Recipe Ratio Masters — Ratios & Proportions worksheet for Grade 8.
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A ratio is a comparison of two quantities (like 2:3 flour to sugar in a recipe). A proportion is an equation stating that two ratios are equal (like 2 cups flour for 3 cups sugar is the same as 4 cups flour for 6 cups sugar). In recipe problems, you use ratios to describe ingredient relationships, and you use proportions when you need to scale a recipe to a different serving size and need to find a missing ingredient amount.
Determine your scaling factor first: divide the new serving size by the original serving size. If the result is greater than 1, you're multiplying (making more). If the result is less than 1, you're dividing (making less). For example: want 12 servings from a recipe that makes 6 servings? The factor is 12÷6 = 2, so multiply all ingredients by 2. Want 2 servings from a recipe that makes 8? The factor is 2÷8 = 0.25, so multiply (or divide by 4) all ingredients.
Cross-multiplication is the most efficient and systematic method for solving proportions with missing values. It works every time and is less prone to errors than trying to find the scale factor mentally. That said, you can also solve by finding the unit rate (the amount per one serving) and multiplying by the desired serving size, but cross-multiplication is faster for most students and is the expected method for Grade 8.
These answers are mathematically correct, but in a real recipe context, you might need to round or simplify. For eggs, you'd round 2.7 to 3 eggs. For very small amounts like 0.05 cups, convert to a smaller unit (teaspoons: 0.05 cups × 48 teaspoons per cup = 2.4 teaspoons, or about ½ teaspoon). Always show your mathematical work first, then explain how you'd adjust for a real recipe.
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Simplify both ratios to their lowest terms by dividing both numbers by their greatest common factor. For example, 6:9 simplifies to 2:3 (divide both by 3), and 4:6 also simplifies to 2:3 (divide both by 2). If the simplified forms match, the ratios are equivalent. Alternatively, you can cross-multiply: if 6 × 6 = 9 × 4, then the ratios 6:9 and 4:6 are equivalent (both equal 36, so yes, they are equivalent).