Solve proportions word problems

Learning Objectives Identify ratios and proportions within word problems. Set up a correct proportion equation from a word problem. Use cross-multiplication to solve for an unknown value in a proportion. Apply scaling factors to solve simpler proportion problems. Interpret the numerical solution in the context of the original word problem. Check the reasonableness of their answers to proportion word problems. Ever wonder how a baker knows how much flour to use if they want to make twice as many cookies? 🍪 It's all about understanding proportions! In this lesson, you will learn how to read word problems, identify the relationships between quantities, and set up equations called proportions to find missing numbers. This skill is super useful for solving everyday puzzles...

TermDefinitionExample RatioA comparison of two quantities, often written as a fraction (e.g., 3/4), with a colon (e.g., 3:4), or using the word 'to' (e.g., 3 to 4).If there are 5 apples and 3 bananas, the ratio of apples to bananas is 5/3. ProportionAn equation stating that two ratios are equal. It shows that two fractions have the same value.2/4 = 1/2 is a proportion because both ratios represent the same value. Equivalent RatiosTwo or more ratios that have the same value or relationship between their quantities.The ratios 1/2, 2/4, and 3/6 are all equivalent ratios. Unknown VariableA letter (like 'x', 'y', or 'n') used to represent a missing or unknown number in an equation.In the equation 2/3 = x/9, 'x' is the unknown variable we need t...

Definition of a Proportion $$\frac{a}{b} = \frac{c}{d}$$ This rule states that two ratios are equal. In word problems, you'll set up two ratios that compare similar quantities in the same order. For example, 'apples to students' should be equal to 'apples to students'. Cross-Multiplication Property If $$\frac{a}{b} = \frac{c}{d}$$, then $$a \times d = b \times c$$ This is the main method for solving proportions when an unknown value is present. You 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. Then, you solve for the unknown variable.