Proportions

Learning Objectives Define and identify ratios and proportions involving decimal numbers. Apply the cross-multiplication property to solve proportions containing decimals. Accurately perform multiplication and division of decimals within proportional equations. Set up and solve real-world problems using proportions with decimal values. Check the validity of their solutions to proportional equations involving decimals. Convert between fractions and decimals when solving proportions to simplify calculations. Ever wonder how chefs scale recipes for different numbers of guests, or how maps accurately represent real-world distances? 🗺️ It's all about understanding proportions! In this lesson, we'll dive into the world of proportions, focusing specifically on how to wor...

TermDefinitionExample RatioA comparison of two quantities by division. Ratios can be written as a:b, a/b, or 'a to b'.The ratio of 0.5 liters of juice to 2 liters of water can be written as 0.5:2 or 0.5/2. ProportionAn equation stating that two ratios are equivalent. It shows that two fractions or ratios are equal.0.5/2 = 1/4 is a proportion because both ratios simplify to 0.25. Equivalent RatiosRatios that have the same value or represent the same relationship between quantities.The ratios 0.6:3 and 1:5 are equivalent because 0.6/3 = 0.2 and 1/5 = 0.2. Cross-MultiplicationA method used to check if two ratios form a proportion or to solve for an unknown in a proportion. You multiply the numerator of one ratio by the denominator of the other.In the proportion 0.5/2 = 1/4, cross-m...

Definition of a Proportion A proportion is an equation that states that two ratios are equal: $\frac{a}{b} = \frac{c}{d}$ This rule defines what a proportion is. For the equation to be true, the ratio 'a to b' must have the same value as the ratio 'c to d'. 'b' and 'd' cannot be zero. Cross-Multiplication Property If $\frac{a}{b} = \frac{c}{d}$, then $ad = bc$. This property is fundamental for solving proportions. It allows you to convert a proportion into a simpler linear equation by multiplying the 'cross' terms. This is especially useful when one of the terms is an unknown variable.