Write an equivalent ratio

Learning Objectives Define ratio and equivalent ratio. Identify equivalent ratios involving decimals. Generate equivalent ratios by multiplying or dividing both parts by the same non-zero number. Convert ratios with decimals into equivalent ratios with whole numbers. Simplify ratios involving decimals to their simplest whole number form. Apply the concept of equivalent ratios to solve real-world problems involving decimals. Have you ever needed to adjust a recipe, maybe doubling it or cutting it in half? 🧑‍🍳 That's exactly when you use equivalent ratios! In this lesson, you'll learn how to create and identify ratios that represent the same relationship, even when they involve decimals. Understanding equivalent ratios is crucial for scaling things up or down prop...

TermDefinitionExample RatioA comparison of two quantities, often expressed as a:b, a/b, or 'a to b'.If there are 3 apples and 2 oranges, the ratio of apples to oranges is 3:2. Equivalent RatioRatios that express the same relationship between two quantities, even if the numbers are different. They have the same value when simplified.The ratio 1:2 is equivalent to 2:4 because both simplify to the same relationship. Decimal RatioA ratio where at least one of the quantities being compared is a decimal number.The ratio of 0.5 meters to 1.5 meters can be written as 0.5:1.5. Scaling FactorThe non-zero number by which both parts of a ratio are multiplied or divided to find an equivalent ratio.To change 1:2 to 3:6, the scaling factor is 3 (you multiply both 1 and 2 by 3). Simplest Form (...

Rule for Finding Equivalent Ratios To find an equivalent ratio, multiply or divide both terms of the ratio by the same non-zero number (the scaling factor). This rule ensures that the relationship between the two quantities remains constant. If you have a ratio $a:b$, then $a:b = (a \times k) : (b \times k)$ and $a:b = (a \div k) : (b \div k)$, where $k \neq 0$. Rule for Converting Decimal Ratios to Whole Number Ratios To convert a ratio with decimals into an equivalent ratio with whole numbers, multiply both terms by the smallest power of 10 (10, 100, 1000, etc.) that will make both terms whole numbers. This is often the first step when simplifying decimal ratios. For example, if you have $0.25:0.5$, you would multiply both by 100 to get $25:50$, which can then be simplifie...