what percent of 60 becomes 15 = W_p times 60.
What does of mean in a percent problem?
In percent problems, of means multiply. So 30% of 80 is written as 0.30 times 80 = 24.
How do you solve for the unknown percent?
Set up the equation with the variable representing the percent, then divide both sides to isolate it. For W_p times 50 = 10, divide both sides by 50 to get W_p = 0.20, which is 20%.
How do you find the whole when given a percent?
Set up the equation as (percent) times W_N = (part), then divide both sides by the percent. For 25% times W_N = 15, divide both sides by 0.25 to get W_N = 60.
When do 7th graders learn to translate percent problems to equations?
Saxon Math, Course 2, Chapter 8 introduces this algebraic approach to percent problems as part of the Grade 7 rational number and percent unit.
Is setting up a percent equation faster than using a proportion?
Both methods work. The equation method is often faster once students master the translation rules. The proportion method (part/whole = percent/100) can be more intuitive for visual learners.