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Math: Basic Tutorials : Rates and Ratios
Ratios and Rates
Both rates and rates allow us to compare numbers or quantities. For example, you may have noticed that some recipes call for certain ingredients in specific ratios, such as two parts flour for every one part water. When we express speeds as kilometres per hour or our pay as dollars per hour, we are using rates. In this module, you will define ratios and rates and review how to write each. You will also explore unit rates and their real-life applications.
Examples & Activity
Examples
Click on the titles below to view each example.
In a recipe, there are 4 cups of flour for every 6 cups of water. What is the ratio of flour to water?
Line 1: Write as a ratio with the number of cups of flour first and the number of cups of water second. 4 to 6.
Line 2: Simplify the ratio by dividing both numbers by two. 2 to 3.
Line 3: The ratio of flour to water in the recipe is 2 to 3.
Write the ratio 2.3 to 0.69 as a fraction.
Line 1: Write as a fraction. 2.3 over 0.69.
Line 2: The numerator has one decimal place and the denominator has two decimals places. To remove both decimals, multiply both the numerator and denominator by 100. 2.3 over 0.69 times 100 over 100.
Line 3: Notice that by multiplying by 100 we ‘moved’ the decimals 2 places to the right. 230 over 69.
Line 4: Simplify. Both the numerator and denominator are divisible by 23. 10 over 3.
Line 5: Therefore, 2.3 to 0.69 is equivalent to 10 to 3 or 10 over 3.
If you work 25 hours and get paid 387.50 dollars, what is your rate of pay?
Line 1: Write as a rate of dollars to hours. 387.5 dollars over 25 hours.
Line 2: Divide the numerator by the denominator to get the pay rate for one hour. 15.50 dollars over 1 hour.
Line 3: Write as a unit rate. 15.50 dollars per hour.
Line 4: Your rate of pay is 15.50 dollars per hour.
You are buying toothpaste and you notice you can buy a 75-millilitre tube for 4.47 dollars or a 135-millilitre tube for 5.97 dollars. Which is the better deal?
Line 1: Write a rate for each tube of toothpaste. The rate for the 75-millilitre tube is 4.47 dollars over 75 milliliters. The rate for the 135-millilitre tube for 5.97 dollars over 135 milliliters.
Line 2: Find the unit price by dividing the numerator by the denominator. The unit price for the smaller tube is 0.0596 dollars for one millilitre. The unit price for the larger tube is 0.0442 dollars for one milliliter.
Line 3: Round to the nearest cent and write as a unit price. The unit price for the small tube is 0.06 dollars per milliliter and the unit price for the larger tube is 0.04 dollars per milliliter.
Line 4: Therefore, the larger 135 mL tube is a better price because the unit price is less.
Summary and Worksheet
- Summary: Ratios and Rates - PDF - Opens in a new windowThis document contains a short (1 – 2 page) summary of this topic as well as detailed examples to illustrate key concepts. Use this summary to review this topic.
- Worksheet: Ratios and Rates - PDF - Opens in a new windowThis document contains practice questions on this topic. Use the worksheet to test your knowledge and practice the skills learned in this module. The answers to the practice questions are provided at the end.
Attribution
Examples Source: "Prealgebra - opens in a new window" by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 - opens in a new window / A derivative from the original work - opens in a new window