Solve proportions word problems

Learning Objectives Identify proportional relationships described in word problems. Translate a word problem into a mathematical proportion with an unknown variable. Set up proportions with consistent units in the numerators and denominators. Solve for the unknown variable in a proportion using the cross-multiplication method. Interpret the solution in the context of the original problem. Verify that their answer is reasonable for the given scenario. Ever wonder how a tiny map can guide you through a huge city or how to adjust a recipe for more people? 🗺️ Proportions are the secret! This tutorial will teach you how to set up and solve proportion word problems, a powerful skill for making accurate comparisons and predictions. You'll learn a step-by-step method to turn r...

TermDefinitionExample RatioA comparison of two quantities by division, often expressed as a fraction (a/b), with a colon (a:b), or using the word 'to' (a to b).In a class with 15 boys and 10 girls, the ratio of boys to girls is 15/10, which simplifies to 3/2. RateA special type of ratio that compares two quantities with different units.A car travels 180 kilometers in 3 hours. The rate is 180 km / 3 hours. Unit RateA rate where the second quantity (the denominator) is one unit.If a car travels 180 km in 3 hours, its unit rate is 60 km/hour (60 kilometers per 1 hour). ProportionAn equation stating that two ratios or rates are equivalent.The ratio 2/4 is proportional to 3/6 because they both simplify to 1/2. The proportion is written as 2/4 = 3/6. Cross-ProductsIn a proportion, the...

Setting Up a Proportion \frac{a}{b} = \frac{c}{d} To set up a proportion from a word problem, create two equivalent ratios. Ensure the units are consistent across the numerators and across the denominators. For example, (kilometers/hours) = (kilometers/hours). Cross-Multiplication Property If \frac{a}{b} = \frac{c}{d}, then a \cdot d = b \cdot c This is the primary method for solving proportions. Multiply the numerator of the first fraction by the denominator of the second, and set it equal to the product of the denominator of the first fraction and the numerator of the second. Then, solve the resulting algebraic equation for the variable.