Equivalent ratios: word problems

Learning Objectives Define and identify equivalent ratios. Set up proportions correctly from word problems involving equivalent ratios. Solve for unknown quantities in equivalent ratio word problems using scaling, unit rates, or cross-multiplication. Interpret solutions in the context of the original word problem. Apply equivalent ratio concepts to real-world scenarios presented as word problems. Check the reasonableness of their answers in equivalent ratio word problems. Ever wonder how bakers adjust recipes for different numbers of servings, or how maps accurately represent distances? 🗺️ It's all about equivalent ratios! In this lesson, you'll learn to identify, create, and solve problems involving equivalent ratios, especially when they're hidden in word p...

TermDefinitionExample RatioA comparison of two quantities by division. It can be written as a:b, a/b, or 'a to b'.If there are 3 red apples and 2 green apples, the ratio of red to green apples is 3:2. Equivalent RatiosTwo or more ratios that express the same relationship between quantities. They can be obtained by multiplying or dividing both parts of a ratio by the same non-zero number.The ratio 3:2 is equivalent to 6:4 because both parts of 3:2 were multiplied by 2. ProportionAn equation that states that two ratios are equivalent.$rac{3}{2} = rac{6}{4}$ is a proportion. Scaling (Up/Down)The process of multiplying or dividing both parts of a ratio by the same non-zero number to find an equivalent ratio. Scaling up means multiplying, scaling down means dividing.To scale up the...

Finding Equivalent Ratios by Scaling $rac{a}{b} = rac{a \times k}{b \times k}$ or $rac{a}{b} = rac{a \div k}{b \div k}$ (where $k \neq 0$) To find an equivalent ratio, multiply or divide both the numerator and the denominator of a ratio by the same non-zero number. This maintains the proportional relationship. Solving Proportions (Cross-Multiplication) If $\frac{a}{b} = \frac{c}{d}$, then $a \times d = b \times c$ This rule is used to find an unknown value in a proportion. Multiply the numerator of one ratio by the denominator of the other, and set the products equal. Then solve the resulting equation. Unit Rate Method for Equivalent Ratios To find an equivalent ratio, first find the unit rate $\frac{a}{b} = \frac{a \div b}{1}$, then multiply the unit rate by the d...