Comparing Ratios Using Ratio Tables 05:30 minutes

Video Transcript

Transcript Comparing Ratios Using Ratio Tables

In the summer, all across America parents are flocking to the grocery store to get ingredients for NATIONAL SMOOTHIE DAY! This year, we're highlighting three parents whose refreshments really pack a healthy punch! Each of the parents chooses blueberries and yogurt for their smoothies, which they combine in a special ratio. But which of their smoothies is the fruitiest?! Let's find out by comparing the fruit to yogurt ratios using ratio tables. Mrs. Castenlleja always makes smoothies in a ratio of 4 cups blueberries to 7 cups yogurt. Mr. Sweet, on the other hand, combines blueberries and yogurt in a 5 to 11 ratio, while Mrs. Harper's recipe calls for a ratio of 3 to 5. But how do you decide whose smoothie is the fruitiest? The fruitiest smoothie recipe is the one with the highest number of cups of blueberries compared to the number of cups of yogurt. To make our determination, let's start with this ratio table for Mrs. Castenlleja's smoothie recipe. If you remember, a ratio table is a table of equivalent ratios. Notice that each of these ratios simplifies to the original we were given of 4 to 7. Let's use this table to make a comparison with Mr. Sweet's recipe. To find out which recipe has the highest concentration of blueberries, we can just look through the tables and try to find a pair of equivalent ratios which have the same amount of blueberries or the same amount of yogurt. Look here: in both tables, there is a ratio which incluides 20 cups blueberries. When Mr. Sweet uses 20 cups of blueberries, he uses 44 cups of yogurt.
Compare that to Mrs. Castenlleja, who adds 35 cups of yogurt when she uses 20 cups of blueberries. That's 9 fewer cups of yogurt for every 20 cups of blueberries than Mr. Sweet, so Mrs. Castenlleja's smoothie is fruitier than Mr. Sweet's! Now let's take a look at Mrs. Castenlleja's recipe and see how it stacks up against Mrs. Harper's ratio table. Can you find where Mrs. C and Mrs. H use the same amount of blueberries or same amount of yogurt? If you said 35 cups of yogurt, you're exactly right! When Mrs. C uses 35 cups of yogurt, she uses 20 cups of blueberries. While Mrs. Harper adds one more cup of blueberries when she uses the same amount of yogurt. So Mrs. Harper's smoothies are fruitier than Mrs. Castenlleja's, and Mrs. Castenllenja's are fruitier than Mr. Sweet's, so Mrs. Harper's recipe should also be fruitier than Mr. Sweet's. Let's check the ratio tables just to make sure. Again, we just need to look in each table and find where the amount of blueberries or the amount of yogurt are the same. So which ratios would YOU use to make a comparison? Looking at the tables, Mr. Sweet and Mrs. Harper both have recipes that require 15 cups of blueberries, so let's compare those. Mr. Sweet uses 33 cups of yogurt for every 15 cups of blueberries, and Mrs. Harper uses only 25 cups yogurt. So which one has a higher fruit to yogurt ratio? Since Mrs. Harper's smoothies use LESS yogurt per 15 cups blueberries, they are fruitier than Mr. Sweet's. To double-check, we could also look at the number of cups of yogurt when making our comparison. To do this, we need to add a few more equivalent ratios to Mrs. H's table until we find an amount that matches one of the entries in Mr. S's table. We can do this with repeated addition by adding 3 cups of blueberries and 5 cups of yogurt. Now we can see that when Mr. Sweet uses 55 cups of yogurt, he uses 25 cups of blueberries, and when Mrs. Harper uses 55 cups of yogurt, she uses 33 cups of blueberries. So Mrs. Harper's smoothies ARE fruitier than Mr. Sweet's, just like we thought. Okay, to review... Ratio tables are a great way to find equivalent ratios and make comparisons. To do that, look through the ratio tables that you are comparing until you find the same number in the same unit. You can always expand the tables, if you don't find a match or if you just want to check your answer. Just make sure that you always compare like-unit with like-unit. So, in our examples, that meant comparing blueberries with blueberries or yogurt with yogurt. Now, who's up for a smoothie? Yeah...maybe National Smoothie Day isn't for everyone.