Identify equivalent ratios

Learning Objectives Define a ratio and an equivalent ratio using precise mathematical language. Generate a series of equivalent ratios from a given ratio by applying multiplication and division. Simplify any given ratio to its simplest form by dividing by the greatest common divisor. Determine if two ratios are equivalent by comparing their simplified forms. Verify if two ratios form a proportion by using the cross-multiplication property. Solve for an unknown variable in a proportion to make two ratios equivalent. Model a real-world scenario using ratios and determine equivalence. Ever scaled a recipe up for a party or noticed that your phone screen has the same shape as your TV? 📱 That's the power of equivalent ratios in action! This tutorial will teach you how to...

TermDefinitionExample RatioA comparison of two or more quantities, showing their relative sizes. Ratios can be written with a colon (a:b), as a fraction (a/b), or in words ('a to b').In a class with 15 boys and 10 girls, the ratio of boys to girls is 15:10. Equivalent RatiosRatios that express the same relationship between two quantities. They represent the same proportional value, even though the numbers are different.The ratios 2:3, 4:6, and 10:15 are all equivalent because they all simplify to the same relationship. ProportionAn equation stating that two ratios are equivalent.The statement 2/5 = 8/20 is a proportion because the two ratios are equivalent. Simplest FormA ratio is in its simplest form when its terms are whole numbers that have no common factors other than 1. Thi...

The Scaling Rule for Equivalence a:b = (a \times k) : (b \times k) a:b = (a \div k) : (b \div k) where k \neq 0 To create an equivalent ratio, you must multiply or divide BOTH terms of the original ratio by the same non-zero number, k. This scales the ratio up or down without changing its fundamental relationship. The Cross-Multiplication Property \frac{a}{b} = \frac{c}{d} \iff a \times d = b \times c Two ratios are equivalent if and only if their cross-products are equal. This is the most reliable method for verifying if two ratios form a proportion, especially with larger numbers or variables. The Simplest Form Test If \frac{a \div \text{GCD}(a,b)}{b \div \text{GCD}(a,b)} = \frac{c \div \text{GCD}(c,d)}{d \div \text{GCD}(c,d)}, then a:b and c:d are equivalent....