Solve proportions: word problems

Learning Objectives Identify proportional relationships within word problems. Set up proportions correctly from given word problem scenarios. Solve proportions using the cross-multiplication method. Interpret the numerical solution of a proportion in the context of the original word problem. Check the reasonableness of their solutions to proportion word problems. Apply proportional reasoning to solve various real-world problems. Ever wonder how bakers scale up a recipe for a big party, or how maps accurately shrink down real distances? 🗺️ It's all about understanding proportions! In this lesson, you'll learn how to translate real-world scenarios into mathematical proportions and solve them. Understanding proportions is a powerful tool for solving many everyday pro...

TermDefinitionExample RatioA comparison of two quantities by division. It can be written as a fraction, with a colon, or with the word 'to'.If there are 3 red apples and 2 green apples, the ratio of red to green apples is 3/2, 3:2, or 3 to 2. ProportionAn equation stating that two ratios are equal. It shows that two quantities are related in the same way.The equation $\frac{1}{2} = \frac{2}{4}$ is a proportion, as both ratios simplify to the same value. VariableA symbol, usually a letter, that represents an unknown quantity in a mathematical expression or equation.In the proportion $\frac{x}{5} = \frac{6}{10}$, 'x' is the variable we need to solve for. Cross-MultiplicationA method used to solve proportions by multiplying the numerator of one ratio by the denominator of...

Definition of a Proportion $\frac{a}{b} = \frac{c}{d}$ This is the fundamental setup for any proportion. It states that two ratios are equivalent. When setting up word problems, ensure that corresponding units or quantities are in the same position (e.g., units in numerators, total in denominators, or vice-versa, consistently across both ratios). Cross-Multiplication Property If $\frac{a}{b} = \frac{c}{d}$, then $ad = bc$. This property is the primary method for solving proportions. It allows you to convert a proportion into a linear equation, which can then be solved for an unknown variable. Multiply the numerator of the first ratio by the denominator of the second, and set it equal to the product of the denominator of the first ratio and the numerator of the second.