Solve proportions: word problems

Learning Objectives Identify proportional relationships described in word problems. Translate verbal descriptions from word problems into mathematical ratios. Set up a correct proportion equation from a given word problem. Solve for an unknown value in a proportion using cross-multiplication. Interpret the numerical solution of a proportion in the context of the original word problem. Check the reasonableness of a solution to a proportion word problem. Ever wonder how chefs perfectly scale a recipe for a big party, or how maps help us figure out real distances? 🗺️ It's all about understanding proportions! In this lesson, you'll learn how to translate everyday situations into mathematical proportions and solve them to find missing information. Understanding proport...

TermDefinitionExample RatioA comparison of two quantities by division. It can be written as a fraction, with a colon, or using the word 'to'.If there are 3 red apples and 5 green apples, the ratio of red to green apples is 3:5 or $\frac{3}{5}$. ProportionAn equation stating that two ratios are equal. It shows that two fractions are equivalent.$\frac{1}{2} = \frac{4}{8}$ is a proportion because both ratios simplify to $\frac{1}{2}$. VariableA symbol, usually a letter, that represents an unknown number or quantity in an equation.In the problem 'If 2 apples cost $1, how much do 6 apples cost?', we can use 'x' to represent the unknown cost: $\frac{2}{1} = \frac{6}{x}$. Cross-MultiplicationA method used to solve proportions by multiplying the numerator of one rati...

Definition of a Proportion $\frac{a}{b} = \frac{c}{d}$ (where $b \neq 0$ and $d \neq 0$) This rule defines what a proportion looks like. It is an equation that states that two ratios are equivalent. The values $a, b, c, d$ can be numbers or expressions representing quantities. Cross-Multiplication Property If $\frac{a}{b} = \frac{c}{d}$, then $ad = bc$. This property is the primary method for solving for an unknown variable in a proportion. You multiply the numerator of the first ratio by the denominator of the second, and the numerator of the second ratio by the denominator of the first, then set these products equal. This converts the proportion into a linear equation.