Compare ratios: word problems

Learning Objectives Identify and extract ratios from real-world word problems. Express ratios in various forms (fraction, colon, 'to'). Calculate unit rates to facilitate ratio comparison. Find equivalent ratios to compare quantities with different total amounts. Apply strategies like unit rates or common denominators to compare two or more ratios. Interpret the comparison of ratios in the context of the original word problem. Solve word problems requiring the comparison of ratios to make informed decisions. Ever wonder which deal is better at the grocery store, or which sports team has a better winning record? 🤔 Comparing ratios helps us make smart choices! In this lesson, you'll learn how to take information from word problems, turn it into ratios, and t...

TermDefinitionExample RatioA comparison of two quantities by division. It shows how much of one quantity there is compared to another.If there are 3 red apples and 5 green apples, the ratio of red to green apples is 3:5, 3 to 5, or 3/5. Equivalent RatiosRatios that express the same relationship between two quantities, even if the numbers are different. They can be obtained by multiplying or dividing both parts of a ratio by the same non-zero number.The ratio 1:2 is equivalent to 2:4 and 5:10 because they all simplify to the same relationship. Unit RateA ratio where the second quantity (denominator) is 1 unit. It tells you 'how much per one' of something.If you drive 120 miles in 2 hours, your unit rate (speed) is 60 miles per 1 hour (60 mph). Simplifying RatiosReducing a ratio t...

Expressing a Ratio $$a:b \quad \text{or} \quad \frac{a}{b} \quad \text{or} \quad a \text{ to } b$$ Ratios can be written in three main ways. The order of the quantities matters. The first quantity mentioned is usually the numerator or the first number in the colon notation. Finding a Unit Rate $$\text{Unit Rate} = \frac{\text{Quantity 1}}{\text{Quantity 2}} \quad \text{(where Quantity 2 becomes 1 unit)}$$ To find a unit rate, divide the first quantity by the second quantity. This is especially useful for comparing 'best buy' scenarios or speeds. Comparing Ratios using Unit Rates $$\text{Ratio 1} = \frac{A}{B} \quad \text{and} \quad \text{Ratio 2} = \frac{C}{D}$$ Calculate Unit Rate 1 = A/B and Unit Rate 2 = C/D. Then compare Unit Rate 1 and Unit Rate 2. Con...