LESSON 15%0D%0AUnit Rates & Proportions Review
In this lesson, we will review unit rates and proportions. Unit rates are ratios that compare two different units, such as cost per item or distance per time. They are used to simplify and compare different quantities.
Proportions, on the other hand, are statements that show two ratios are equal. They are used to solve problems involving unknown quantities.
To find a unit rate, you divide one quantity by the other. For example, if you want to find the cost per item, you divide the total cost by the number of items.
Proportions can be solved by cross multiplying. If you have a proportion with two ratios, such as 2:4 = 5:x, you can cross multiply by multiplying 2 by x and 4 by 5. Then, you set the two products equal to each other and solve for x.
Proportions can also be used to solve real-world problems. For example, if you know that a car travels 50 miles in 2 hours, you can set up the proportion 50 miles / 2 hours = x miles / 3 hours. Then, you can solve for x to find the distance the car travels in 3 hours.
Remember to always simplify your ratios and proportions by dividing both sides by the greatest common factor. This will give you the simplest form of the ratio or proportion.
Practice problems:
1. The ratio of boys to girls in a classroom is 3:5. If there are 24 students in the class, how many are boys?
2. A car travels 250 miles in 5 hours. What is the car's average speed in miles per hour?
3. If 5 bags of apples cost $15, what is the cost of 12 bags of apples?
4. A recipe calls for 2 cups of flour to make 12 cookies. How many cups of flour are needed to make 36 cookies?
These problems can be solved using unit rates and proportions. Remember to set up the proportions correctly and solve for the unknown quantity.