Compare ratios: word problem

Learning Objectives Identify and extract relevant quantities to form ratios from word problems. Express ratios in various forms (fraction, colon, 'to') and convert them for comparison. Calculate and use unit rates to compare different ratios. Find common denominators to compare ratios expressed as fractions. Solve real-world problems by comparing two or more ratios. Interpret the meaning of ratio comparisons within the context of the original word problem. Ever wonder which deal is truly better at the grocery store, or which athlete has a stronger performance? 🍎🛒 Comparing ratios helps us answer these questions! In this lesson, you'll learn how to take information from word problems, turn it into ratios, and then use different strategies to compare those ra...

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 represent the same relationship between two quantities. 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 because (1x2):(2x2) = 2:4. Unit RateA ratio where the second quantity (denominator) is 1. 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). ProportionAn equation that states that two ratios are equal. It's often used to find an unknown quantit...

Expressing Ratios A ratio comparing quantity 'a' to quantity 'b' can be written as $a:b$, $a \text{ to } b$, or $\frac{a}{b}$. Choose the form that is most convenient for the problem, often the fraction form $\frac{a}{b}$ for comparisons. Finding Equivalent Ratios To find an equivalent ratio, multiply or divide both parts of the ratio by the same non-zero number $k$: $(a \times k) : (b \times k)$ or $(a \div k) : (b \div k)$. This rule is essential for simplifying ratios or for converting them to a common denominator or unit rate. Comparing Ratios using Unit Rates To compare two ratios, convert each ratio into its unit rate by dividing the first quantity by the second quantity. Then, compare the resulting unit rates. This method is particularly us...