Solve the proportion

Learning Objectives Identify and write proportions involving decimal values. Apply the Cross-Multiplication Property to set up equations from proportions. Solve one-step linear equations containing decimal coefficients or constants. Accurately perform multiplication and division operations with decimals to find unknown values in proportions. Verify the solution to a proportion by substituting the found value back into the original equation. Solve real-world problems by setting up and solving proportions that include decimals. Ever wondered how chefs adjust recipes for more or fewer people, or how maps shrink the real world? 🗺️ It's all about keeping things in proportion! In this lesson, you'll learn how to solve equations called proportions, especially when they i...

TermDefinitionExample RatioA comparison of two quantities by division.If a recipe uses 0.5 cups of sugar for 1 cup of flour, the ratio of sugar to flour is 0.5:1 or $\frac{0.5}{1}$. ProportionAn equation that states two ratios are equal.$\frac{0.5}{1} = \frac{x}{2}$ is a proportion. Terms of a ProportionThe four numbers or expressions that make up a proportion.In $\frac{a}{b} = \frac{c}{d}$, the terms are $a, b, c, d$. ExtremesThe first and last terms of a proportion (the outer terms).In $\frac{a}{b} = \frac{c}{d}$, $a$ and $d$ are the extremes. MeansThe middle terms of a proportion (the inner terms).In $\frac{a}{b} = \frac{c}{d}$, $b$ and $c$ are the means. Cross ProductsThe product of the means and the product of the extremes. In a true proportion, these products are equal.For $\frac{a}...

Definition of a Proportion $\frac{a}{b} = \frac{c}{d}$ A proportion is an equation stating that two ratios are equivalent. Here, $a, b, c, d$ are numbers, and $b \neq 0, d \neq 0$. Cross-Multiplication Property If $\frac{a}{b} = \frac{c}{d}$, then $ad = bc$. In any true proportion, the product of the extremes ($a \cdot d$) is equal to the product of the means ($b \cdot c$). This property is fundamental for solving for an unknown variable. Solving for an Unknown in a Proportion If $N \cdot x = M$, then $x = \frac{M}{N}$. After applying cross-multiplication, you will often have a linear equation where a number is multiplied by the variable. To find the variable, divide both sides of the equation by the number multiplying the variable.